CURRICULUM VITAE

Roxana SmarandacheAssociate Professor

Department of Mathematics and StatisticsSan Diego State University, San Diego, CA 92182

Education

2001: Ph.D.: Mathematics, University of Notre Dame.

Thesis advisor: Joachim Rosenthal, Mathematics, University of Zurich, Switzerland.

1997: M.S.: Mathematics, University of Notre Dame.

1996: B.S.: Mathematics, University of Bucharest, Bucharest.

Appointments

2007 - now Associate Professor, San Diego State University, Dept. of Mathematics andStatistics.

2001 - 2007 Assistant Professor, San Diego State University, Dept. of Mathematics andStatistics.

1997 - 2001 Teaching Assistant, University of Notre Dame, Dept. of Mathematics.

2008 - 2009 Sabbatical: Guest Professor in the “Institut fur Mathematik” at the University ofZurich, and in the “Forschungsinstitut fur Mathematik” of ETH, Zurich, Switzerland(8 months), and in the Mathematics Dept. of the University of Notre Dame (4months).

2005 - 2006 Leave: Visiting Assistant Professor, University of Notre Dame, Dept. ofMathematics.

1999 - 2000 Visiting Student: Swiss Federal Institute of Technology, Lausanne, Switzerland(EPFL), Department of Communication Systems.

Grants and Awards

2011-2014 NSF Grant DMS-1109868, “Analysis and Design of Protograph-based LDPC Codesand Impact on Linear Programming in Compressed Sensing”, $250,000, PrincipalInvestigator, submitted.

2008-2011 NSF Grant CCF-0830608, “Collaborative Research: New Directions in Graph-Based Code Design”, $130,000, Principal Investigator. Collaborative research withD. Costello and T. Fuja at the University of Notre Dame.

2007-2011 NSF Grant DMS-0708033, “Pseudo-Codeword Analysis and Design of Quasi-Cyclicand Convolutional Codes”, $120,000, Principal Investigator.

2007 The most influential teacher award of best undergraduate of class 2007.

1997-2005 IEEE Travel awards from IEEE International Symposium on Information Theory.

1998-1999 Fellowship of the Center for Applied Mathematics, University of Notre Dame.

1997 Richard Sady Prize Award for the best first year graduate student in Mathematics,University of Notre Dame.

Book Chapter

[1] R. Smarandache, “Unit memory convolutional codes with maximum distance”, Codes, Systemsand Graphical Models, IMA Volume 123 (2000), 381–396, Springer-Verlag.

Transactions and Journals

[2] R. Smarandache and P. O. Vontobel, “Absdet-Pseudo-Codewords and Perm-Pseudo-Codewords”, in preparation.

[3] A. G. Dimakis, R. Smarandache and P. O. Vontobel, “LP Decoding meets LP Decoding:Connections between Channel Coding and Compressed Sensing”, in preparation.

[4] V. Tomas, J. Rosenthal and R. Smarandache, “Decoding of Convolutional Codes over theErasure Channel”, submitted to IEEE Trans. Inform. Theory, June 2010.

[5] A. E. Pusane, R. Smarandache, P. O. Vontobel and D. J. Costello, Jr., “Deriving Good LDPCConvolutional Codes from LDPC Block Codes”, to appear in IEEE Trans. Inform. Theory,February 2011.

[6] R. Smarandache and P. O. Vontobel, “Quasi-Cyclic LDPC Codes: Influence of Proto- andTanner-Graph Structure on Minimum Hamming Distance Upper Bounds”, to appear in IEEETrans. Inform. Theory (submitted Jan. 2009).

[7] R. Smarandache, A. Pusane, P. O. Vontobel and D. J. Costello, Jr., “Pseudo-CodewordPerformance Analysis for LDPC Convolutional Codes”, IEEE Trans. Inf. Theory, Volume 55,Issue 6 (2009), 2577–2598.

[8] R. Hutchinson, R. Smarandache and J. Trumpf, “Superregular Matrices and the Construc-tion of Convolutional Codes having a Maximum Distance Profile”, Linear Algebra and ItsApplications 428 (2008), 2585-2596.

[9] R. Smarandache and P. O. Vontobel, “Pseudo-codeword analysis of Tanner graphs from pro-jective and Euclidean planes”, IEEE Trans. Inform. Theory, Volume 53, Issue 7 (2007), 2376–2393.

[10] R. Smarandache and M. Wauer, “Bounds on the pseudo-weight of minimal pseudo-codewordsof projective geometry codes”, Contemporary Mathematics, Algebra and Its Applications,vol. 419 (2006), 285–296.

[11] H. Glusing-Luerßen, J. Rosenthal and R. Smarandache, “Strongly MDS convolutional codes”,IEEE Trans. Inform. Theory, Volume 52, Issue 2 (2006), 584–598.

[12] R. Hutchinson, J. Rosenthal and R. Smarandache, “Convolutional codes with maximum dis-tance profile”, Systems & Control Letters, Volume 54, Issue 1 (2005), 53-63.

[13] R. Smarandache, H. Glusing-Luerßen and J. Rosenthal, “Constructions for MDS-convolutionalcodes”, IEEE Trans. Inform. Theory, Volume 47, Issue 5 (2001), 2045–2049.

[14] J. Rosenthal and R. Smarandache, “Maximum distance separable convolutional codes”, Appl.Algebra Engrg. Comm. Comput., vol. 10 (1999), 15–32.

Conference Publications

[15] R. Smarandache, D. G. M. Mitchell, and D. J. Costello, Jr., “Partially quasi-cyclic protograph-based LDPC codes”, IEEE International Conference on Communications (ICC), Kyoto,Japan, June 2011. Submitted.

[16] D. G. M. Mitchell, R. Smarandache, M. Lentmaier and D. J. Costello, Jr., “Quasi-cyclicasymptotically regular LDPC codes”, IEEE Int. Symp. Information Theory Workshop,Dublin, Ireland, Aug. 30-Sept. 3, 2010.

[17] V. Tomas, J. Rosenthal and R. Smarandache, “Reverse Maximum Distance Profile Convo-lutional Codes over the Erasure Channel”, 19th International Symposium on MathematicalTheory of Networks and Systems, Budapest, Hungary, July 4-9, 2010.

[18] R. Smarandache, “On Minimal Pseudo-Codewords”, IEEE Int. Symp. Information Theory,Austin, Texas, June 2010.

[19] A. E. Pusane, R. Smarandache, P. O. Vontobel and D. J. Costello, Jr., “On the iterativedecoding of LDPC convolutional codes”, 18th IEEE Signal Processing and CommunicationsApplications Conference (SIU), 519-522, Turkey, April, 2010.

[20] A. G. Dimakis, R. Smarandache and P. O. Vontobel, “Channel coding LP decoding andcompressed sensing LP decoding: further connections”, Intern. Zurich Seminar on Commu-nications, Zurich, Switzerland, Mar. 3–5 2010.

[21] R. Smarandache and M. F. Flanagan, “Spectral Graph Analysis of Quasi-Cyclic Codes”, IEEEGlobecom Communication Theory Symposium, Dec. 2009.

[22] R. Smarandache and P. O. Vontobel, “Absdet-Pseudo-Codewords and Perm-Pseudo-Codewords: Definitions and Properties”, IEEE Int. Symp. Information Theory, Seoul, SouthKorea, July 6, 2009.

[23] V. Tomas, J. Rosenthal and R. Smarandache, “Decoding of MDP convolutional codes over theerasure channel”, IEEE Int. Symp. Information Theory, pages 556–560, Seoul, South Korea,2009.

[24] A. E. Pusane, R. Smarandache, P. O. Vontobel and D. J. Costello, Jr., “On deriving goodLDPC convolutional codes from QC LDPC block codes”, IEEE Int. Symp. Information The-ory, 1221–1225, Nice, France, Jun. 24–29, 2007.

[25] R. Smarandache, A. Pusane, D. J. Costello, Jr. and P. O. Vontobel, “Pseudo-codewords inLDPC convolutional codes”, IEEE Intern. Symp. on Inform. Theory, 2006.

[26] P. O. Vontobel and R. Smarandache, “On minimal pseudo-codewords of Tanner graphs fromprojective planes”, 43rd Allerton Conf. on Communications, Control, and Computing, 2005.

[27] P. Vontobel, R. Smarandache, N. Kiyavash, J. Teutsch and D. Vukobratovic, “On the MinimalPseudo-Codewords of Codes from Finite Geometries”, IEEE Intern. Symp. on Inform. Theory,2005, 980–984.

[28] R. Smarandache and P. O. Vontobel, “On regular quasi-cyclic LDPC codes from binomials”,IEEE Intern. Symp. on Inform. Theory, 2004, p. 274.

[29] M. Greferath, M. O’Sullivan and R. Smarandache, “Construction of good LDPC codes usingdilation matrices”, IEEE Intern. Symp. on Inform. Theory, 2004, p. 237.

[30] H. Glusing-Luerßen, R. Hutchinson, J. Rosenthal and R. Smarandache, “Convolutional Codeswhich are Maximum Distance Separable and which have a Maximum Distance Profile”, 41-thAnnual Allerton Conference on Communication, Control, and Computing, 2003.

[31] M. O’Sullivan and R. Smarandache, “High-rate, short length, (3, 3s)-regular LDPC Codes ofgirth 6 and 8”, IEEE Intern. Symp. on Inform. Theory, 2003, p. 59.

[32] M. O’Sullivan, M. Greferath and R. Smarandache, “Construction of LDPC Codes from A!nePermutation Matrices”, 40-th Annual Allerton Conference on Communication, Control, andComputing, 2002.

[33] M. O’Sullivan, M. Greferath and R. Smarandache, “Analysis of Iterative Decoding Algo-rithms”, 15th International Symposium on the Mathematical Theory of Networks and Systems,2002.

[34] R. Smarandache, H. Glusing-Luerßen and J. Rosenthal, “Strongly MDS Convolutional Codeswith Maximal Decoding Capability”, IEEE Intern. Symp. on Inform. Theory, 2002.

[35] R. Smarandache, H. Glusing-Luerßen and J. Rosenthal, “Construction and Decoding ofStrongly MDS Convolutional Codes”, 15th International Symposium on the MathematicalTheory of Networks and Systems, 2002.

[36] R. Smarandache and J. Rosenthal, “Construction Results for MDS-Convolutional Codes”,IEEE Intern. Symp. on Inform. Theory, 2000, p. 294.

[37] J. Rosenthal and R. Smarandache, “On the dual of MDS convolutional codes”, 36-th AnnualAllerton Conference on Communication, Control, and Computing, 1998, 576–583.

[38] R. Smarandache and J. Rosenthal, “Convolutional code constructions resulting in maximalor near maximal free distance”, IEEE Intern. Symp. on Inform. Theory, 1998, p. 308.

[39] R. Smarandache, H. Glusing-Luerßen and J. Rosenthal, “Generalized first order descriptionsand canonical forms for convolutional codes”, 13th International Symposium on MathematicalTheory of Networks and Systems, 1998, 1091–1094.

[40] R. Smarandache and J. Rosenthal, “A state space approach for constructing MDS rate 1/nconvolutional codes”, IEEE Information Theory Workshop on Information Theory, 1998, 116–117.

[41] J. Rosenthal and R. Smarandache, “Construction of convolutional codes using methods fromlinear system theory”, 35-th Annual Allerton Conference on Communication, Control, andComputing, 1997, 953–960.

Invited Talks and Professional Visits

1. “Measurement matrices of compressed sensing in LP decoding”, 2010 Information Theoryand Applications Workshop, Jan. 31- Feb. 5, 2010, UCSD

2. “Absdet and Perm Codewords and Pseudo-Codewords”, ENSEA, Universite de Cergy-Pontoise- CNRS, ETIS group, Paris, France, March 3, 2009.

3. “Quasi-Cyclic LDPC Codes: Influence of Proto- and Tanner-Graph Structure on MinimumHamming Distance Upper Bounds”, EPFL, Lausanne, Switzerland, December 4, 2008.

4. “Pseudo-codewords for LDPC Convolutional Codes”, EE Department, Ulm, Germany, Oc-tober 27, 2008.

5. “Quasi-Cyclic LDPC Codes: Influence of Proto- and Tanner-Graph Structure on MinimumHamming Distance Upper Bounds”, University of Zurich, Switzerland, October 23, 2008.

6. “Families of Unwrapped LDPC Convolutional Codes”, poster, IEEE Communication TheoryWorkshop, Virgin Islands, May 12, 2008.

7. Coding Theory workshop, Oberwolfach, Germany, Dec. 02 -08, 2007.

8. “Deriving Good LDPC Convolutional Codes from LDPC Block Codes, University of Cali-fornia at San Diego, Information Theory and Applications (ITA) Seminar, June 12, 2007.

9. IMA Annual Program Year Workshop on Complexity, Coding, and Communications, Min-neapolis, MN, April 15-22, 2007.

10. “Algebraic Analysis of the Performance of Low-Density Parity-Check Convolutional Codes”,University of Arizona, Mathematics Department, Applied Mathematics Colloquim, Tucson,Arizona, October 6, 2006.

11. “Expander graphs tutorial lectures in number theory”, Univ. of Notre Dame, Mathematics,Spring 2006.

12. “Minimal Pseudo-codewords of Codes from Finite Geometries”, AMS National Meeting,Lincoln, Nebraska, October 21-23, 2005.

13. University of Zurich, Department of Mathematics, Switzerland, July 4-12, 2005.

14. “On Minimal Vectors of Codes from Finite Geometries”, Conference on Algebra and itsApplications, Ohio University Center of Ring Theory and its Applications, Department ofMathematics, Athens, Ohio, March 22-26, 2005.

15. “On the Minimal Pseudo-Codewords of Codes from Finite Geometries”, at the Universityof Arizona, ECE Department, in the Communication Theory Seminar, Tucson, Arizona,February 18, 2005.

16. “Convolutional Codes and The Viterbi Algorithm Tutorials”, 2004 IMA Summer Programfor Graduate Students in Coding and Cryptography, June 8- 27, 2004, University of NotreDame.

17. “Quasi-cyclic LDPC Codes”, AMS National Meeting, Athens, Ohio, March 25-27, 2004.

18. “Strongly-MDS and MDP Convolutional Codes”, University of Salamanca, Spain, March13-20, 2004.

19. “Convolutional Codes which are Maximum Distance Separable and which have a MaximumDistance Profile”, 41-th Annual Allerton Conference on Communication, Control, and Com-puting, Allerton, October, 2003.

20. “Construction and Decoding of Strongly MDS Convolutional Codes”, International Sym-posium on the Mathematical Theory of Networks and Systems, University of Notre Dame,August 2002.

21. “Convolutional Codes with Maximum Distance Profile”, AMS National Meeting, Boulder,Colorado, October 3-5, 2003.

22. Visit, University of Notre Dame, Department of Mathematics, August 4-11, 2003.

23. “Algebraic Convolutional Codes”, tutorial lecture at the University of California at SanDiego, Department of Mathematics, San Diego, CA, April 16, 2003.

24. “Algebraic Constructions of Convolutional Codes”, University of California at San Diego,Center for Magnetic Recording Research, San Diego, CA, November 12, 2002.

25. “Construction and Decoding of Strongly MDS Convolutional Codes”, University of NotreDame, Notre Dame, IN, the 15th International Symposium on the Mathematical Theory ofNetworks and Systems, August 2002.

26. Bell Laboratories, Mathematical Sciences Research Center, Mathematics of CommunicationsDepartment, Murray Hill, NJ, January 30, 2001.

27. “Convolutional Codes with Large Free Distance”, University of Groningen, Department ofMathematics and Computing Science, Groningen, Netherlands, June 13, 2000.

28. “Constructions of MDS Convolutional Codes”, EPFL, Communication Systems Department,Lausanne, Switzerland, December 6, 2000.

29. “Algebraic Constructions of Convolutional Codes”, University of Kaiserslautern, Departmentof Mathematics, Kaiserslautern, Germany, October 18, 1999.

30. “Algebraic Constructions of Convolutional Codes”, University Oldenburg, Department ofMathematics, Oldenburg, Germany, October 13, 1999.

31. “Constructions of MDS convolutional codes”, University of Illinois, Coordinated ScienceLaboratory, Urbana-Champaign, April 19, 1999.

32. “1/n-MDS Convolutional Codes”, University College Cork, Department of Mathematics,Cork, Ireland, June 18, 1998.

Professional Societies

Member of AMS, IEEE.

Synergistic Activities

• Organizing committee of- AMS Sectional Meeting, Bloomington, Indiana, April 4-6, 2008.- AMS National Meeting, New Orleans, January 5-7, 2007.- AMS National Meeting, San Diego, California, January 5-7, 2002.

• TPC of IMA Summer School in Coding and Cryptography, Univ. of Notre Dame, Indiana, 2004.• TPC of 5th International Symposium on Turbo Codes & Related Topics, EPFL, Lausanne, 2008.

• TPC of ITW 2010 Dublin IEEE Information Theory Workshop, Dublin, Aug. 30– Sept. 3,2010.• Reviewer for several journals, transactions, and conferences in both mathematics and engineer-

ing: Linear Algebra and its Applications Journal, IEEE Transactions on Information Theory,EURASIP Journal on Wireless Communications and Networking, Electronics and Telecommuni-cations Research Institute (ETRI) Journal (Daejeon, South Korea), Proc. of IEEE Inter. Symp.on Inform. Theory, Proc. of IEEE International Communications Conference, Proc. of IEEEGlobecom - Communications Theory.

Collaborators and their A!liations

Collaborators: B. Butler (EE, Univ. of California at San Diego), D. J. Costello Jr. (EE, NotreDame, IN), A. G. Dimakis (EE - Systems, U. of Southern California, Los Angeles, CA), T. Fuja(EE, Notre Dame, IN) M. Flanagan (EE, U. College Dublin, Ireland), M. Greferath (Math., U.College Dublin, Ireland), R. Hutchinson (Math., Bemidji State U., MN), H. Gluesing-Luerssen(Math., U. of Kentucky , Lexington, KY), M. Lentmaier, (Mobile Communications Systems, Dres-den U. of Technology, Germany), D. Mitchell (EE, Notre Dame, IN); A. E. Pusane (EE, BogaziciU., Bebek, Istanbul), M. O’Sullivan (Math., SDSU, San Diego, CA), J. Rosenthal (Math., U. ofZurich, Switzerland), P. Siegel (EE, Univ. of California at San Diego), J. Trumpf (Systems Engi-neering, RSISE, The Australian National U., Canberra ACT 0200, Australia), V. Tomas, (Math.,U. of Alicante, Spain), P. O. Vontobel (Hewlett-Packard Laboratories, Palo Alto, CA), M. Wauer(U. of Ulm, Germany).

Students

MA Students:Osvaldo Soto (2004), Desson Chriswan Ginting (2004), Marcel Wauer (2005), Holly Bass (2006),Eric Gorenstein (2007), Andrea Sholtes (2007), Gibsen Gina (2010), Robert Lazar (2010), Ben-jamin Thorn (2010).

Undergraduates:Ryan Rosenbaum (2007), Donald Adams (2007).

Courses Taught

Fall 2010 MATH 623 - Linear Algebra and Matrix Theory

MATH 524 - Linear Algebra

Spring 2010 MATH 151 - Calculus for Science

MATH 625 - Algebraic Coding Theory

Fall 2009 MATH 151 - Calculus for Science

MATH 623 - Linear Algebra and Matrix Theory

Spring 2008 MATH 254 - Intro to Linear Algebra

MATH 627b - Modern Algebra II

Fall 2007 MATH 623 - Linear Algebra and Matrix Theory

MATH 627a - Modern Algebra I

Spring 2007 MATH 521a - Abstract Algebra I

MATH 521b - Abstract Algebra II

Fall 2006 MATH 524 - Linear Algebra

MATH 521a - Abstract Algebra I

Spring 2005 MATH 521a - Abstract Algebra I

MATH 524 - Linear Algebra

Fall 2004 MATH 623 - Linear Algebra and Matrix Theory

MATH 254 - Intro to Linear Algebra

Spring 2004 MATH 120 - Calculus for Business

MATH 254 - Intro to Linear Algebra

Fall 2003 MATH 120 - Calculus for Business

MATH 254 - Intro to Linear Algebra

Spring 2003 MATH 524 - Linear Algebra

MATH 254 - Intro to Linear Algebra

Fall 2002 MATH 525 - Algebraic Coding Theory

MATH 254 - Intro to Linear Algebra

Spring 2002 MATH 254 - Intro to Linear Algebra

MATH 254 - Intro to Linear Algebra

Fall 2001 MATH 525 - Algebraic Coding Theory

Prof. Dr. Joan-Josep Climent

December 2, 2010

Professor Steven BuechlerDepartment of Applied and Computational Mathematics and StatisticsUniversity of Notre Dame262 Hurley Hall,Notre Dame, IN 46556USA

Dear Professor Buechler

I am a full professor in the Department of Statistics and Operations Research of the Universityof Alicante (Spain). It is with great pleasure that I write in support of Dr. Roxana Smarandachefor a Full Professor position in the Department of Applied and Computational Mathematicsand Statistics.

I met Roxana during my first visit to the University of Notre Dame when she was still doingher PhD in the Department of Mathematics.

I think Roxana is an excellent applied mathematician. She has various research interests whichled her to obtain important results in coding theory, especially in the areas of LDPC codes andconvolutional codes.

Among her many results, I like for example those related to the construction of LDPC convo-lutional codes from LDPC block codes, or the use of superregular matrices for the constructionof convolutional codes with a maximum distance profile.

However, I think that some of the best results obtained by Roxana are those related to theconstruction of maximum distance separable (MDS) convolutional codes. In this work shegeneralized the Singleton Bound on the minimum distance of block codes to an upper boundon the free distance of convolutional codes. She called this bound the generalized Singletonbound and codes which achieve this bound MDS convolutional codes. She was able to establishthe existence of MDS convolutional codes for each rate k/n and each degree !, by using theconnection between quasi-cyclic codes and convolutional codes.

Roxana’s work on convolutional codes had an impact on my own research in this subject, inparticular the above results about MDS convolutional codes were widely used in the PhD thesis

Tel.: (+34) 96 590 3655 – Fax: (+34) 96 590 3667Campus de Sant Vicent del RaspeigAp. Correus 99 – E-03080 Alacant

SPAINjcliment@ua.es

http://www.eio.ua.es/jcliment

Prof. Dr. Joan-Josep Climent

of my former student Victoria Herranz (2007).

My confidence in Roxana is so great that I arranged for one of my recent PhD students (Vir-tudes Tomas, 2010) to spend three months at San Diego State University last fall to benefitfrom her influence and advise. The PhD thesis of Virtudes investigates the decoding of MDSconvolutional codes over the erasure channel and is therefore directly linked to the original workof Roxana.

My recommendation is only based on her research achievements. However, her outstandingrecord as a lecturer and teacher makes my recommendation for a full professor position evenstronger.

If you need further assistance, please do not hesitate to contact me via email (jcliment@ua.es).

Sincerely

Joan-Josep Climent

Tel.: (+34) 96 590 3655 – Fax: (+34) 96 590 3667Campus de Sant Vicent del RaspeigAp. Correus 99 – E-03080 Alacant

SPAINjcliment@ua.es

http://www.eio.ua.es/jcliment

1

Jet Propulsion Laboratory California Institute of Technology M/S 238-420 4800 Oak Grove Drive Pasadena, CA 91109-8099

December 5,2010 Steven Buechler Professor, Department Chair Department of Applied and Computational Mathematics and Statistics 262 Hurley Hall University of Notre Dame Notre Dame, IN 46556 Dear Prof. Buechler, It is indeed a pleasure for me to write a recommendation letter on behalf of Dr. Roxana Smarandache for a joint faculty position in the Department of Applied and Computational Mathematics and Statistics and Electrical Engineering at the University of Notre Dame. I have known Dr. Smarandache now for more than three years. I have great respect for her talents and ability in research. Dr. Smarandache in a very short time made significant technical contributions in the area of applied mathematics with application to coding. Having contributed to this area myself, I feel extremely well qualified to comment on and assess the quality of her work. I have met Dr. Smarandache on several occasions during conferences to discuss technical matters of mutual interest. Speaking with her peer researchers, I got the distinct impression that Dr. Smarandache’s work and accomplishments were considered to be of very high value. Aside from these personal encounters, I have had the opportunity on several occasions to listen to Dr. Smarandache’s lectures primarily in the form of technical presentations at conferences and similar symposia. She is an enthusiastic, well-informed, and extremely lucid speaker and exudes the highest degree of confidence in what she says. Although I have never had the opportunity of formally attending or sitting in on one of her classes, I am confident that she exhibits the same characteristics in class. Her main research contributions are in the area of low-density parity check codes (LDPC), convolutional codes, and LDPC convolutional codes. In my view she became a well-known researcher due to her significant contributions to analysis of pseudo-code-words both for LDPC and LDPC convolutional codes in recent years. These contributions for example were reported in the following papers, “Pseudo-Codeword Analysis of Tanner Graphs From Projective and Euclidean Planes,” “Bounds on the pseudo-weight of minimal pseudo-code-words of projective geometry codes,” “On the minimal pseudo-code-words of codes from finite geometries,” “Absdet-pseudo-code-words and perm-pseudo-code-words: Definitions and properties,” and “Pseudo-code-word performance analysis of LDPC convolutional codes.” Protograph codes were invented in 2003 at Jet Propulsion Laboratory/ California Institute

2

of Technology. Since then we designed a family of protograph based LDPC codes that now are CCSDS standard for space applications. Her recent paper on ``Quasi-cyclic LDPC codes: Influence of proto- and tanner-graph structure on minimum hamming distance upper bounds,” has been very useful in understanding these new codes and in determining the upper bound on minimum distance of these CCSDS standard codes. Her paper opened a new area of research for LDPC codes when circulant permutation matrices are used to construct the LDPC codes. I was a reviewer for her recent papers on LDPC convolutional codes. Using theory of graph covers, she contributed in unification theory for construction of LDPC convolutional codes. Two construction methods proposed previously in the literature. She has shown that the two previously construction methods for LDPC convolutional codes are in fact equivalent. This is an important result that was not realized before. She also proved that minimum pseudo-weight of LDPC convolutional codes is better than the underlying block codes for such construction. Her recent paper on “Channel coding LP decoding and compressed sensing LP decoding: further connections,” shows how connected are problems in compressed sensing and channel coding. This means known solution in channel coding can be applied in solving compressed sensing problems and vice versa. Her research on MDS convolutional codes goes back to her Ph.D. thesis. She made significant theoretical and mathematical understanding of these codes. Her contribution is in developing the algebraic theory of convolutional codes using a module theoretic approach versus vector space approach. These results made a significant impact on the research community working on convolutional codes. I consider the following as her important contributions in this area: “Maximum Distance Separable Convolutional Codes,” “Constructions of MDS-convolutional codes,” “Convolutional codes with maximum distance profile,” Strongly-MDS convolutional codes,” and “On super regular matrices and MDP convolutional codes.” In summary, Dr. Roxana Smarandache has made numerous significant contributions in the area of applied mathematics with application to coding. I highly recommend her for an appointment in your department. If you have any questions, please feel free to contact me. Sincerely, ____________________ Dariush Divsalar Principal Scientist, and Senior Research Scientist Jet Propulsion Laboratory California Institute of Technology

3

Bio: Dariush Divsalar received the Ph.D. degree in electrical engineering from UCLA, with minor in Applied Mathematics in 1978. Since then, he has been with the Jet Propulsion Laboratory (JPL), California Institute of Technology (Caltech), where he is a Principal Scientist. At JPL, he has been involved with developing state-of-the-art technology for advanced deep space communications systems and future NASA space exploration. Since 1986, he has taught graduate courses in communications, and coding at UCLA and Caltech. He has published more than 150 papers, coauthored a book entitled An Introduction to Trellis Coded Modulation with Applications, contributed to two other books, and holds 15 U.S. patents in the above areas. He was co recipient of the 1986 paper award of the IEEE Transactions on Vehicular Technology. He was also co recipient of the joint paper award of the IEEE Information Theory and IEEE Communication Theory societies in 2008. The IEEE Communication Society has selected one of his papers for inclusion in a book entitled The Best of the Best: Fifty Years of Communications and Networking Research, containing the best 56 key research papers ever published in the Society’s 50-year history. He has received over 38 NASA Tech Brief awards and a NASA Exceptional Engineering Achievement Medal in 1996. He served as an Area Editor for the IEEE Transactions on Communications from 1989 to 1996. He became a Fellow of IEEE in 1997 for contributions to the analysis and design of coding and modulation techniques for satellite, mobile, and deep-space communication systems.

Department of Mathematics

Michigan State University

Wells Hall East Lansing, MI 48824-1027

517-353-0844

Fax: 517-432-1562

MSU is an affirmative-action, equal opportunity employer.

Professor S. Buechler, Chair Department of Applied and Computational Mathematics and Statistics 262 Hurley Hall University of Notre Dame Notre Dame, IN 46556

13 December 2010 Dear Professor Buechler, I am pleased to write to you in support of Roxana Smarandache who is a candidate for a position in your department. I apologize for not having written sooner. I am on sabbatical this semester and only returned late last week from an extended trip to Europe. I have known Roxana for over ten years, having first met her while she was a graduate student working with Joachim Rosenthal at Notre Dame. Since then I have encountered her often at mathematics and engineering meetings. I find her to be bright, enthusiastic, and full of energy and ability. Roxana’s main area of interest is coding theory—one of the primary branches of applied algebra. Perhaps encouraged by her supervisor Rosenthal, she has always been active in those aspects of coding theory that are of interest both mathematically and from an engineering point of view. Around fifteen years ago, the study of turbo codes and low density parity check (LDPC) codes revealed codes of near Shannon optimality. This produced a revolution in the engineering world of coding and opened up interesting mathematical problems of real value in applications. However the initial results were asymptotic in nature or, for finite lengths, centered upon computer generated examples that were seen to be good by simulation. This is unsatisfying—both from the engineering point of view, since implementation of unstructured computer generated codes has high overhead, and from the mathematical point of view, where pattern and proof are the goal and norm. Roxana’s recent work on QC LDPC codes, protographs, and pseudocodewords is all concerned with the mathematical construction of and analysis of codes and families of codes that are good in both the engineering and mathematical context. This work certainly represents a substantive contribution to the field. Furthermore it has been communicated to the appropriate audience via publication in the IEEE Transactions in Information Theory (the primary journal for such results) and regular presentations at the IEEE ISIT and ICC (the corresponding primary international conferences) and Allerton (a long running and highly respected annual conference run by the University of Illinois).

Department of Mathematics

Michigan State University

Wells Hall East Lansing, MI 48824-1027

517-353-0844

Fax: 517-432-1562

MSU is an affirmative-action, equal opportunity employer.

Roxana has eight published journal articles and two more accepted for publication. For mathematicians this is undeniably a little thin. But I believe it to be misleading. She has three further articles submitted or close thereto. She has recently begun work on compressed sensing, a timely and dynamic area that is very open and is clearly informed by error correction methods. Additionally Roxana has many articles appearing in refereed conference proceedings, particularly IEEE ISIT, IEEE ICC, and Allerton. Such publication is very common and accepted in the engineering world; and, as I mentioned above, I think Roxana’s continuing interaction with the engineers is a strong point in her favor. Furthermore, these three famous annual conferences are very popular, so the standard of refereeing for conference submissions is high. Thus to me Roxana’s publication record is more extensive than it might initially seem. I believe that Roxana Smarandache would be a valuable member of your department in many ways. She will continue to be mathematically productive and engaged with the outside world. I have heard her give excellent lectures and conclude that she is a teacher of good quality. Her record of master's level advising suggests that she would be an active and successful doctoral supervisor. She is personable and responsible, so she can be of help in departmental administration and related activities. In short, she seems to possess all the qualities that we wish for in a colleague. Her already strong connections with the Mathematics and Electrical Engineering Departments at Notre Dame make this even more the case for you. In summary, I give Roxana Smarandache my enthusiastic recommendation for a position in your department. Again I apologize for my delay and the somewhat rushed result. Please feel free to contact me for any additional information I can provide. Respectfully yours, Jonathan I. Hall, Professor of Mathematics Michigan State University jhall@math.msu.edu tel: (517)353-4653 fax: (517)432-1562

Universitat ZurichInstitut fur Mathematik

Winterthurerstrasse 190

CH-8057 Zurich

Tel. +41 44 635 5884

Fax +41 44 635 5706

rosen@math.uzh.ch

www.math.uzh.ch

Prof. Dr. J. Rosenthal

Professor Steven BuechlerDepartment ChairDepartment ACMSUniversity of Notre DameNotre Dame, IN 46556

December 12, 2010

Dear Steve,

This letter strongly supports the application of Dr. Roxana Smaran-dache for a tenured professorship at Notre Dame. I understand that itwould be a joint appointment between the Departments ACMS and theDepartment of Electrical Engineering.

As you well know Roxana is a former PhD student of mine. Already atNotre Dame she did extremely well, e.g. she obtained the Richard Sadyaward honoring her as the strongest graduate student of the enteringgraduate class. As a doctoral student she completed as (co)-author 4conference papers and 2 journal papers.

After graduation in 2001 she obtained immediately a tenure track posi-tion at San Diego State University. In the regular time she was promotedat San Diego State to Associate Professor and tenure in 2007.

In her dissertation and immediately after graduation she was mainlyworking on convolutional codes. These are essentially linear systemsover finite fields and Dan Costello and myself are experts in this area. Inher dissertation she came up with a generalized Singleton bound and shecalled codes meeting this bound MDS convolutional codes. This resultedin several papers where MDS convolutional codes were constructed. –MDS convolutional codes have the property that they have the maximumpossible free distance among all convolutional codes of a given rate anda given degree.

The original main paper “Maximum distance separable convolutionalcodes” has been cited by now on Google Scholar more than 60 times andthere are quite a few researchers who have taken up these concepts.

Shortly after she arrived at San Diego State she started to become inter-ested in LDPC codes and more general codes on graphs. This has become

a main focus in modern coding theory. Her early paper on the sub-ject were with Mike O’Sullivan (San Diego State) and Marcus Greferath(Shannon Institute in Dublin). But soon thereafter she started also tocollaborate on the subject with Pascal Vontobel (HP Research) and DanCostello and some of Dan’s students. She also has a paper with one ofher Master students at San Diego State, M. Wauer.

Among the papers in this area I like in particular the one entitled “Pseudo-codeword analysis of Tanner graphs from projective and Euclidean planes”.The paper investigates the decoding performance of minimal pseudo-codewords of Tanner graphs. This is a very important subject for theunderstanding of the performand of codes on graphs.

Another area where Roxana contributed significantly was on the ques-tion of constructing LDPC convolutional codes. This is an area whichwas mainly started by Dan Costello. Among the best papers in the areaI believe is “Pseudo-Codeword Performance Analysis for LDPC Convo-lutional Codes” which has been joint work with Costello, Vontobel andPusane, a former PhD and MSAM student at Notre Dame who benefiteda lot from the collaboration with Roxana.

While preparing this letter I found also on the arXiv a very interestingpreprint entitled “LDPC Codes for Compressed Sensing” which Roxanacompleted recently with Dimakis (USC) and Vontobel. This is a longerand fascinating paper where connections between linear programmingdecoding and compressed sensing are established. – You might be awarethat compressed sensing became a hot research topic after Fields medalistTerence Tao has contributed significantly.

As my remarks should make it clear Roxana matured to a broad re-searcher in coding theory. Many of her papers are published in the IEEETransactions of Information Theory, the very top journal in coding the-ory and a journal with a very high impact index. (Impact Factor 2.3).Her strength in research is also reflected in the fact that she has beenvery well funded by NSF in recent years. Note that she achieved thisbeing in a mathematics department of a University which is not allowedto have a PhD program and where teaching is a main emphasis. Lastbut not least she gets regularly invited for talks and she has served onthe program committee of several international conferences.

Let me conclude with some remarks about Roxana as a teacher: Onthe undergraduate level Roxana has been teaching also at Notre Dameand I am sure you have all the required data available. Nontheless myimpression is that she performs very well in classroom.

2

On the graduate level, she has been very inspiring for several Master andPhD students in the past. E.g. in the fall of 2008 she had a sabbaticalyear which she spent to a large degree here in Zurich. (Both at theUniversity and at ETH). While here she discussed mathematics withseveral of my PhD students and Post-Docs. This resulted in concretepublications with Virtudes Tomas (who also went to visit Roxana for amonth in 2009) and Mark Flanagan who is now a lecturer at UCD inDublin. I think she would really like to take on PhD students and amove to Notre Dame would help to make this happen.

I hope my evaluation will be helpful. Hiring Roxana would help tostrengthen applied discrete mathematics at Notre Dame. The connectionto the strong coding group in the Electrical Engineering Department atNotre Dame will also be very beneficial. I am convinced that hiring heron a tenured joint position would bring many benefits to Notre Dame.At this point she will be 4 years past tenure at San Diego State and ahiring on the full professor level can be considered.

Summarizing my letter I support Roxana’s application very strongly. IfI can be of any further assistance, please do not hesitate to contact me.

With best regards,

Joachim RosenthalCo-DirectorInstitut fur Mathematik

3

Research Statement – Roxana Smarandache

1 Background

The field of information and coding theory started with Shannon’s founding paper 62 years ago [29].He showed that every communication channel has an associated capacity C ! 0, such that thedecoding error probability can be made arbitrarily small at transmission rates below C. His proofis based on randomly chosen codes with optimal decoding and thus non-constructive. As a con-sequence, the goal of finding codes that approach the predicted limits became the challenge tothe succeeding generations of coding researchers. Until the last two decades, the most impor-tant results and advances in coding theory were almost exclusively algebraic, with each advancenarrowing but not eliminating the gap between real system performance and channel capacity(see [2, 16]). In the last fifteen years, the area of channel coding has undergone a revolutionarychange with the introduction of graph-based codes together with iterative decoding algorithms, inparticular turbo codes [1] and LDPC codes [11] that have been shown to approach capacity whendecoded using low complexity iterative message passing algorithms, such as belief propagation(BP). Iterative message passing algorithms [11] operate by passing messages along the edges of agraphical representation of the code known as the Tanner graph. While the algorithms are optimalwhen the underlying graph is a tree [25], such codes unfortunately perform poorly [7]. Therefore,bipartite graphs with cycles are desirable over trees. However, on graphs with cycles, the decodingalgorithms perform sub-optimally. LDPC codes perform nevertheless so well that some engineersdeclared that channel coding is “dead”, in the sense that Shannon’s quest has been already solved.However, simulation results are mathematically unsatisfying and have only limited value in deep-ening the understanding of turbo and LDPC codes. In addition, codes chosen even from a goodensemble can exhibit any possible behavior due to the lack of predictability of the performance ofsingle codes. This leads to errors in practical applications and keeps industry from embracing thegains of these codes and iterative processing in many areas where they are currently not selected.We can therefore say that finite-length analysis (vs. asymptotic analysis) became the new quest incoding theory.

Addressing this problem represents an important research direction in coding theory and a maintopic in my current research. A short introduction to my main research topics is given below.

Protograph-based LDPC Codes An [n, k] linear block code C is a k-dimensional subspace ofFn. It may be specified as the null space of a parity-check matrix H " Mm,n(F), m ! n # k, andby an undirected bipartite graph G, called the Tanner graph of H [47], for which H is the real-valued incidence matrix. Protograph-based codes LDPC codes [48] are a large class of codes fromwhich the codes used in most of the standards are chosen because they have, for suitably-designedprotographs, linear minimum distance growth [6]. A protograph is a relatively small Tanner graphdescribed by an m $ n incidence matrix B, known as a protomatrix, with non-negative integerentries bij that correspond to bij parallel edges in the graph. A protograph-based LDPC code [48]corresponds to an r-graph cover [45] of the protograph, for some positive integer r. An importantsubclass of protograph-based LDPC codes is that of QC LDPC codes, which are cover codesdescribed by m $ n arrays of r $ r circulant matrices [10]. Early papers on LDPC codes focusedmainly on QC LDPC codes based on protographs with single edges. In our work, we study thegeneral case of codes based on protographs with multiple edges.

Pseudo-codeword and Trapping Set Analysis The typical performance measures of a de-coder for a fixed code are the bit-error-rate (BER) or/and the frame-error-rate (FER) as functionsof the signal-to-noise ratio (SNR). A typical BER/FER vs. SNR curve consists of two distinctregions: at small SNR, the error probability decreases rapidly with the SNR, and the curve forms

1

the so-called waterfall region, then the decrease slows down abruptly at moderate SNR values; theresult is a flattening of the curve forming the “bottom of the waterfall” referred to as the errorfloor [23]. An important problem is the development of mathematical methods to predict errorfloors and evaluate the performance of LDPC codes in the low FER region [23]. In the case of thebinary erasure channel (BEC), the error floor region of LDPC codes is reasonably well understood:certain subsets of variable nodes in the Tanner graph of the LDPC code, called stopping sets [3],may include final undetermined variable nodes under most iterative decoding algorithms. Forchannels with additive noise, it was shown in [23] that in the error floor region virtually all failuresare due pseudo-codewords, if the sum-product algorithm or any linear programming algorithm isused, and to near codewords or trapping sets (sets of a relatively small number of variable nodessuch that the induced sub-graph has only a small number of odd-degree check nodes), if GallagerA/B type iterative decoding algorithms are used [11]. Our work was one of the first to analyze theset of pseudo-codewords. We extend our techniques to investigate the set of trapping sets.

Convolutional Codes A rate bc

convolutional code can be defined as a rank-b F[D]-submoduleof (F[D])c. It can be naturally mapped into a family of quasi-cyclic codes. LDPC convolutionalcodes are the convolutional counterparts of LDPC block codes. Two major methods, [46] and [17],have been proposed in the literature for the construction of LDPC convolutional codes which infact started the field of LDPC convolutional codes. My work on convolutional codes started duringmy Ph.D. years with results on convolutional codes over large fields. It has taken recently newdirections: 1) an investigation of the properties and parameters of the LDPC (binary) convolutionalcodes leading to a set of constructions of good codes, and 2) an analysis of properties that aconvolutional code needs to have to optimize its decoding capability over the erasure channel.

Connection to Compressed Sensing In its simplest form, the optimal compressed sensingproblem consists of finding the sparsest real vector e of length n that satisfies HCS · e = s, whereHCS " Rm!n is called a measurement matrix, and s " Rm is a measurement vector. In ourresearch we showed a connection between a class of pseudo-codewords of H, called in [32] of thenullspace type, and sparse real solutions of H · e = 0, allowing us to give performance guaranteesin compressed sensing [4, 5]. We plan to further investigate this connection.

2 Our Key Results

• The minimum distance of protograph-based codes is always upper bounded; the bounds dependon the protograph and are influenced by the girth [40,43].

• A single-edge protograph-based code can be modified to obtain a multiple-edge protograph-based code with the same regularity and possibly better minimum distance properties. Con-versely, a single-edge protograph-based code can be constructed from a multiple-edge proto-graph-based code by taking a 2-cover. This sequence of code transformations of a single-edgeprotograph-based code exhibiting good girth and minimum distance properties results into anew single-edge protograph-based code with up to twice the minimum distance of the multiple-edge ones [43].

• The minimum pseudo-weight of codes derived from projective and Euclidean planes is alwaysequal to the minimum distance (over AWGNC); this provides with an explanation for theirgood performance [41].

• The importance of minimal pseudo-codewords under linear programming decoding varies de-pending on which binary-input/output-symmetric memoryless channel is used. We obtainedbound results that hold for pseudo-codewords and minimal pseudo-codewords of any Tannergraph [43,44,51,52].

2

• The problem of computing the eigenvalues of large quasi-cyclic codes reduces to that of com-puting the eigenvalues of some smaller matrices that are computationally easier; this results isrelevant in spectral graph analysis [33].

• We classified the minimal pseudo-codewords of the nullspace type. We showed that the compo-nent-wise absolut-value of a vector in the nullspace of a parity-check matrix is a pseudo-codewordof the nullspace type. This gives a map between points in the real nullspace of the measurementmatrix H with 0 and 1 entries in compressed sensing into points in the fundamental cone ofthe matrix H seen as a parity-check matrix of a code. We extended the above map beyond(0, 1)-real measurement matrices to complex measurement matrices where the absolute value ofevery entry is a non-negative integer [4, 32,42].

• The minimum pseudo-weight of an LDPC convolutional code is at least as large as the minimumpseudo-weight of an underlying QC code; this result parallels the relationship between theminimum Hamming weight of convolutional codes and the minimum Hamming weight of theirquasi-cyclic counterparts. The two classic LDPC convolutional code constructions methods areequivalent. Any [k, n] T -periodic time-varying convolutional code obtained from unwrapping ablock-code is a time-invariant code of length N = nT [20–22,37].

• We generalized the Singleton bound on the minimum distance of block codes to convolutionalcodes and showed that it is always attained over a su!ciently large field. We constructed MDSconvolutional codes (codes attaining the bound) and their duals [26–28,30,31,34,35,38,39].

• We constructed convolutional codes with stronger properties: strongly-MDS codes and maxi-mum distance profile (MDP) convolutional codes, which are convolutional codes with fast andmaximum, respectively, possible column distance increase, i.e., in a window of time of lengthless than an upper bound set by the code parameters, these codes behave like MDS block codes:they have the best decoding ability [12,14,15].

• We showed that MDP convolutional codes perform better over the erasure channels in certainerror situations in which MDS block codes fail. We defined reverse-MDP codes, which havethe capability to recover a maximum of erasures using an algorithm which runs backward intime, and complete-MDP convolutional codes, which are both MDP and reverse-MDP codes,and showed how these optimize the error correction over the erasure channel [49,50].

3 Goals and Research Agenda

The following are my main research goals for the next three years1.

• To construct algebraically families of partially-QC LDPC codes with a predicted girth and min-imum distance linear in n, and to analyze their performance in terms of trapping sets, pseudo-codewords, and the interdependencies between all important parameters and relevant metrics.– Investigate the algebraic structure of partially-QC LDPC codes based on a given protograph

(with single and multiple edges), which will yield codes with potential for good performance,and, in comparison, the structure of non-QC vs. QC codes in a protograph-based LDPCensemble, and construct non-QC codes with better properties than the QC codes.

– Determine whether it is possible to construct sets of codewords for non-QC parity-checkmatrices that yield minimum distance upper bounds linear in n. Use the quasi-determinantdefined for non-commutative rings in the place of determinant; avoid all substructures thatled to the same upper bounds for QC codes, like commuting submatrices, “array” codes [36].

1I recently submitted a proposal to the NSF applied mathematics where some of these goals, my methods, and

promising preliminary results are described in detail.

3

– Investigate the girth of non-QC codes, and in particular, if there is an upper bound linearin n on the girth for codes over non-commutative rings. Investigate if there is a connectionbetween minimum distance increase and girth similar to the one for QC codes displayedin [43]. In general, we would like to explore if any connection between parameters can bedrawn and how to optimize both parameters in a code.

– Analyze the non-QC codes that are “towers of QC codes”: these are non-QC codes of lengthnrt that are QC-covers of codes of length nt, which in turn, are QC covers of a given proto-graph of length n. Given a protograph, study the cover degree and the type of cover (a purenon-QC cover or a tower of QC covers) that is needed to obtain a non-QC code based onthe protograph with parameters strictly larger than the upper bound that holds for the QCcodes based on that protograph.

• To study and classify all trapping sets and design or modify codes that avoid the worst of thesestructures and, consequently, to lower the error floor.– Study the e"ect that girth and cycle length profile have on all parameters that provide a

measure of the performance (e.g., minimum pseudo-weight, minimum trapping set size and,implicitly, minimum distance) for both QC and non-QC codes, and to design codes withguaranteed good performance. Analyze the connection between minimum distance and girthof a non-QC code and the impact that code modifications leading to an increase in minimumdistance like in [40, 43] have on breaking the trapping sets, and vice-versa, to design codemodifications that maximize both—if possible.

– Investigate all possible connections between trapping sets and pseudo-codewords, which willanswer the question if codes have the same good or bad performance under two di"erentdecoding algorithms (sum-product or Gallager A/B type). Can one display “bad” pseudo-codewords based on “bad” trapping sets, or vice-versa? The canonical completion of [18]could be used and possibly modified to construct such pseudo-codewords.

– Analyze, in addition to trapping sets, the properties of and relations to the fundamental cones[8] and computation trees [53] associated with a given matrix that describe the code; theseare also significant objects in iterative decoding and provide powerful tools to characterizethe behavior of locally operating, message-passing decoding algorithms.

• To translate results between channel coding linear programming and compressed sensing linearprogramming and to deepen our understanding of the role of linear programming relaxations forsparse recovery and for channel coding.

– Analyze the e"ect that certain modifications of the matrix (like removing short cycles) haveon its performance as a measurement matrix, and the theoretical guarantees that result fromit. Answering this would allow us to use (deterministic or randomized) results from codingtheory (e.g., see [24]) to create good measurement matrices for compressed sensing.

– Draw a connection between (a, b) trapping sets and sparse solutions of H · e = b of supporta, with b being a binary vector having weight b. This connection has potential to lead tostronger results in compressed sensing and vice-versa.

– Investigate the properties and metrics of all families of pseudo-codewords that can be obtainedthrough the bridging maps in [4] and, in particular, through the “non-conic” way of combiningpseudo-codewords to obtain a new one given in [4, Corollary 6]:

– Find and classify all families of matrices for which the absdet-pseudo-codewords are alwaysminimal. Classify the minimal pseudo-codewords that are not of the nullspace type and findpossible connections to trapping sets. Investigate the impact that nullspace pseudo-codewordshave in code performance.

4

4 Relevance of Research to the Research Community

My overall contribution to the research community and the discipline is to provide algebraic viewsand theoretical answers to questions in coding theory and to make connections and help bridgetopics and fields seemingly unconnected. In particular:

• Topics in my area (modern coding) are relevant in many aspects of our daily lives, since reliabledigital communication and storage penetrates every aspect of information technology. Turboand LDPC codes are used extensively in 3G and 4G mobile telephony standards, in new NASAmissions such as Mars Reconnaissance Orbiter as an alternative to Reed-Solomon codes withViterbi decoding, and in IEEE 802.16 (WiMAX), a wireless metropolitan networking standard.

• My work permits a rigorous mathematical analysis of the properties of modern codes. Inparticular, it significantly extends the finite-length analysis, which is critical but not well de-veloped. Generally, my research foci are highly interdisciplinary and have practical potential,which makes them relevant for the whole research community (including both mathematics andengineering).

• Our bounds on the minimum distance of QC codes are used in designing protograph-basedcodes that are used in standards, e.g., a tower of QC codes is the AR4JA code proposed fordeep-space usage in an experimental standard [6,9].

• My work on convolutional codes has a theoretical importance—it can be thought of as a referencepoint and a foundation for a theory of convolutional codes, which, ideally, will become as rich andcomplete as that of the block codes and practical potential when transmitting over an erasurechannel. It also has an interdisciplinary value: by identifying a convolutional code over a finitealphabet with a finite linear state machine (LFSM) having redundancy and which is capable ofcorrecting processing errors, my work gives a way to error-protect a given LFSM with a largerredundant LFSM [13]. In addition, LDPC convolutional codes are now shown to perform reallywell over the BEC due to the so-called “threshold saturation via spatial coupling” [19].

5 Relevance of Research to the University of Notre Dame

I have advised 9 MA or MS projects and 2 undergraduate projects, I have submitted 41 papers torefereed journals and conferences with a record of zero declined papers. Among these 13 are journalpapers (10 published or to appear, 1 submitted, 2 in preparation) for highly ranked journals.2

During the past seven years, I have attended and presented papers at the major conferences incoding theory (ISIT, AMS, Allerton, ICC), in seminars and colloquia, I have co-organized codingsessions at three AMS National Meetings and was on the TPC of three other conferences. I am areviewer for well-regarded journals and conferences.

One important missing component in my research is the opportunity of working with graduatestudents. Being a state university in California, SDSU is allowed Ph.D. programs only if jointwith other Ph.D. granting schools. We do not have such a program in mathematics yet. At theUniversity of Notre Dame, I would be able to work with and guide Ph.D. students, which wouldhelp me expand my research in other possible interdisciplinary areas of interest, e.g., networkcoding, DNA computing, probabilistic analysis, statistical coding. Many of these subjects overlapwith fields and areas of research of members of the ACMS department at Notre Dame. I hopethat it would give us a common ground for collaborative research and co-advising of students.In addition, my ongoing collaboration with members of the EE department could only becomeeasier and more fruitful. The reduced teaching load at Notre Dame would allow me to continue todevelop my research while maintaining the same quality and level of commitment in teaching.

2Among the 246 journals in electrical and electronic engineering listed in Thomson Web of Science, IEEE Trans.on Information Theory is the top journal in terms of the total citation count in 2009.

5

References

[1] C. Berrou, A. Glavieux, and P. Thitimajshima. Near Shannon limit error-correcting codingand decoding: Turbo-codes. In IEEE Int. Conference on Communication, pages 1064–1070,Geneva, Switzerland, May 1993.

[2] D. J. Costello. Applications of error-control coding. IEEE Trans. on Inform. Theory, 44:2531–2560, 1998.

[3] C. Di, D. Proietti, I.. E. Telatar, T. J. Richardson, and R. L. Urbanke. Finite-length analysisof low-density parity-check codes on the binary erasure channel. IEEE Trans. on Inform.Theory, 48(6):1570–1579, 2002.

[4] A. G. Dimakis, R. Smarandache, and P. O. Vontobel. Channel coding LP decoding andcompressed sensing LP decoding: further connections. In 2010 Intern. Zurich Seminar onCommunications, March 2010.

[5] A. G. Dimakis and P. O. Vontobel. LP decoding meets LP decoding: a connection betweenchannel coding and compressed sensing. In 47th Allerton Conf. on Communications, Control,and Computing, Allerton House, Monticello, Illinois, USA, Sep. 30–Oct. 2 2009.

[6] D. Divsalar, C. Jones, S. Dolinar, and J. Thorpe. Protograph based LDPC codes with mini-mum distance linearly growing with block size. In IEEE GLOBECOM, 2005.

[7] T. Etzion, A. Trachtenberg, and A. Vardy. Which codes have cycle-free Tanner graphs? IEEETrans. on Inform. Theory, 45:2173–2183, September 1999.

[8] J. Feldman. Decoding Error-Correcting Codes via Linear Programming. PhD thesis, Mas-sachusetts Institute of Technology, Cambridge, MA, 2003.

[9] The Consultative Committee for Space Data Systems (CCSDS). Low density parity checkcodes for use in near-earth and deep space applications, Experimental Specification CCSDS,131.1-O-2. September 2007.

[10] M. P. C. Fossorier. Quasi-cyclic low-density parity-check codes from circulant permutationmatrices. IEEE Trans. on Inform. Theory, 50(8):1788–1793, 2004.

[11] R. G. Gallager. Low-density parity-check codes. IRE Trans. on Info. Theory, IT-8:21–28,1962.

[12] H. Gluesing-Luerssen, J. Rosenthal, and R. Smarandache. Strongly MDS convolutional codes.IEEE Trans. Inform. Theory, 52(2):584–598, 2006.

[13] C. N. Hadjicostis. Non-concurrent error detection and correction in fault-tolerant linear finite-state machines. IEEE Trans. Automat. Contr., 2003.

[14] R. Hutchinson, J. Rosenthal, and R. Smarandache. Convolutional codes with maximumdistance profile. Systems and Control Letters, 54(1): 53–63, 2005.

[15] R. Hutchinson, R. Smarandache, and J. Trumpf. Superregular matrices and the construction ofconvolutional codes having a maximum distance profile. Linear Algebra and Its Applications,428:2585–2596, 2008.

[16] I. M. Jacobs. Practical applications of coding. IEEE Trans. on Inform. Theory, 20:305–310,1974.

[17] A. Jimenez-Feltstrom and K. Sh. Zigangirov. Time-varying periodic convolutional codes withlow-density parity-check matrix. IEEE Trans. on Inform. Theory, 45(6):2181–2191, September1999.

[18] R. Koetter and P. O. Vontobel. Graph covers and iterative decoding of finite-length codes. In3rd Intern. Symp. on Turbo Codes and Related Topics, pages 75–82, Brest, France, Sept. 1–52003.

6

[19] S. Kudekar, T. Richardson, and R. Urbanke. Threshold saturation via spatial coupling: Whyconvolutional LDPC ensembles perform so well over the BEC. to appear, IEEE Trans. Inf.Theory, 2011.

[20] A. E. Pusane, R. Smarandache, P. O. Vontobel, and D. J. Costello, Jr. On deriving goodLDPC convolutional codes from QC LDPC block codes. In IEEE Intern. Symp. on Inform.Theory, January 2007.

[21] A. E. Pusane, R. Smarandache, P. O. Vontobel, and D. J. Costello, Jr. On the iterativedecoding of LDPC convolutional codes. In 18th IEEE Signal Processing and CommunicationsApplications Conference (SIU), pages 519–522, April 2010.

[22] A. E. Pusane, R. Smarandache, P. O. Vontobel, and D. J. Costello, Jr. Deriving good LDPCconvolutional codes from LDPC block codes. IEEE Trans. on Inform. Theory, February 2011.To appear. Available at http://arxiv.org/abs/1004.5157.

[23] T. Richardson. Error floors of LDPC codes. In 41st Allerton Conf. on Communications,Control, and Computing, Allerton House, Monticello, Illinois, USA, October 2003.

[24] T. Richardson and R. Urbanke. Modern Coding Theory. Cambridge University Press, NewYork, NY, 2008.

[25] T. J. Richardson and R. L. Urbanke. E!cient encoding of low-density parity-check codes.IEEE Trans. on Inform. Theory, 47(2):638–656, 2001.

[26] J. Rosenthal and R. Smarandache. Construction of convolutional codes using methods fromlinear systems theory. In 35-th Annual Allerton Conference on Communication, Control, andComputing, pages 953–960, 1997.

[27] J. Rosenthal and R. Smarandache. On the dual of MDS convolutional codes. In 36-th AnnualAllerton Conference on Communication, Control, and Computing, pages 576–583, 1998.

[28] J. Rosenthal and R. Smarandache. Maximum distance separable convolutional codes. Appl.Algebra Engrg. Comm. Comput., 10(1):15–32, 1999.

[29] C.E. Shannon. A mathematical theory of communication. Bell Syst. Tech. J., 27:379–423 and623–656, 1948.

[30] R. Smarandache. Maximum Distance Separable Convolutional Codes, Constructionand Decoding. PhD thesis, University of Notre Dame, August 2001. Available athttp://www.nd.edu/˜rosen/preprints.html.

[31] R. Smarandache. Unit memory convolutional codes with maximum distance. Codes, Systemsand Graphical Models, 123:381–396, 2001.

[32] R. Smarandache. On minimal pseudo-codewords. In IEEE Intern. Symp. on Inform. Theory,Austin, Texas, USA, June 2010.

[33] R. Smarandache and M. F. Flanagan. Spectral graph analysis of quasi-cyclic codes. In IEEEGLOBECOM, December 2009. Available online at http://arxiv.org/abs/0908.1966.

[34] R. Smarandache, H. Gluesing-Luerssen, and J. Rosenthal. Construction results for MDS-convolutional codes. In Proceedings of the 2000 IEEE International Symposium on Informa-tion Theory, page 294, Sorrento, Italy, 2000.

[35] R. Smarandache, H. Gluesing-Luerssen, and J. Rosenthal. Constructions for MDS-convolutional codes. IEEE Trans. on Inform. Theory, 47(5):2045–2049, 2001.

[36] R. Smarandache, D. G. M. Mitchell, and D. J. Costello, Jr. Partially quasi-cyclic protograph-based LDPC codes. In IEEE International Conference on Communications (ICC), June 2011.Submitted.

[37] R. Smarandache, A. Pusane, P. O. Vontobel, and D. J. Costello, Jr. Pseudo-codeword perfor-mance analysis of LDPC convolutional codes. IEEE Trans. on Inform. Theory, 55(6):2577–2598, 2009. Available at http://arxiv.org/abs/cs/0609148.

7

[38] R. Smarandache and J. Rosenthal. Convolutional code constructions resulting in maximal ornear maximal free distance. In Proceedings of the 1998 IEEE International Symposium onInformation Theory, page 308, Boston, MA, 1998.

[39] R. Smarandache and J. Rosenthal. A state space approach for constructing MDS rate 1/nconvolutional codes. In Proceedings of the 1998 IEEE Information Theory Workshop onInformation Theory, pages 116–117, Killarney, Kerry, Ireland, June 1998.

[40] R. Smarandache and P. O. Vontobel. On regular quasi-cyclic LDPC codes from binomials. InIEEE Intern. Symp. on Inform. Theory, page 274, Chicago, IL, USA, June 27–July 2 2004.

[41] R. Smarandache and P. O. Vontobel. Pseudo-codeword analysis of Tanner graphs from projec-tive and Euclidean planes. IEEE Trans. on Inform. Theory, 53(7):2376–2393, 2007. Availableat http://arxiv.org/abs/cs/0602089.

[42] R. Smarandache and P. O. Vontobel. Absdet-pseudo-codewords and perm-pseudo-codewords:definitions and properties. In IEEE Intern. Symp. on Inform. Theory, Seoul, Korea, June 28–July 3 2009. Available at http://arxiv.org/abs/0904.2022.

[43] R. Smarandache and P. O. Vontobel. Quasi-cyclic LDPC codes: Influence of proto- and tanner-graph structure on minimum hamming distance upper bounds. IEEE Trans. on Inform.Theory, 2010. Accepted. Available online at http://arxiv.org/abs/0901.4129.

[44] R. Smarandache and M. Wauer. Bounds on the pseudo-weight of minimal pseudo-codewords ofprojective geometry codes. Contemporary Mathematics, Algebra and its Applications, 419:285–296, December 2006.

[45] H. M. Stark and A. A. Terras. Zeta functions of finite graphs and coverings. Adv. Math.,121(1):124–165, 1996.

[46] R. M. Tanner. Error-correcting coding system. U.S. Patent # 4,295,218, October 1981.

[47] R. M. Tanner. A recursive approach to low-complexity codes. IEEE Trans. on Inform. Theory,27(5):533–547, 1981.

[48] J. Thorpe. Low-density parity-check (LDPC) codes constructed from protographs. IPNProgress Report, 42-154:1–7, 2003.

[49] V. Tomas, J. Rosenthal, and R. Smarandache. Decoding of convolutional codes over theerasure channel. IEEE Trans. on Inform. Theory, 2010. Submitted. Available at http:

//arxiv.org/abs/1006.3156.

[50] V. Tomas, J. Rosenthal, and R. Smarandache. Reverse maximum distance profile convolu-tional codes over the erasure channel. In 19th International Symposium on MathematicalTheory of Networks and Systems, July 2010.

[51] P. O. Vontobel and R. Smarandache. On minimal pseudo-codewords of Tanner graphs fromprojective planes. In 43rd Allerton Conference on Communications, Control, and Computing,Allerton House, Monticello, Illinois, USA, September 2005. Available at http://arxiv.org/abs/cs/0510043.

[52] P. O. Vontobel, R Smarandache, N. Kiyavash, J. Teutsch, and D. Vukobratovic. On the mini-mal pseudo-codewords of codes from finite geometries. In IEEE Intern. Symp. on Inform. The-ory, Adelaide, Australia, September 2005. Available at http://arxiv.org/abs/cs/0508019.

[53] N. Wiberg. Codes and Decoding on General Graphs. PhD thesis, Linkoping University,Sweden, 1996.

8

Teaching statement – Roxana Smarandache

Achievements These are what I consider my “personal best” achievements as a teacher:

• I was chosen the “most influential teacher” by the best (highest GPA) undergraduate studentof the class of 2007.

• I could o!er, through an NSF grant I had, small research stipends to two talented undergrad-uate students majoring in mathematics to get involved in research during 2007-2008. Theyare now both in Ph.D. programs at very good universities (University of Colorado, Boulder,and UCSD).

• Several times I have encouraged students, women in particular, (sometimes they are shierand not aware of their talent) to consider pursuing mathematics further to a Ph.D. program.

• Several times I got my students amazed at how the theoretical concepts are applied and giveso nice and easy results. Their “wow!” was satisfying.

Teaching Philosophy The personal qualities that made the few teachers I dearly remembergreat teachers to me (all in mathematics, the subject I always liked) were that they were challengingus with questions, they were asking us to give examples, counterexamples, sketches of proofs, orthey were posing excellent homework assignments that could not be done without a deep andcomplete understanding of the material. Coming out of those classes left me with a feeling ofsatisfaction and accomplishment because by answering the questions, I knew I had a good graspof the content of the lecture and that in turn made me feel richer and to want to learn more as ifI was discovering how my brain was working; it was fun. When young, we have a very dim ideaof what we are capable and we need people—later remembered as having had a “mentoring” roleon us—to help us discover our potential and develop it fully. Such mentoring can happen whenwe are really young, through parents, family, teachers, or, in some cases, not until college or in ajob, if at all. Of course the person has more or less a sense of his/her own capabilities, but he/shelacks the confidence to take full advantage of them. On a show around Thanksgiving on NPR,the listeners were asked to recall stories in which people made a di!erence in people’s life thusdeserving their gratitude. I was impressed to see how many callers were acknowledging a teacherthat made a di!erence in their life. Teachers can turn a class into lasting memory, even a life-timeexperience, and I would like to be one of the teachers that makes such a di!erence.

From my above described experience and also from my current experience as a learner and asa teacher of learning students, I believe the we all learn better if we are interested in what weread, and this happens if we are involved and engaged in the learning process. Learning becomesthen useful because it has been developed through a personal intellectual engagement that createsnew understanding. Learners learn best when they have thought out the process through whichthe answer is achieved. However, new material needs to be exposed to students sometimes at ahigher speed than desired by the students, which can be overwhelming and tiring if the class goalsare not conveyed first and a class agenda clearly drawn. I believe that students should be helpedto understand the biger picture or the direction in which the lecture in going, so that they canfollow it actively and better store the material, and it is the teacher’s task to keep the lecturesclear and organized and explain the larger context. I craft each of my lecture with this in mind:goal, directions, context, and potential for involvement.

1

Experience and Teaching Methods During the past 10 years, I have taught courses at alllevels to an extremely diverse body of undergraduate and graduate students at SDSU (among themwere young women supporting a child or a family, middle-age adults, minorities without good homeeducation, and students who are not very committed): introductory and advanced linear algebra,calculus, coding theory, abstract algebra, matrix theory, and at the University of Notre Dame (asa TA 1997-2001 and as a visiting professor 2005-2006): combinatorics, calculus, linear algebra anddi!erential equations. I have always tried, many times successfully, to create “magic” in my classes;I experimented with di!erent methods and di!erent levels of student involvement depending on thenumber of students and the class level: quizzes to check on learned techniques, pre-quizzes, used abrain-storming tool, WebWork and WebCT to exploit the students inclination towards technology,group homework method to allow students to teach one another, and student projects that givestudents a chance to learn about applications of the subjects to other fields and present it to theclass. A few of the less common methods that I have used in my courses are summarized below:

• Coding Theory as applied Matrix Theory. In the Matrix Theory course, I used assignmentsrelated to coding theory on how matrices and vector spaces are notions that form the back-ground for coding theory. In abstract algebra, I explained why the prime factorization hasan immense impact on secure communication.

• Independent projects were assigned in the Coding Theory and Matrix Theory courses. Theyconsisted of reading about a certain topic not covered in class and presenting it briefly to theclass. The projects were having an applied theme with the intention of having the studentsapply or see applied the topics introduced in class that the students researched by themselves.

• Computer components were used in lectures and homework to help visualize mathematics andovercome the students possible math phobia: WebWork, WebCT, Matlab, Magma, Maple.

• Guest lecturers were invited to my Linear Algebra classes to talk about coding theory, wirelesscommunication and dynamical systems. These lectures were well received by my students.Listening to people working in industry or in more applied fields gave students a betterappreciation of the value of abstract mathematics.

Educational Goals In my student evaluations during the years, a few attributes are invariant:I am enthusiastic, I care about the students’ progress and get them involved in the learningprocess, and I answer all the questions. Other characteristics of my teaching, perhaps less visibleto students, but important nonetheless, are: I encourage independent thinking by following thestudents’ reasoning although di!erent from my original solution and, if wrong, showing where andwhy it fails; I draw on the previous material or the material from other courses that are relevantto the lecture. For example, I hope to make freshmen in business realize that mathematics is notthat hard and it is pretty and useful, and I hope to make math majors learn more than just asubject but fundamental techniques and reasoning and an appreciation of mathematical elegance.I hope that students will retain from my classes a set of tools and methodologies that will remainreadily accessible in the future, a comfort with the subject taught, a desire to explore more, andan organized chart-like mind with the main points of the material.

My educational goals can be summarized as: to communicate an enthusiasm for mathematics,to develop students’ research skills, to cultivate mathematical self-confidence and independence,to promote success in graduate school, to enable the students to obtain a deep understanding ofbasic concepts in several areas of mathematics, to teach how to do independent work, and to gainexperience in expressing mathematical ideas orally and in writing.

2