Advanced CodingTheory

PURPOSEThis course is about the fundamental aspects that make error control coding work and their implementation in practical applications.

INSTRUCTIONAL OBJECTIVESAt the end of the semester, the student should be able to

Design a system using a convolutional code o Determine the distance properties of a convolutional codeo Implement Viterbi and sequential decoders for convolutional codeso Analyze the performance of the decoder over binary symmetric and additive

white Gaussian noise channels Design codes to correct burst errors

o Design single burst error correcting codes o Design phased burst error correcting codes o Design concatenated codes

Understand the motivation for and theory of trellis coded modulation o Design, one, two and multi-dimensional TCM systemso Develop decoding algorithms for TCM systemso Analyze the performance of TCM systems

Design a system using turbo codes o Develop turbo codes for various rateso Develop turbo codes using iterative decoderso Evaluate the performance of turbo codes using bounding techniques

Design error control for channels with feedback

SYLLABUS CONTENTSLinear convolutional encoders - Structural properties of convolutional codes - State diagrams - Transparent convolutional codes - Receiver phase offset and Differential decoding - Trellis diagrams - Viterbi algorithm - Performance analysis - Design and Implementation of Viterbi decoder - Punctured convolutional codes.

Tree diagrams - The Fano algorithm - The Stack algorithm - Performance analysis for Sequential decoders - Burst error correcting codes - Decoding of single burst error correcting cyclic codes - Fire interleaved codes - Phased burst error correcting codes - Concatenated codes.

M-ary signaling - One and Two-dimensional TCM - Multiple TCM - Decoding and performance analysis - Implementational considerations.

Turbo codes - Encoding - Performance Evaluation using bounding techniques - BCJR algorithm for decoding - Applications.

Pure ARQ Protocols - Noisy feedback channels - Type I Hybrid ARQ Protocols - Type II Hybrid ARQ Protocols and Packet combining.

L = 45    TOTAL = 45

TEXT BOOKS

Stephen B. Wicker, "Error control systems for Digital communication and storage", Prentice Hall, Upper Saddle River, NJ, 1994

Shu Lin, Daniel Costello, "Error control coding - Fundamentals and Applications", Second Edition, Prentice Hall, Upper Saddle River, NJ, 2004

E. Biglieri, et al. "Introduction to Trellis coded modulation with Applications", Macmillan Publishers, 1991

R. Johannesson and K.S. Zigangirov, "Fundamentals of Convolutional coding", IEEE Series on Digital and Mobile Communication, Wiley-IEEE Press, 1999