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EC63ageNo... 1USN

SixthSemesterB.E.DegreeExamination,July/August2005ElectronicsandCommunicationrelecommunicationsEngineering

Information Theory and Codingime: 3 hrs.) [Max.Marks : 100

Note: AnsweranyFIVEfullquestions.All questionscarryequalmarks.

1. (a) Explainwhythe logarithmicunctions usedto definea measureof information.Findtheinformationontentof a messagehatconsistsof a digitalword12digitslonginwhicheachdigitmaytakeon oneof fourpossibleevels.Theprobabilityof sendinganyof thefourlevelsis assumedo be equal,andthe levelin anydigitdoesnotdependon thevaluestakenonbypreviousdigits. (6Marks)(b) Whatisa Markoffnformationource?Whatis theuseofthetreediagramepresentationfor sucha source?DefinethetermsEntropyandinformationateof Markoffsources.

(6Marks)(c) Supposehatit is requiredodesigna systemhatprovidesheattitudeofthe70outgoingEandC engineeringtudentsofan instituteof engineeringntheyear2004.Theattitudeis to bequantisedntothreelevels:

Goingfora PGprogramn a foreignuniversityF),Goingfora job in a dreamcompanyn India(D),Goingfora job in anycompanyC).Basedon theirattitudein the followingyeargivenbelow,constructa firstorderMarkoffmodelfor thesourceandcalculateheentropyi) 40 studentswereundercategoryG, 15studentswereundercategory0 and 15studentswentforcategoryFwithassistantship.ii) Outof 40studentswhowentforjobunderCduringthesaidyear,20of themontheaveragecontinuednCduringthenextyearand10of themwentfora PGprogramunderF andthe remainingwentfora job in a dreamcompany.iii) Ontheaverage,outof 20studentswhoweregoingfora PGprogramanda dream

company,duringthe nextyear10of themcontinuedn the samedirectionn the. nextyear and the remainingmovedin the directionof acquiringa job in an Indiancompanyin the nextyear.iv) For those studentsunder category (ii) and (iii), the administrativepoliciesdonotpermitthemto changefrom a dreamcompanyto aPG programmeor from a PG

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2 EC63(b) A discretechannelacceptsat its inputa binarysequencewith a bit rateof r/; bits/sec.Thechannelsignalsare selectedfrom a set of eightpossiblewaveforms,eachhavinga

duration (;b) seconds. Thus, each waveformmay conveyupto 3 bits of information.Thechannelnoiseis suchthat whenthe receivedwaveformis decoded,eachblockof 3inputbits is receivedwith no errorsor with exactlyone error in the first, second,or thirdbit position.Assumingthat theseoutcomesare equal!ylikelyto occur:i) Findthe capacityof the discretechannelii) Supposethat you want to transmitthe ourput of an informaiionsource havinga

rate R = !f over this channel. How wouldyou encodethe data so that errorlesstransmissionis possible? (11Marks)3. (a) Whatisa continuoushannel?Discussbrieflytheeffectsofthispartof thecommunicationsystemwhiletransmittinga signalfrom a transmitterto a receiver.Howdo you compute

the capacityof such a channel?' (7Marks)(b) i) Calculatethe capacityof a Gaussianchannelwitha bandwidthof one megahertzanda (S/N) ratio of 30 dB.

ii) How longwill it taketo transmitone millionASCII charactersover this channel?(4Marks)(c) DescribeShannon'sencodingalgorithmto designa sourceencoder.Mentiontheproperties

possessedby the encodingprocedurededucedfromthe algorithm. (9Marks)4, (a) Whatis a discretememorylesssource? Showthat the entropyof sucha sourcewith anarbitraryprobabilitydistributionfor the symbolsof its alphabet( is boundedas

H(() :SlO92J{with usualnotation. (7 Marks)

(b) What do you mean by data compaction? How is this achievedbasically? Nametwo. commonlyusedschemesfor data compaction. (6Marks)(C)Showthatthemutualnformationfa channels relatedothejointentropyof thechannel

inputandchanneloutput~y :I(X, Y) = H(X) + H(Y) - H(X, Y) with usual notations. (7Marks)

5. (a) Whatare Huffmancodes?Whatis the basicideabehindHuffmancoding?Writethevariousstepsof thisencodingalgorithm. (8Marks)(b)Considerdiscretememoryesssourcewithalphabet

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3 EC636. (a) Brieflydiscussthe causesfor transmissionerrorsin a digitalcommunicationsystem.Whatis errorcontrolcoding?Mentionthe functionalblocksthat accomplisherrorcontrolcodingand indicatetheir functions. (9Marks)

(b) Startingfromfundamentals,provethat an n-type C is a codewordgeneratedby G if andonly if CHT = o. Where,H is the paritycheckmatrixof the code and G = [I.z.~P],the generatormatrix. (5Marks)

(C) Assumethat the codewordC=101110for the (6,3) case is transmittedand the vectorR=001110s received.Showhowa decoderusingthe syndromelookuptable,cancorrectthe error.Take generatormatrixas

[1 1 0 1 0 0

]G= 0 1 1 0 1 0101 001Use standard array method. (6 Marks)

7. (a) Whatis a binarycycliccode? Describehe featuresof encoderanddecoderusedforcycliccodesusingan (n - k) bit shift register. (9Marks)(b) Considerthe (15,11)cycliccode generatedby g(X) = 1 + X + X4

i) Devicea feedbackregisterencoderfor this code.ii) Illustratethe encodingprocedurewith the messagevector 11001101011by listingthe statesof the register(the rightmostbit is the earliestbit) (9Marks)

(C) What are shortenedcycliccodes? (2 Marks)8. Figure0.8 showsheencoderora rater = t.constraintengthK=4convolutionalode.i) Determinethe encoderoutputproducedby the messagesequence10111....

INPvr

1

1-------.----- ,--------.......-

Wfv'{-

r'r I 9UK'E Q.g ...:'~~II) Constructthe code tree for the encoder. Trace the path through the tree thatcorrespondsto the messagesequence10111.....Comparethe resultingencoderoutputwith that foundin part(i). (8+12=20arks)** * ** I" r~. ',,~~-~~I.~

'(, Q-~ / \.\~rv-R'( '-'- ~