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# Performance Evaluation of RS codes with AWGN & Rayleigh Channel

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### Performance Evaluation of RS codes with AWGN & Rayleigh Channel

1. 1. Performance Evaluation of RSPerformance Evaluation of RScodes with AWGN & Rayleighcodes with AWGN & RayleighChannelChannelPresented by-:Sarbjeet SinghNITTTRRegular (2011 Batch)
2. 2. ContentsContents Introduction of RS CodesIntroduction of RS Codes Its advantages & disadvantagesIts advantages & disadvantages MotivationMotivation Literature SurveyLiterature Survey ObjectiveObjective Time PlanTime Plan Proposed workProposed work
3. 3. Continued….Continued…. ResultsResults ConclusionConclusion Future WorkFuture Work ReferencesReferences
4. 4. Introduction of RS CodesIntroduction of RS Codes Reed-Solomon codes are nonbinary cyclic codes with symbolsmade up of m-bit sequences, where m is any positive integer having a value greater than 2. R-S (n, k) codes on m-bit symbols exist for all n and k forwhich 0 < k < n < 2m + 2 where k is the number of data symbols being encoded, and n is the total number of code symbols in the encodedblock. Reed-Solomon codes is also a systematic linear block code,in which the message to be transmitted is divided into separateblocks of data.
5. 5. Continued….Continued…. Each block has parity protection information added to it toform a self-contained code word. It is also a systematic code where the encoding process doesnot alter the message symbols and the protection symbols areadded as a separate part of the block It is particularly good at dealing with bursts errors because,although a symbol may have all its bits in error, this counts asonly one symbol error in terms of the correction capability ofthe code. For Reed-Solomon codes, the code minimum distance is givenby dmin = n - k + 1
6. 6. Advantages of RS codesAdvantages of RS codes Burst error correction they are effective for channels that have memory. they can be used efficiently on channels where the set of inputsymbols is large. In R-S code as many as two information symbols can be addedto an R-S code of length n without reducing its minimumdistance.
7. 7. DisadvantagesDisadvantages As the redundancy of an R-S code increases(lower code rate), its implementation getscomplex
8. 8. MotivationMotivation Correct retrieval of message despite of errors in receivedCorrect retrieval of message despite of errors in receivedsequence by adding redundant bits at the end of mrssagesequence by adding redundant bits at the end of mrssage RS Codes performs well against burst noiseRS Codes performs well against burst noise It can be applied to different applications like-:It can be applied to different applications like-:(a) C D Players(a) C D Players(b) Digital TV(b) Digital TV(c) D VD Players(c) D VD Players(d) Cable modems(d) Cable modems
9. 9. Literature SurveyLiterature Survey(1) Kar-Peo Yar; Do-Sik Yoo; Stark, W; “(1) Kar-Peo Yar; Do-Sik Yoo; Stark, W; “Performance of RSPerformance of RScoded M-ary modulation with and without symbolcoded M-ary modulation with and without symboloverlappingoverlapping” Communications, IEEE Transactions on” Communications, IEEE Transactions onVolume 56, Issue 3, March 2008 Page(s):445 - 453Volume 56, Issue 3, March 2008 Page(s):445 - 453This paper tells us about that how rs codes are concatenatedThis paper tells us about that how rs codes are concatenatedusing M-ary modulation and Markov chain method is used.using M-ary modulation and Markov chain method is used.Performance of rs coding over awgn channel is evaluated.Performance of rs coding over awgn channel is evaluated.From the result we saw that stronger inner code gives betterFrom the result we saw that stronger inner code gives bettererror probability.and minimum SNR is attained.error probability.and minimum SNR is attained.
10. 10. Continued….Continued….(2) Ping Shi; Ming-rui Hou; Rui Lv; “(2) Ping Shi; Ming-rui Hou; Rui Lv; “Performance of Non-Performance of Non-Binary RS-Turbo Concatenated CodesBinary RS-Turbo Concatenated Codes” Circuits and” Circuits andSystems for Communications, 2008. ICCSC 2008. 4th IEEESystems for Communications, 2008. ICCSC 2008. 4th IEEEInternational Conference on 26-28 May 2008 Page(s):773 -International Conference on 26-28 May 2008 Page(s):773 -776776This paper tells us about a new scheme of RS TurboThis paper tells us about a new scheme of RS Turboconcatenated codes which includes RS codes & non –binaryconcatenated codes which includes RS codes & non –binaryTurbo codeTurbo code The results shows us improved BER performance at highThe results shows us improved BER performance at highSNR & reduce the iteration number as compared toSNR & reduce the iteration number as compared toconventional non-binary turbo code.conventional non-binary turbo code.
11. 11. Continued….Continued….(3) Ibraheem, O.W.; Khamiss, N.N.; “(3) Ibraheem, O.W.; Khamiss, N.N.; “Design and Simulation ofDesign and Simulation ofAsymmetric Digital Subscriber Line (ADSL) ModemAsymmetric Digital Subscriber Line (ADSL) Modem” Information” Informationand Communication Technologies: From Theory to Applications,and Communication Technologies: From Theory to Applications,2008. ICTTA 2008. 3rd International Conference on2008. ICTTA 2008. 3rd International Conference on7-11 April 2008 Page(s):1 - 67-11 April 2008 Page(s):1 - 6This paper tells us that how by using ADSL modem is divided intoThis paper tells us that how by using ADSL modem is divided intomodulation system that uses multicarrier modulation technique calledmodulation system that uses multicarrier modulation technique calleddicrete multitone modulation &error control system is used to detectdicrete multitone modulation &error control system is used to detect&correct codes to achieve low bit error rate&correct codes to achieve low bit error rate
12. 12. Continued….Continued….(4) J Cai, M. Tomlinson,C.Tijhai,M.Ambroze & M.Ahmed(4) J Cai, M. Tomlinson,C.Tijhai,M.Ambroze & M.Ahmed““Comparison of Concatenated Reed – Solomon codingComparison of Concatenated Reed – Solomon codingwith Hard –decision to Soft decision LDPC coding forwith Hard –decision to Soft decision LDPC coding forrayleigh fading channelrayleigh fading channel” Fixed & Mobile communication” Fixed & Mobile communicationResearch , proceedings of 2006 IEEE Information theoryResearch , proceedings of 2006 IEEE Information theoryWorkshopWorkshop This paper tells us about : that rs codes used over binaryThis paper tells us about : that rs codes used over binaryerasure channel optimal results are obtained .erasure channel optimal results are obtained . It is shown thatby using an RS code concatenated with BCH codes andusing hard decisions, better results are obtained than usingbit interleaved LDPC codes, with soft-decision decoding. The BCH code is used to correct small numbers of errorsdue to noise and also to detect the presence of deep fades,in which case the entire packet is erased. Erased packetsare corrected by the RS code
13. 13. ObjectiveObjective(1)The objective of this thesis work is to evaluate theperformance of RS Codes using different modulationschemes & channel(2) The purpose is to increase data rate and decrease error rate
14. 14. Random integer RS EncoderQAM ModulatorAWGN ChannelQAM DemodulatorRS DecoderDisplayError statisticsBlock diagram of the system
15. 15. Proposed work for Pre -thesisProposed work for Pre -thesis Evaluate performance of RS Codes using QAM Scheme inEvaluate performance of RS Codes using QAM Scheme inAWGN Channel -:AWGN Channel -:(a)(a) 16 QAM16 QAM(b)(b) 32 QAM32 QAM(c)(c) 64 QAM64 QAM
16. 16. Proposed work for final thesisProposed work for final thesis Evaluate performance of RS Codes using QAM Scheme inEvaluate performance of RS Codes using QAM Scheme inRayleigh Channel -:Rayleigh Channel -:(a)(a) 16 QAM16 QAM(b)(b) 32 QAM32 QAM(c)(c) 64 QAM64 QAMfor final thesis and also evaluating DQPSK , & MSK usingfor final thesis and also evaluating DQPSK , & MSK usingAWGN & Rayleigh ChannelAWGN & Rayleigh Channel
17. 17. Time plan for Pre thesisTime plan for Pre thesis
18. 18. Series 10123456JAN-FEB FEB-MAR MAR-APR APR-MAYevaluate rscodes usingqam+rayleighchannelevaluate rs codesusing DQPSK&MSK in AWGNCHANNELevaluate rs codesusing DQPSK&MSK in RayleighchannelSUBMISSION OFTHESISTime plan for thesisTime plan for thesis
19. 19. ResultsResults Results of RS Codes using QAM Scheme in AWGN ChannelResults of RS Codes using QAM Scheme in AWGN Channel(a)(a) 16 QAM16 QAM(b)(b) 32 QAM32 QAM(c)(c) 64 QAM64 QAM
20. 20. Figure 1 – :16 qam using awgnFigure 1 – :16 qam using awgnchannel using RS codechannel using RS code
21. 21. Figure 2 – :32 qam using awgnFigure 2 – :32 qam using awgnchannel using RS codechannel using RS code
22. 22. Eb/No(db)Eb/No(db) TheorticalTheorticalSERSERSimulatedSimulatedSERSER00 0.73970.7397 0.73970.739722 0.92370.9237 0.67710.677144 0.71770.7177 0.58630.586366 0.55830.5583 0.48220.482288 0.3540.354 0.3540.3541010 0.22140.2214 0.22140.22141414 0.03680.0368 0.03680.03681616 0.0070450.007045 0.0070450.0070452020 0.0109150.010915 0.00010.0001Results of RS Codes using 16 QAM in awgn channel
23. 23. Eb/No(db)Eb/No(db) Theortical SERTheortical SER Simulated SERSimulated SER00 0.81230.8123 0.81230.812322 0.77220.7722 0.77220.772244 0.71590.7159 0.71590.715988 0.54580.5458 0.54580.54581212 0.29740.2974 0.29740.29741616 0.073040.07304 0.073040.073042020 0.0029590.002959 0.0029590.0029592222 0.00015140.0001514 0.00015140.00015142323 0.0123370.012337 7.70147*107.70147*10-3-3Results of RS Codes using 32 QAM in awgn channel
24. 24. Eb/No(db)Eb/No(db) Theortical SERTheortical SER Simulated SERSimulated SER00 0.9240.924 0.9240.92422 0.90190.9019 0.90190.901944 0.87010.8701 0.87010.870188 0.76090.7609 0.76090.76091212 0.56030.5603 0.56030.56031616 0.2740.274 0.2740.2742020 0.050430.05043 0.050430.050432424 0.00086710.0008671 0.00086710.00086712626 0.015760050.01576005 9.62852626*9.62852626*10-310-3Results of RS Codes using 64 QAM in awgn channel
25. 25. ConclusionConclusion(1) It has better simulation results as to compared to theoreticalresults in respect of SER performance.(2) As data rate increases , bit error rate decreases
26. 26. Future workFuture work To Evaluate RS Code using different modulation scheme ie.To Evaluate RS Code using different modulation scheme ie.QAM , DQPSK, PSK using rician fading channelQAM , DQPSK, PSK using rician fading channel
27. 27. ReferencesReferencesBin Ibrahim, M;Ahmed,N.B; “SER Performance of Reed-Solomon Codeswith QAM Modulation Scheme in AWGN Channel” Signal processing&its applications, 2009 , CSPA 2009 , 5THInternational Collaquium on 6-8march 2009 , pages 391-394 Lekkakos, Dimitrios; Kragh, Frank; Robertson, Clark;”Performanceanalysis of a Link-16 compatible waveform using errors-and-erasuresdecoding when corrupted by pulse-noise interference” MilitaryCommunications Conference, 2009. MILCOM 2009. IEEE18-21 Oct. 2009 Page(s):1 - 6 Li, K.H.; Kam, P.Y. “On the error performance of 8-QAM involving aπ/2-wedge-shaped decision region” Information, Communications andSignal Processing, 2003 and the Fourth Pacific Rim Conference onMultimedia. Proceedings of the 2003 Joint Conference of the FourthInternational Conference on Volume 2, Issue , 15-18 Dec. 2003 Page(s): 884- 887 vol.2
28. 28. Continued…Continued… Nie Mingxin; Dai Peng “A Novel RS+ConvolutionalConcatenated Code in VHF CommunicationSystem”Networking, Sensing and Control, 2008. ICNSC2008. IEEE International Conference on Volume , Issue , 6-8April 2008 Page(s):736 - 738 G. C. Cardarilli, M. Ottavi, S. Pontarelli, M. Re, A. Salsano,"Data Integrity Evaluations of Reed Solomon Codes forStorage Systems,“ Defect and Fault –Tolerance in VLSISystems ,IEEE International Symposium on, pp. 158-164, 19thIEEE International Symposium on Defect and Fault Tolerancein VLSI Systems (DFT04), 2004.
29. 29. Continued….Continued…. Jin Wenyi; Fossorier, M.; “Jin Wenyi; Fossorier, M.; “Towards Maximum LikelihoodTowards Maximum LikelihoodSoft Decision Decoding of the (255,239) Reed SolomonSoft Decision Decoding of the (255,239) Reed SolomonCodeCode” Magnetics, IEEE Transactions on Volume 44, Issue 3,” Magnetics, IEEE Transactions on Volume 44, Issue 3,March 2008 Page(s):423 - 428March 2008 Page(s):423 - 428 Soyjaudah, K.M.S.; Oolun, M.K.; Jahmeerbacus, I.; Bhurtun,Soyjaudah, K.M.S.; Oolun, M.K.; Jahmeerbacus, I.; Bhurtun,C “C “Adaptive coding technique employing concatenatedAdaptive coding technique employing concatenatedReed Solomon and convolutional codesReed Solomon and convolutional codes” 6 th Africon” 6 th AfriconConference in Africa, 2002. IEEE AFRICON. Volume 1, 2-4Conference in Africa, 2002. IEEE AFRICON. Volume 1, 2-4Oct. 2002 Page(s):173 - 176 vol.1Oct. 2002 Page(s):173 - 176 vol.1 Ping Shi; Ming-rui Hou; Rui Lv; “Ping Shi; Ming-rui Hou; Rui Lv; “Performance of Non-Performance of Non-Binary RS-Turbo Concatenated CodesBinary RS-Turbo Concatenated Codes” Circuits and” Circuits andSystems for Communications, 2008. ICCSC 2008. 4th IEEESystems for Communications, 2008. ICCSC 2008. 4th IEEEInternational Conference on 26-28 May 2008 Page(s):773 -International Conference on 26-28 May 2008 Page(s):773 -776776
30. 30. Continued….Continued…. Hermes, D.J.; Kragh, F.E. “Hermes, D.J.; Kragh, F.E. “A Bandwidth Efficient ConstantA Bandwidth Efficient ConstantEnvelope Modulation with Reed-Solomon Coding”Envelope Modulation with Reed-Solomon Coding”CommunicationsCommunications, Computers and Signal Processing, 2007., Computers and Signal Processing, 2007.PacRim 2007. IEEE Pacific Rim Conference on 22-24 Aug.PacRim 2007. IEEE Pacific Rim Conference on 22-24 Aug.2007 Page(s):434 – 4372007 Page(s):434 – 437 Pauluzzi, D.R.; Beaulieu, N.C.; “Pauluzzi, D.R.; Beaulieu, N.C.; “A comparison of SNRA comparison of SNRestimation techniques for the AWGN channelestimation techniques for the AWGN channel””Communications, IEEE Transactions on Volume 48, IssueCommunications, IEEE Transactions on Volume 48, Issue10, Oct. 2000 Page(s):1681 - 169110, Oct. 2000 Page(s):1681 - 1691
31. 31. Continued….Continued…. Dural, O.; Proakis, J.G.; “Dural, O.; Proakis, J.G.; “Upper bounds on errorUpper bounds on errorprobability of serially concatenated convolutional codesprobability of serially concatenated convolutional codesand MSK in AWGNand MSK in AWGN and fading channels”and fading channels”CommunicationsCommunications, 2003. ICC 03. IEEE International, 2003. ICC 03. IEEE InternationalConference on Volume 5, 11-15 May 2003 Page(s):3095 -Conference on Volume 5, 11-15 May 2003 Page(s):3095 -30993099 Diatta; De Geest, D; Geller, B; “Reed Solomon turbo codesfor high data rate transmission” IEEE 59th VehicularTechnology Conference, 2004. VTC 2004-Spring. 2004Volume 2, 17-19 May 2004 Page(s):1023 - 1027
32. 32. THANK YOU