Reed-Muller Codes for Single Bit Error Correction in 16-bit

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llth Semins onISSN: 2087-33LXThe rcsulting codeword is reverted backto data infqmatioa using combinations ofmodulo-2 a.Her.prograrnming.Scbematic used to gsnqate md add single bit error togenerated codeword is shown in Fig.7 below, which isimplemented using Mathscript, along with thecodeword gercr-ating o,peration- Schematic sbown inFigT pro'duces single bit error which may contain inaDy bit within 32-bit codewordk-t.l.Tbe lGbit bioary data are cooverted backto decimal uumbers, which ae theacqverted back to digital waveform-Dgital wavefom produced is convertedback to annlog waveform, which is thendisplayed and played bacL4. Experimenhl ResultsThe schematic of Analog to Digitat Converter isshown in Fig.3 below. The schematic extractswaveform from the ssund file and converts it todigital. There is also functioo for sound data pla$ack(Play Waveform), which is also shown in Fis,3.Figue 5. Codcword gpffrating scbematicTo make tbc implemeotation informative to use,r, asimple Graphical User tnterface (G[IO is alsodesigned to displsy wavefom of tbe original sounddat4 waveform of error cootained sormd data, andwaveform of recovered sound data- GUI will provideinformation about processed datat-,.liFigurc 6. Error generator schernaticFigure 3- Aralog to digial converter schematicSchematic us€d to create II and Itr is showu in Fig.gbelow. The schematic shown in Fig.8 creates paritycheck matrix II by taking matrix G withoui anymodifications sisnce (32,1Q RM codes are self dualcodes. Thus, taosposing II will produce Hr.The schematic of Decimal to Bioary Converter isshowu in Fig.4 below. The schematic coosists of 16dividing operation to cotrvert decimal ntrmberoroduced to tcbit bimrv data-Figure 7. Padtycheck gcneration schenraticFigure 4. Decirml to binaqr convefier schcmticSchematic used to produce codeword, which mnintycusists of geoerator matrix multiplicatiog is showain Fig.6 bslow. Gen€rator mauix rsed to generatecodeword is also shown in Fig.6. Mathscriil iJused tosimpliS some operatioos 19fts1 than qsing graphicalScbematic used for erru estimation is shown in Fig.9bclow. Schematic showu in Fig.9 below implementsthe lookup table to €stimatc eror contained in thereceived codeword bascd oo corresponding syndromeproduced. In this irylerneatation, every possiblesingle-bit error is included from MSB to LSB.
1 trt Seninq on Intelligence Technologt otd It Applicatbns, SITM 2010 /SSM ; 2087-3i lXFigue 10. Combinatioo of modulo-2 addersFigure 8. Error cstimation schermticlnside the lookup table are possibilities ofconectablcerrors, which arc vectors eacb cootaining single nonzero element and also one vector sqgtaining all zeroelements. By multiplying each possibility with II1which issyn&ome loohrp table will beused fq estioating eror contained in thecorresponding received codeword by comparing thesyndrome fu the received codewod wilhthe syndrome from the lookup table-Schematic used for correcting received codeword isshown in Figl0 below. Schematic shown in Fig.l0will add the corresponding received codeword withthe produced estimated error to rcvert the receivedcodeword back to the original codeword-132,:..:,i:i; :': trb- !{.:r'.:!- '.:'O ,
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Reed-Muller Codes for Single Bit Error Correction in 16-bit

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