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1、InternationalJournalofComputerApplications(0975–8887)Volume71–No.7,May2013FPGAImplementationof3bitsBCHErrorCorrectingCodesSamirJasamMohammedHayderFadhilAbdulsadaCollegeofEngineering,UniversityofBabylon.CollegeofEngineering,UniversityofBabylon.Babylon,IraqBabylon,IraqABSTRACT2.B
2、CHCODESThispaperdescribestheprototypingofaBCH(Bose,BCHcodesarepolynomialcodesthatcapableofcorrectingChaudhuri,andHocquenghem)codeusingaFieldanycombinationoftorfewererrorsinablockof?=2?−ProgrammableGateArray(FPGA)reconfigurablechip.BCH1digits.ToknowtheencodinganddecodingoftheBCH
3、codeisoneofthemostimportantcyclicblockcodes.code,theknowledgeoffinitefieldsisnecessary[5].DesigningonFPGAleadstoahighcalculationrateusingparallelization(implementationisveryfast),anditiseasyto2.1BCHEncodermodify.BCHencoderanddecoderhavebeendesignedandAn(n,k)binaryBCHcodeencodes
4、k-bitsmessageinton-bitssimulatedusingMATLAB,Xilinx-ISE10.1WebPACKandcodeword.Themessagevectorcanbeexpressedinaimplementedinaxc3s700a-4fg484FPGA.Inthispolynomialformasfollows[6]:implementationweused15bit-sizecodewordand5bitsdata,mx=m0+m1x+m2x2+⋯+mk−1xk−1(2)any3bitserrorinanyposi
5、tionof15bitshasbeencorrected.Themessagedigitsareutilizedasapartofthecodeword.TheTheresultsshowthatthesystemworksquitewell.systematicencodingcanbeimplementedby:Keywordsn−kcx=p(x)+xmx(3)Errorcorrectingcodes,BCHcodes,encoding,decoding,FPGAWherep(X)isthereminderandcanbeexpressedas1
6、.INTRODUCTIONpX=xn−kmxmodg(x)(4)Theerrorcontrolcodingisoneofthebasicrequirementsofdigitalinformationandcommunicationsystems.ItisItfollowsfromthedefinitionofat-error-correctingBCHcodeimportanttoensurereliabletransmissionofinformationoveroflength?=2?−1that-eachcodepolynomialhas?,
7、?2,noisychannels.Errorcorrectioncodingisthemeanswhereby…,?2?asroots,c??=0,for(1≤?≤2?)[7].errorswhichmaybeintroducedintodigitaldataasaresultoftransmissionthroughacommunicationchannelcanbe2.2BCHDecodercorrectedbaseduponreceiveddata[1,2].ErrorcorrectingThebiggestadvantageofBCHcode
8、sistheexistenceofcodeshaveawiderangeofapplicationsindi
