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1、Page737—EntropyCodingBinaryencodingofdataisanaturalmeansofrepresentingcomputationaldataonmoderndigitalcomputers.Whenthevaluestobeencodedareuniformlydistributed,thisisanspace-efficientmeansofrepresentingthedataaswell.Informationtheorygivesusseveralefficientmethodsof
2、encoding''alphabets"wherethelikelihoodofsymboloccurrencevariessymbolbysymbol.Codingtechniquesthatminimizespaceintherepresentationofrandomsequencesofsymbols(optimizespaceusedintherepresentationofsymbolsbasedupontheprobabilitythesymbol)areknownasentropycodingtechniqu
3、es.Therearetwopopularmethodsofentropycodingintheliterature,Huffmancodingandarithmeticcoding.Huffmancodingrepresentssymbolswithwordsofintegerlengthwhilearithmeticcodingisnotlimitedtointeger-lengthcodes.Huffmancodingiscomputationallylessexpensivetoimplementandtypical
4、lygivescompressionratiosclosetothoseofarithmeticcoding.XYZcompressionisdevelopedtosupportHuffmancoding[Huf52].7.1—HuffmanCodingConsidertheproblemofencodingthesixsymbolsdefinedinTable7.1.TheamountofinformationtransferredinasymbolAthatoccurswithprobabilitypis:whereIA
5、isthenumberofbitsrequiredtoexpresstheamountofinformationconveyedbysymbolA,andpAistheprobabilitythatsymbolAwilloccur.Page74Theentropyofacodesequenceistheaverageamountofinformationcontainedineachsymbolofthesequence:whereHistheentropyofthecodingrepresentation,andsrang
6、esthroughallsymbolsinthealphabetofsymbols.Table7.1SymbolsandtheirassociatedHuffmancode.SymbolProbabilityInformationCodeA1/21bit0B1/42bits10C1/164bits1100D1/164bits1101E1/164bits1110F1/164bits1111Theentropyofthesequencerepresentsthelowerboundofthespaceneededtocommun
7、icatetheinformationcontainedinthesequence.AfixedwordlengthofthreebitsmaybeusedtorepresentthesixsymbolsinTable7.1.UsingtheHuffmancodingrepresentation,wegetanaveragecodelengthof2,whichfortheseprobabilitieshappensalsotobetheentropy,orlowerlimitoftheaveragecodelength:A
8、ssignmentofHuffmancodesisdonebydevelopingaHuffmancodingtree,asillustratedinFigure7.1.Thetreeisdeveloped"lefttoright"(orbottomtotop).Symbolsarelis
