Basicinformation
Intermsofsourcecoding,Shannonprovedin1951thatwhenthesourceoutputhasredundantmessages,theoutputofthesourcecanbechangedbycodingtomaketheinformationtransmissionrateclosetoChannelcapacity.In1948,ShannonproposedaShannoncodethatcouldmatchthesourceandchannel.In1949,R.M.FenooftheMassachusettsInstituteofTechnologyproposedFenocoding.In1951,AmericantelecommunicationsengineerD.A.HoffmanproposedamoreeffectiveHuffmancode.Afterthat,facsimilecoding,imagecoding,andvoicecodingappeared.In-depthresearchondatacompressionhassolvedmanypracticalproblemsraisedindigitalcommunications.
Intermsoferrorcorrectioncoding,Shannonproposedanerrorcorrectioncodein1948(codelength=7,numberofinformationsymbols=4).In1949,athree-biterror-correctingGraycode(codelength=23,numberofinformationsymbols=12)appeared.In1950,AmericanmathematicianR.W.Hammingpublishedapaper"ErrorDetectionCodesandErrorCorrectionCodes",andproposedthefamousHammingcode,whichhadanimportantinfluenceonerrorcorrectioncodes.Convolutionalcodesappearedin1955.Convolutionalcodesarestillwidelyused.In1957,cycliccodeswereintroduced.Thestructureofthecycliccodeissimple,itisconvenienttodesignwithalgebratheory,anditisalsoeasytorealize.In1959,HagbergcodesandFaircodesthatcancorrectsuddenerrorsappeared.In1959,R.C.BossandD.K.RayGiordalioftheUnitedStatesandA.OkungaonofFranceindependentlypublishedafamouscycliccodealmostatthesametime,whichwaslatercalledtheBCHcode(ieBose-Chaudhuri-Hocquenghemcode).Sequentialdecodingwasproposedin1965.Sequentialdecodinghasbeenusedinspacecommunication.In1967,A.J.Viterbiproposedmaximumlikelihoodconvolutionaldecoding,whichiscalledViterbidecoding.In1978,vectorcodingappeared.Thevectorcodingmethodisahighlyefficientcodingtechnique.In1980,thenumbertheorymethodwasusedtorealizeReed-Solomoncode(Reed-Solomoncode),referredtoasRScode.Itisactuallyamulti-aryBCHcode.Thiserrorcorrectioncodingtechnologycanreducethenumberofcomponentsoftheencoderintegratedcircuitbyanorderofmagnitude.Ithasbeenwidelyusedinsatellitecommunications.TheconcatenatedcodeconstructedbycombiningRScodeandconvolutionalcodecanbeusedindeepspacecommunication.
Detailedintroduction
Intermsofcryptography,Shannonpublished"CommunicationTheoryofSecrecySystems"in1949,whichisgenerallyregardedasapioneeringworkincryptography.In1976,DiffiandHermanproposedthepublickeysystemforthefirsttime,whichopenedupanewdirectionfortheresearchofcryptography.Theapplicationofverylargescaleintegratedcircuitsandhigh-speedcomputerspromotesthedevelopmentofsecurecodingtheory,andatthesametimebringsgreatthreatstothesecurityofsecurecommunications.Sincetheintroductionofcomputercomplexitytheoryintocryptographyinthe1970s,so-calledP-type,NP-typeandNP-completeproblemshaveappeared.Thecomplexityfunctionofthealgorithmgrowsexponentially,sothekeyspaceexpands,whichmakestheanalysisandsearchofthecipherfaceseriouschallenges.Cryptographybegantodevelopindepth.
SourcecodingThegeneralizedsourcecodingincludestwoaspects:analog-to-digitalconversion(thatis,convertinganalogintobinarydigitalquantities)anddatacompression(thatis,encodingthesedigitalquantitiestoreducethedigitalrate)..Themaintaskofsourcecodingistocompressdata.Ithasfourbasicmethods:,
Matchingcode
Thismethodisbasedontheoccurrenceprobability(probabilitydistribution)oftheencodingobject,andcodesofdifferentlengthsaregiven,thegreatertheprobabilityofoccurrence,Theshorterthegivencodelength.Theso-calledmatchingheremeansthatthecodelengthmatchestheprobabilitydistribution.Morsecodeisamatchingcode.Matchingcodingoftenusesdecorrelationmethodstofurthercompressthedata.
Transformcoding
Thismethodistotransformthesignalfirst,fromonesignalspacetoanothersignalspace,andthenencodethetransformedsignal.Transformcodinghasawiderangeofapplicationsinvoiceandimagecoding.Atpresent,thecommonlyusedtransformcodinghastwotypes:predictivecodingandfunctioncoding.Predictivecodingistopredicttheupcomingchangesofthesignalbasedonsomeknownconditionsofthesignal.Itdoesnottransmitthesampledvalueofthesignal,butthedifferencebetweenthesampledvalueofthesignalandthepredictedvalue.Predictivecodingisusedindigitaltelephonesanddigitaltelevisions.ThemostcommonlyusedfunctiontransformationsareFastFourierTransform(FFT),CosineTransform,WalshTransform,HaarTransformandHadamardTransform.Thefrequencyspectrumcharacteristicsofthesignalcanbeobtainedthroughthetransformation,sothedigitalcanbecompressedaccordingtothefrequencyspectrumcharacteristics.
Vectorencoding
Thismethodistoclassifythepossibletransmittedmessagesandstorethemintheelectroniccomputerdatabaseofthereceivingendbyaddress,andthesenderonlysendstheaddressofthedatabasetofindoutthemessageContent,whichgreatlycompressesthesentdata.
Identificationcode
Thismethodismainlyusedforthecodingoftext,symbolsanddatawithstandardshapes.Butvoicecanalsobeidentifiedandcoded.Theroleofidentificationcodeisnotlimitedtocompresseddata,italsohasawiderangeofapplicationsinpatternrecognition.Commonlyusedidentificationmethodsincludeassociationidentificationandlogicalidentification.Identificationcodescangreatlycompressdata.Forexample,usingthevoicerecognitionmethodtotransmitvoice,theaveragebitrateislessthan100bitspersecond.ThemethodofΔmodulatingvoiceisusedtotransmitvoice,andthedigitalratereaches38,400bitspersecond.Thedifferencebetweenthetwoisabout400times.However,theidentificationcoderestoresastandardvoicebasedonacodewhenitisrestored,andcanonlybeusedforspecialtelephonesandquestion-and-answerdevicesthatdonotneedtoknowwhothecalleris.Whentheidentificationcodeisusedfortexttransmission,allprintedsymbolsarerecoveredandcanonlybeusedforordinarytelegrams.