Chapter_4._Channel_Capacity_Notes

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1、ChannelCapacity容量抽象的过滤器InInformationTheory,thetransmissionmediumistreatedasanabstractandnoisyfiltercalledthechannel.Wemayreasonthatasweincreasetheamountofinformationpassingthroughthechannel,thatinturntheprobabilityoferroralsoincreases.Thishoweverisnotthecase.Foreverychannel,anupperboundexis

2、tswhichdefinesthemaximumrateofinformationtransmissionthroughachannel.Thisupperboundisknownasthechannelcapacity,C.Theprobabilityoferrorininformationtransmittedthroughsuchachannelapproacheszeroiftherateofinformationtransmissionislessthanthechannelcapacity.ChannelCodingTheormClaudeShannon(1916

3、-2001)showedthat,iftheinformationrateR[R=rsHbits/sec],isequalto,orlessthan,thechannelcapacityC,(i.e.RC),thenthereexistsacodingtechniquewhichenablestransmissionoverthenoisychannelwithanarbitrarilysmallfrequencyoferrors.武断地Thetheoremdoesnotstatethecodingtechniquetobeused,merelythatsuchacodee

4、xists.Theconversetothetheoremstatesthatitisnotpossibletotransmitmessageswithouterror,iftheinformationrateisgreaterthanthechannelcapacity(i.e.R>C]Thusthechannelcapacitycanbedefinedas;themaximumrateofreliable(error-free)informationtransmissionthroughthechannel.考虑Nowconsiderabinarysourcewithan

5、availablealphabetofkdiscretesymbols.Assumethesymbolsareequiprobableandstatisticallyindependent.组成Sourcemessagescanbeeithersingledigitsymbolsorcouldbecomposedofseveralsymbols.确定Wealsoassumethateachmessagesentcanbeidentifiedatthereceiver.Suchconditionsdescribewhatisreferredtoasa“discretenoise

6、lesschannel”.Themaximumentropy(i.e.averageinformationpersymbol)ofthesourceislog2kbits.1IfthesourcetransmitsasymboleveryTsecs,thenrs=Tsymbols/sec,andthechannelcapacitythereforeisgivenas;CRrHrlogkEqn.1ss2达到Toattainthismaximum,themessagesmustbeequiprobableandstatisticallyindependent.Theseco

7、nditionsformabasisforthecodingofinformationtobetransmittedoverthechannel.存在Inthepresenceofnoise,thecapacityofadiscretechannel(asdefinedabove)decreases,arisingoutoftheerrorsthatoccurduringthetransmission,whichareduetothenoise.产生BandwidthBandwidth(B)isapar