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Joint source channel decoding in the factor graph framework

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Academic year: 2021

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(18) À$Á |$ywÂàÁZÄ@Å7Æ z{|. Ú:x{x‹x. ¡ Ì­HsI‚„stŒTˆŠyv€stx‹Œ÷ˆw|:Ž^Չ–Dstu uАuFuЁ`vys~z£‡u\‚m‡u x‹ÕT–‹s~–{stŒTZv€ærtd†Tst†‚gAv€stuŠŒTuw| ž>‡u ©‡ƒ‚ÜˆŠ”/u rtstˆ\Þ~x—vy²vyTsKˆŠ‡Ž²1s ­Hêð ª Ö׳ d 3š ØÝ³ã× d ŒT† ÚÞ³ãׇ׍¬ ŒT†‘ˆª g‡××‡š{և׍ׇ¬H­H¤<¢êërtd†Tst¡癐x‹Œ€vàˆŠ‡”TuŠrts±rÝTŒTŒTst–é†Tstrtd†Tx‹ŒTFx{ˆDrtuŠu x‹st† ƒ‚„stuPØÛ–{ƒ|„stu*z£‡rIv€‡u*uЁ’T›‡az =x{‡”TuŠsA؍h¡ ¡G¡K¡K¡~¡K¡K¡K¡~¡K¡K¡~¡K¡K¡~¡K¡ f‡× g¡ d fÌ «|:Ž^ÕӐ‡–mstu uАu=u Zv€s4z£‡uÓv€TsŸv€stuŠŒTuw|ž>‡u ©‡ƒ‚ˆŠ‡”Tu rtsj‡z/ÕT–‹ß s g‡¡{Ø<rtd†Tst† ÞKx“v€â†Tx‹õÓstuŠstŒ€v8ˆƒ”TuŠrts,rtd†Tstˆ4Œ/†~‚m‡uw|‰x‹ŒTáuЁ`vys,­H¤8¢±ê!róT‡ŒTŒTst–‰rtd†TstˆŠš strÝÛrt™†Ts*ÕT–{drÝ©^rt‡ŒTˆŠx{ˆ v€ˆ±oz g‡××AÕTx“v€ˆƒ¡jç鐍x‹ŒyvFˆŠ”TuŠrtsPrÝT‡ŒTŒTst–T†Tstrtd†Tx{ŒT x{ˆ*r€uŠu x‹st†›ƒ‚/s€uPÛÖ²–‹ƒ|/s€uPz•rIvyu*uЁ‡’TT¡Ì¡~¡K¡K¡~¡K¡K¡K¡~¡K¡K¡~¡K¡K¡~¡K¡ f‡Ø g¡ dZr  «|:Ž^ÕӐ‡–mstu uАu=u Zv€s4z£‡uÓv€TsŸv€stuŠŒTuw|ž>‡u ©‡ƒ‚ˆŠ‡”Tu rtsj‡z/ÕT–‹ß s g‡¡{Ø<rtd†Tst† ÞKx“v€â†Tx‹õÓstuŠstŒ€v8ˆƒ”TuŠrts,rtd†Tstˆ4Œ/†~‚m‡uw|‰x‹ŒTáuЁ`vys,­H¤8¢±ê!róT‡ŒTŒTst–‰rtd†TstˆŠš strÝÛrt™†Ts*ÕT–{drÝ©^rt‡ŒTˆŠx{ˆ v€ˆ±oz g‡××AÕTx“v€ˆƒ¡jç鐍x‹ŒyvFˆŠ”TuŠrtsPrÝT‡ŒTŒTst–T†Tstrtd†Tx{ŒT x{ˆ*r€uŠu x‹st†›ƒ‚/s€uPÛز–‹ƒ|/s€uPz•rIvyu*uЁ‡’TT¡Ì¡~¡K¡K¡~¡K¡K¡K¡~¡K¡K¡~¡K¡K¡~¡K¡ f‡Ø g¡ d Ì «|:Ž^ÕӐ‡–/stu uАu±uЁ`vys*z•‡u±ž>‡u ©‡ƒ‚툊‡”Tu rtsFz:ÕT–‹q s g‡¡{ØKrtd†Tst†AÞKx“v€ò–“v€stuwå ŒT`vyx—‚„sˆŠ”TuŠrtsŒT†~rÝTŒTŒTst–értd†TstˆD©‡stst’Tx{ŒTÔ­H¤<¢êërtd†Ts±Õ/–{drÝ©™–‹stŒT`vy~`v g×‡×²ŒT¨ † àâáÙã· `v d ág¡* Tx{Žá”T–{Zv€x‹ŒTˆ*uŠs8†T‡ŒTs8x‹ŒávyTs8rt‡ˆŠstˆP‡z/Þ~x—vyT”«v uRÞKx“v€÷çé TêP¤ ƒ‚/stu*‡’T’Tu ‡’Tu x‹`vysAz•rIvyu*uЁ’TTˆƒ¡6¡K¡K¡~¡K¡K¡~¡K¡K¡~¡K¡ fu g¡‹Ö×Ì «|:Ž^ÕӐ‡–/stu uАu±uЁ`vys*z•‡u±ž>‡u ©‡ƒ‚툊‡”Tu rtsFz:ÕT–‹q s g‡¡{ØKrtd†Tst†AÞKx“v€ò–“v€stuwå ŒT`vyx—‚„sˆŠ”TuŠrtsŒT†~rÝTŒTŒTst–értd†TstˆD©‡stst’Tx{ŒTÔ­H¤<¢êërtd†Ts±Õ/–{drÝ©™–‹stŒT`vy~`v † àâáÙã· `v d ág¡* Tx{Žá”T–{Zv€x‹ŒTˆ*uŠs8†T‡ŒTs8x‹ŒávyTs8rt‡ˆŠstˆP‡z/Þ~x—vyT”«v r ׇײŒT¨ uRÞKx“v€÷çé TêP¤ ƒ‚/stu*‡’T’Tu ‡’Tu x‹`vysAz•rIvyu*uЁ’TTˆƒ¡6¡K¡K¡~¡K¡K¡~¡K¡K¡~¡K¡ fe g¡‹Ö d  «|:Ž^ÕӐ‡–/stu uАu±uЁ`vys*z•‡u±ž>‡u ©‡ƒ‚툊‡”Tu rtsFz:ÕT–‹q s g‡¡{ØKrtd†Tst†AÞKx“v€ò–“v€stuwå ŒT`vyx—‚„sˆŠ‡”Tu rts²ŒT†ÈrÝT‡ŒTŒTst–=rtd†TstˆA©stst’Tx‹ŒTâ­H¤8¢êGrtd†TsÕT–‹™rÝ©d–{stŒ/`vy `v d e×‡×¸‡ŒTä † àâáã· `v d á.g‡¡ð Tx{Žá”T–{Zv€x‹ŒTˆâuŠs>†T‡ŒTs>x{Œ¸v€Ts>rt‡ˆŠstˆ‘‡z ÞKx“v€T‡”«v~uRÞKx“v€›çé Tê*¤Gó‚/stu*’T’TuА’TuŠx‹`vysAz£‡rIv€‡u*uЁ’TTˆŠ¡R¡K¡~¡K¡K¡~¡K¡ fe g¡‹ÖÖÌ «|:Ž^ÕӐ‡–éstuŠuАuDu Zv€sz•‡uHžuŠ©ó‚²ˆƒ”TuŠrtsz°îŸ‡ÕT–{å s g‡¡ d Ôrtd†Tst†*ÞKx“v€^–“v€stuwå ŒT`vyx—‚„sˆŠ”TuŠrtsŒT†~rÝTŒTŒTst–értd†TstˆD©‡stst’Tx{ŒTÔ­H¤<¢êërtd†Ts±Õ/–{drÝ©™–‹stŒT`vy~`v g×‡×²ŒT¨ † àâáÙã· `v d ág¡* Tx{Žá”T–{Zv€x‹ŒTˆ*uŠs8†T‡ŒTs8x‹ŒávyTs8rt‡ˆŠstˆP‡z/Þ~x—vyT”«v uRÞKx“v€÷çé TêP¤ ƒ‚/stu*‡’T’Tu ‡’Tu x‹`vysAz•rIvyu*uЁ’TTˆƒ¡6¡K¡K¡~¡K¡K¡~¡K¡K¡~¡K¡ r Ø g d e.

(19) À$Á |$ywÂàÁZÄ@Å7Æ z{|. ¡‹ÖØÌ «|:Ž^ÕӐ‡–éstuŠuАuDu Zv€sz•‡uHžuŠ©ó‚²ˆƒ”TuŠrtsz°îŸ‡ÕT–{såg‡¡ d Ôrtd†Tst†*ÞKx“v€^–“v€stuwå ŒT`vyx—‚„sˆŠ”TuŠrtsŒT†~rÝTŒTŒTst–értd†TstˆD©‡stst’Tx{ŒTÔ­H¤<¢êërtd†Ts±Õ/–{drÝ©™–‹stŒT`vy~`v † àâáÙã· `v d ág¡* Tx{Žá”T–{Zv€x‹ŒTˆ*uŠs8†T‡ŒTs8x‹ŒávyTs8rt‡ˆŠstˆP‡z/Þ~x—vyT”«v r ׇײŒT¨ uRÞKx“v€÷çé TêP¤ ƒ‚/stu*‡’T’Tu ‡’Tu x‹`vysAz•rIvyu*uЁ’TTˆƒ¡6¡K¡K¡~¡K¡K¡~¡K¡K¡~¡K¡ g¡‹ Ö gÌ «|:Ž^ÕӐ‡–éstuŠuАuDu Zv€sz•‡uHžuŠ©ó‚²ˆƒ”TuŠrtsz°îŸ‡ÕT–{ås g‡¡ d Ôrtd†Tst†*ÞKx“v€^–“v€stuwå ŒT`vyx—‚„sˆŠ‡”Tu rts²ŒT†ÈrÝT‡ŒTŒTst–=rtd†TstˆA©stst’Tx‹ŒTâ­H¤8¢êGrtd†TsÕT–‹™rÝ©d–{stŒ/`vy `v d e×‡×¸‡ŒTä † àâáã· `v d á.g‡¡ð Tx{Žá”T–{Zv€x‹ŒTˆâuŠs>†T‡ŒTs>x{Œ¸v€Ts>rt‡ˆŠstˆ‘‡z ÞKx“v€T‡”«v~uRÞKx“v€›çé Tê*¤Gó‚/stu*’T’TuА’TuŠx‹`vysAz£‡rIv€‡u*uЁ’TTˆŠ¡R¡K¡~¡K¡K¡~¡K¡. Ú:x—‚. g. r g. r g.

(20) ؍¡ d êP‡Ž²’/”«v€Zv€x‹ŒT‡–òŒT† ˆŠ’T‡rts$rtŽÛ’T–{sIÚ:x—v0| ‡z␇ŒTs$x—vystu Zv€x‹Œ z툊”TŽ8å ’Tu d†T”TrIv$–‹‡u x“v€TŽ uŠ”TŒ ƒ‚„stuܒTuА’‰ˆŠst† z•‡rIv€‡uܝ‡u ‡’TTˆïz•uïçé Tê*¤<š ÞKTstuŠp s æ †/stŒT`vystˆíˆwvy`vysȈƒxËtsȐ‡z*vyTsȈА‡”Tu rtstšl x‹ˆávyTsÈÕT–‹™rÝ©d–{stŒ/`vy zŸ­H¤8¢±êÁrtd†TstšQ‡ŒT† Ž uŠst’Tu stˆŠstŒyvyˆRv€/sAu Zv€sA‡zDrÝT‡ŒTŒTst–Qrtd†Tst¡ ¡K¡~¡K¡. gf. ¡ ¥ì²rtx‹stŒTrI|Rª¶ç‰¬ò‡zjv€Tsæˆw|:ˆwvystŽ Zv>ÕTx“v>stuŠu ‡uòuЁ`vys損z d ×è ­ z•‡uA‚m‡u x‹”/ˆ u Zv€stˆ^ˆª ŽF¬*ŒT†›Õ/–{drÝ©™–‹stŒT`vyTˆ~ªwÕT–{¬ ¡K¡K¡K¡~¡K¡K¡~¡K¡K¡K¡~¡K¡K¡~¡K¡K¡~¡K¡ u‡Ö g¡‹Ö îŸu ‡ŒTˆŠx—vyx{‡Œô’Tu ‡ÕTÕTx‹–{x“v€x‹stˆŠâš ÇÛª é$ê ëd¬Šš,z•uòïÕTx{ŒT‡uè|ñäTu ˆwv>uІTstu۞>‡u ©‡ƒ‚ ˆŠ‡”Tu rts ¡~¡K¡K¡~¡K¡K¡~¡K¡K¡K¡~¡K¡K¡~¡K¡K¡K¡~¡K¡K¡~¡K¡K¡K¡~¡K¡K¡~¡K¡K¡~¡K¡ u‡Ø g¡‹Ø îŸu ‡ŒTˆŠx—vyx{‡Œ›’TuАÕT‡ÕTx{–‹x—vyx{stˆŠ$š Çò ª é$ê ëm¬ š§z£‡uPÛØÛˆw|‰ŽáÕӐ‡–Qž>‡u ©‡ƒ‚ÈˆŠ‡”Tu rts ¡K¡ uu gh¡ g  «|:Ž^ÕӐ‡–‡ˆwvyst‡†«|™åƒˆ v€Zv€s±’TuАÕT‡ÕTx{–‹x—vyx{st!ˆ ìH¶ª ©H¬HŒT†~rtuŠu stˆŠ’‰ŒT†Tx‹ŒT*ä«Ú:st†K‡ŒT† ‚m‡u x‹ÕT–‹sA–{stŒTZv€›rtd†TstˆFz£‡uPžuŠ©ƒ‚Ȉƒ”TuŠrtsAzŸîŸÕT–‹Js g¡‹Ø ¡K¡~¡K¡K¡~¡K¡ uu gh¡ u ¥ì²rtx‹stŒTrI|‡zvyTsjˆ |‰ˆwvystŽGz•uRØ<ˆw|:Ž^Չ–f‚m‡uŠx{Õ/–{s4–{stŒTZv€rtd†Tst†ž>‡u ©‡ƒ‚ ˆŠ‡”Tu rtstšTßI‡x{Œyv^ˆŠ‡”Tu rts~rÝTŒTŒTst–H†Tstrtd†Tst†æƒ‚/stuF’TuА‡’Ӑˆƒst†÷z•rIvyuF‡u ‡’TTˆŠ¡ îPTsÔuŠstˆŠ”T–“v€ˆà‡u sÔz•‡uÕTx“v€šÓˆ |‰ŽáÕӐ‡–„‡ŒT†­HsI‚/stŒTˆƒ€vystx{Œˆw|:ŽáÕӐ–Óstu uАuàuЁ`vystˆ z d × è ­ ¡ ¡K¡K¡~¡K¡K¡~¡K¡K¡K¡~¡K¡K¡~¡K¡K¡K¡~¡K¡K¡~¡K¡K¡K¡~¡K¡K¡~¡K¡K¡~¡K¡ e‡× gh¡ e îŸu ‡ŒTˆŠx—vyx{‡Œ›’TuАÕT‡ÕTx{–‹x—vyx{stˆŠ$š Çò ª é$ê ëm¬ š§z£‡uPÛØÛˆw|‰ŽáÕӐ‡–Qž>‡u ©‡ƒ‚ÈˆŠ‡”Tu rts ¡K¡ e d gh¡ f  «|:Ž^ÕӐ‡–‡ˆwvyst‡†«|™åƒˆ v€Zv€s±’TuАÕT‡ÕTx{–‹x—vyx{st!ˆ ìH¶ª ©H¬HŒT†~rtuŠu stˆŠ’‰ŒT†Tx‹ŒT*ä«Ú:st†K‡ŒT† ‚m‡u x‹ÕT–‹sA–{stŒTZv€›rtd†TstˆFz£‡uPžuŠ©ƒ‚Ȉƒ”TuŠrtsAzŸîŸÕT–‹Js gh¡ e‘¡K¡K¡~¡K¡K¡~¡K¡ e d g d. Úd‚.

(21) À$Á |$ywÂy!íî À zå|. Úd‚:x. ¡ ¥ì²rtx‹stŒTrI|GzFvyTs܈w|:ˆwvystŽ z£‡ußIx‹Œ€v눃”TuŠrtsÜrÝTŒTŒTs€–8†Tstrtd†Tx‹ŒT¼z r ˆw|:Ž^ÕӐ‡–é‚m‡u x‹ÕT–‹s,–{stŒTZv€‘rtd†Tst†žuŠ©ó‚÷ˆŠ‡”Tu rtstš‰ƒ‚„stuà’TuА’‰ˆŠst†‘z•rIvyu uЁ’T/ˆŠ¡¸î*Ts‘u stˆƒ”T–—vyˆáuŠsz•‡u^ÕTx“v€šPˆw|:Ž^ÕӐ‡–à‡ŒT†i­HsI‚/stŒTˆƒ€vystx{Œiˆw|:Ž^Չ– stu uАu*uЁ`vystˆ*z d × è ­ ¡ã¡K¡K¡K¡~¡K¡K¡~¡K¡K¡K¡~¡K¡K¡~¡K¡K¡K¡~¡K¡K¡~¡K¡K¡~¡K¡ eu gh¡  ¥Œ€vyu ‡’y|éšmƒ‚„stu ‡3s á­Dê¸rtd†TsIÞ<‡u †^–‹stŒT`vy^‡ŒT†^rtuŠu stˆŠ’‰ŒT†Tx‹ŒTÔuŠstˆŠx‹†T”T– u st†T”/ŒT†TŒTrI|‚m–‹”TstˆPz•u g‡uŠÕTx—vyu ‡u x‹–—|ˆŠst–{strIvyst†áv€stuŠŒTuw|>žuŠ©ƒ‚ˆŠ”/u rtstˆŠ¡ee g¡ d ×ÌîPTsstì²rtx‹stŒTrI| ‡zArtŒy‚/stŒyvyx{‡ŒT–,ˆŠst’T‡uЁ`vys>ˆŠ‡”Tu rtsróT‡ŒTŒTst–,†Tstrtd†Tx{ŒT ˆŠrÝTst޲s~Zv^stuŠu ‡uFuЁ`vystˆÔz d × è ­ z•ïu gAvystu ŒT‡uw|ܞ>‡u ©‡ƒ‚‡”Tu rtstˆÔ‡z=Zå ÕT–{*s g‡Ë¡ ÷rt™†Tst†íÞ~x—vyív€TsۈЁ‡Ž²âs ­Hê ª Öð³ d ,š Øñ³ × d ŒTŠ † Úò³ ׇ׍¬ ŒT†ë ª g‡××‡š{և׍ׇ¬P­H¤8¢±êÁrtd†Tst¡~¡K¡K¡~¡K¡K¡K¡~¡K¡K¡~¡K¡K¡K¡~¡K¡K¡~¡K¡K¡~¡K¡ f‡× g¡ dd îPTsAstì²rtx‹stŒTrI|zDçé Tê*¤Gx{ŒávyTsjvœÞ8–‹ƒ|„stu4z•‡rIv€‡uPuЁ’T퐇3 z =x‹”TuŠs8؇ˡ g `vístuŠu ‡uáu Zv€stˆz d × è ­ z•lu gv€s€u ŒT‡uè|$žuŠ©ƒ‚$ˆƒ”TuŠrtstˆá‡z*ÕT–‹Ûs g‡Ë¡  rtd†Tst†ïÞKx“v€ïvyTs戊ŽÛ*s á­Dêª Öó³ d Jš Ø ³ × d ŒT• † Úô³ ׍ׇ¬ò‡ŒT† ˆª g‡××‡š{և׍ׇ¬*­H¤<¢êñrtd†Tst¡ ¡K¡~¡K¡K¡~¡K¡K¡K¡~¡K¡K¡~¡K¡K¡K¡~¡K¡K¡~¡K¡K¡~¡K¡ f d g¡ d ÖÌîPTsPstìÛrtx{stŒTrI|␍zÓçé TêP¤!x{Œ<v€Ts=vyTu stsP–{ó|/stu\z£‡rIv€‡uR‡u ‡’T‡! z Rx{‡”Tu sP؇ˡ  ­ `vístuŠu ‡uáu Zv€stˆz d × è z•lu gv€s€u ŒT‡uè|$žuŠ©ƒ‚$ˆƒ”TuŠrtstˆá‡z*ÕT–‹Ûs g‡Ë¡  rtd†Tst†ïÞKx“v€ïvyTs戊ŽÛ*s á­Dêª Öó³ d Jš Ø ³ × d ŒT• † Úô³ ׍ׇ¬ò‡ŒT† ˆª g‡××‡š{և׍ׇ¬*­H¤<¢êñrtd†Tst¡ ¡K¡~¡K¡K¡~¡K¡K¡K¡~¡K¡K¡~¡K¡K¡K¡~¡K¡K¡~¡K¡K¡~¡K¡ f d g¡ d ØÌ¦‚/stuЁ‡sòrtd†TsIÞ<uŠ†ë–‹stŒT`vyÌõª R ã· ¬~x{Œ÷v€stuŠŽ²ˆ^z4ÕTx—vyNˆ ¹‡ˆw|:Ž^ÕӐ‡–±‡ŒT†ërt‡u uŠsIå ˆŠ’Ó‡ŒT†Tx{Œ/uŠstˆŠx‹†T”T–QuŠst†T”TŒT†TŒTrI|‚°–‹”TstˆK¶ª ö„¬Pz•u=vyTs8زˆw|:Ž^ÕӐ‡–Qž>‡u ©‡ƒ‚ ˆŠ‡”Tu rts\†/`vyP‡zdÕT–‹&s g‡¡{Ø*rtd†Tst†4Þ~x—vyA‡–—vystu ŒTZvyx—‚„s\ˆŠ‡”Tu rts±rt™†Tstˆƒš™*ä«Ú:st† –{stŒTZv€rtd†Ts^ ª =­Hê*¬ š„ tԔ/õӎ²‡Œòrtd†Ts\Þ~x—vyòÕT–‹dró©d–‹stŒT`vy d ª tÔê d ¬‡ŒT†  t,”TõӎہŒ>rtd†Ts*Þ~x—vy>ÕT–{drÝ©™–‹stŒT`vy>Öˆª t,ê*֍¬±Þ~x—vy>u stˆŠ’‰strIvÔv€‘ˆwv€st‡†«| @ ˆwvy`vysA’Tu ‡ÕTÕTx‹–{x“v€x‹stˆ*‡z/vyTsAˆw|:Ž^Չ–§ÕT–{drÝ©™ˆƒ¡Ó¡K¡K¡~¡K¡K¡K¡~¡K¡K¡~¡K¡K¡~¡K¡ fg g¡ d gÌ¥ì²rtx‹stŒTrI|損zHçé Tê*¤ªª ço÷Nø ¿'ù ¬jx‹Œ~vyTs<’Tu ‡’Ӑˆƒst†‘z•‡rIv€‡ujuЁ’TTˆA ª $K¬j`v v€TsP T{¥ Žôz d × è ­ z•uRž>‡u ©‡ƒ‚‘ˆŠ‡”Tu r€s4z„‡ÕT–{1s g¡‹Ø<rtd†Tst†<ÞKx“v€<‚muw|:x{ŒT u Zv€sAˆƒ”TuŠrtsArtd†Tstˆ~ªè Tê*¬*ŒT†‚m‡uè|:x‹ŒT²ÕT–‹dró©d–‹stŒT`vyëªèÕT–‹¬P­D¤<¢êñrtd†TstˆŠ¡ f g r.

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