5. The Channel Gding Problem Discrete Memisschannel
l DMS ) N : = plylx)
decodernn.it#O'-T-nCoderateR-f.Error
probabilitgiR-P.im#injShannon'squestioniWhatisthemaxcoderate
Ésuchthatlim pě
) *
= o ?
Isthereasequenceofhtoo
maximal.li?n)coaekiii'Dnexists?
6. Arate Ris
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achievable
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if 彐
{( ⼼, D
(
以及
⼦ eīm Pě
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= 0 .
pǒnmiPrlhmlhsao
Channel Capacity CW) : ⼆
SUPIRIR isachivable}
S
hannonschannelcapacitytheorem.letN-Pylylxjisac.lassicalchannel
(W) =
max Ilx ; Y ) = : I W)
Wewantto Pxlx) Interpretation : IcxjY )
lstleamowwtofinfocho.se
prob-s-nofxwhichcanbeinferfromY.infotsiiir
7. Wecansplitthetheoremintotwopart
II) Thedīrectcodingtheorem
Fora DMCN ,
allrates R below IW)
isachievable.ern-o.c.n.se/-ofachievablerates-nInsCWRIW )I W)
(⼆) Theconversetheorem
Ifareliablesequenceofli只 )
codesexisttetherateRofthesequenceofc.desislessthan IW)
[ -
ˋ ˋ _ _ _ _
. n e t CCN) EIW)
Ìm
8. Typicakty
WeaklawoflargenumbeiletfS-IRwithfilflsnjc.no
È 三点 fcs :)
⼀⽇
yfls》
⇐> H > 0
,
比 E (0,1 ),
⼆ hothz.no
Prli 三点 fcsi) EGHSD-8.IT》 +8 ] } = 1 -
E
Nowweconsiderflsi ) =
logfy
V 870,
limprlliilog点,
⼀
Esllog 前) 1 _
< S } = 1
MN cnn.no
lnersampleentropyĀlsn) Hls)
15. lstepz )
Gding
Alie Sends
Xncmjīutothechannel 。
( Step 3 ) Decoding Bobrecēwesywfromthechanneloutput
Then Bobhastodothefollowingtests
② WhetheryhETYorrespondingtoR.ly) =
f[Pylylxj
If yna TY reporterror
② Checkwhether ⼆
someintjETYNnIfisuc.hnreport 不
If ⺺ Such 不 reporterror (I )
If 彐 肛, inandh 千 元 reporterrorg
16. Define 3 kindoferrorevents ,
Eolm ) :
yna TY
am )
iyhETY.yhqfjxhlmlczlmiiynETY.am4 miyne 壪
⼼以
Theexpectatiowofaverageerrorprob.is
成 ⼀ Ec 偷 丟 Prkolm)
UE.cm?UEzlmBWlOG-nr.2
= Ec Pri Eoll ) UEHDU 92 ( 1 ) }
EIEPrkillBThisgivetheanswerofl.tl0
17. Let IA (X ) ⼆ ⼆ ( XEA )
Focuson 9。 ( I ) :
Ecpr化 𠮨} =
Exnnyn { 1 -
Iij M ) }
= 1 -
Eyn { Iij M ) } =
BIYGTY} f
Focuson E.CI ) :
因為 typicalseq 7占 pnob 很 ⼤
ˊ
E I
E {Prlc )}} =
EnniilfjhllIyxn, ⼼ ) }
E E
… ( 喊ùii
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} ] E E