国家重点实验室 Channel Splitting W→W9 (1≤i≤W) U C(W)=I(UN;YN) U =∑1U,;YN,U) =1 =∑Cw) WN o Define bit-channels →y U WW9:U→Yw×U- U 04')2现 o Successive-cancellation(SC)译码结构建立信道分裂 11
Channel Splitting Define bit-channels Successive-cancellation (SC)译码结构建立信道分裂 11 ( )i W W N N → (1 ) ≤ ≤i N () 1 : i Ni WUYU N → × − 1 1 1 ( ) 1 () (;) ( ; , ) ( ) N N N N N i i i N i N i CW IU Y IU Y U C W − = = = = = 1 () 1 11 i 1 1 1 1 ( , |) ( | ) N Ni 2 i i Ni N N N N N u X W yu u Wy u − + − − ∈ =
国家重点实验室 How to polarize:Basic module Combine two copies of W x2=4G2 w, W(y,yl4,4)=W(y4田4)W(y22） oand split to create two bit-channels W-:U1→(Y1,Y2) W+:U2→(Y1,Y2,U1) 12
How to polarize: Basic module Combine two copies of W and split to create two bit-channels 12 2 1 0 1 1 G 2 2 1 12 x u = G ( ) ( )( ) 2 12 12 1 1 2 2 2 W y y, | uu W , = ⊕ y | | u uW y u
国家重点实验室 o The bad channel W W:U1→(Y,Y2) ⊕ W C(W）=I(UY,Y) 随机U2 W The good channel W+ W+:U2→(Y,Y2,U) U W C(W)=I(U:Y,Y,U) U2 W 13
The bad channel WThe good channel W + 13 1 12 W U YY : (, ) − → CW IU YY ( ) = ;, ( ) 112 − 2 12 1 W U YYU : (, , ) + → ( ) ( ) CW IU YY U = ;, 212 1 +
国家重点实验室 。信道总容量保持不变，但是被不均等分配了 o Conservation: 2C(W)=I(X X2;YY)=I(UU,;YY) =I(U;YY)+1(U,;YY,IU) =I(U;YY)+I(U2;YY,U)=C(W-)+C(W+) o Extremization: C(W-)≤C(W)≤C(W+) with equality iff C(W)=0 or 1. 14
信道总容量保持不变，但是被不均等分配了 Conservation: Extremization: with equality iff C(W) = 0 or 1. 14 ( ) ( ) 1 2 12 1 2 12 1 12 2 12 1 1 12 2 12 1 2( ) ( ; ) ( ; ) ( ; ) ; | ( ; ) ; ( ) ( ) C W I X X YY I UU YY I U YY I U YY U I U YY I U YYU C W C W − + = = = + = + =+ CW CW CW ( ) () ( ) − + ≤ ≤
国家重点实验室 o Problem >The channel w+:U,(Y,.U poses the problem: Y1Y2 is observed by the receiver,but U1 is not observed by the receiver. >We can synthesize W+by first processing the output of W-to estimate U1.We have instead of U1 for a implementable receiver. o Implementable receiver 01=4(Y2) 02=4(Y20) >Successively decode U1,U2. 15
Problem The channel poses the problem: Y1Y2 is observed by the receiver, but U1 is not observed by the receiver. We can synthesize W+ by first processing the output of W- to estimate U1. We have instead of U1 for a implementable receiver. Implementable receiver Successively decode U1, U2. 15 2 12 1 W U YYU : (, , ) + → 1 U ˆ 2 1 1 2 22 1 ˆ ( ) ˆ ˆ ( ) U Y U YU φ φ = =