igure 5.11.7 Cairel provided in]comprehensive analysis of BICM in terms of information rates and error probability,showing that in fact the loss incurred by the BICM interface may be very small.Furthermore,this loss can essentially be recovered by using iterative decoding. Coded-modulation capacity for various signal constellation in the AWGN channel has apter 2.Here,we briefly review the results on the achievable rates for BICM by following Caire Define the sets -g'={x∈X|b,(x)=b4,b(x)=b} as the subsets of signal points having the binary labels bin positions Under the assumption of an infinite-length interleaver,capacity and cutoff rate were studied in [Caire98].This assumption yields a set of m independent parallel binary-input channels,for which the corresponding mutual information is the sum of the corresponding rates of each subchannel,and are given by (x:r)-E log ∑(Y) ∑B(VIx) -m-E log rVI Br(YIx) where B is a random variables taking values on (0.1).The joint distribution p(B,)of the channel-iis pB,YI)=2∑ePr(ylx) The BICM capacity is given by CHCM =(XY) Since BICM can be regarded as MLC with (Gray mapping and)parallel independent decoding (i.e.,decoder at level i makes no use of decisions of other levels),it is shown that [Wachsmann-Huber99] c(c) where C is the capacity (information rate)for coded modulation over a general constellationA. The BICM (MLC/PDL)approach is simply a suboptimum approximation of an 2626 Figure 5.11.7 Caire et al. provided in [IT1998] a comprehensive analysis of BICM in terms of information rates and error probability, showing that in fact the loss incurred by the BICM interface may be very small. Furthermore, this loss can essentially be recovered by using iterative decoding. Coded-modulation capacity for various signal constellation in the AWGN channel has been discussed in Chapter 2. Here, we briefly review the results on the achievable rates for BICM by following Caire. Define the sets { } 1 1 1 11 ( . ) ,., | ( ) ,., ( ) j jl jj j j l l i i bb i j i j X X =∈ = = x bx b bx b as the subsets of signal points having the l binary labels 1 ,., l j j b b in positions 1 . l j j i i . Under the assumption of an infinite-length interleaver, capacity and cutoff rate were studied in [Caire98]. This assumption yields a set of m independent parallel binary-input channels, for which the corresponding mutual information is the sum of the corresponding rates of each subchannel, and are given by ( ) ( ) | ind 1 | | ( ; ) log 1 | 2 i B m x Y X i x Y X P Yx I XY P Yx ′∈ = ′∈ ⎡ ⎤ ′ ⎢ ⎥ = ⎢ ⎥ ⎢ ′ ⎥ ⎣ ⎦ ∑ ∑ ∑ X X E ( ) ( ) | , 1 | | log | i B m x Y X B Y i x Y X P Yx m P Yx ′∈ = ′∈ ⎡ ′ ⎤ = − ⎢ ⎥ ′ ⎢ ⎥ ⎣ ⎦ ∑ ∑ ∑ E X X where B is a random variables taking values on {0,1}. The joint distribution p(B, Y) of the channel-i is ( ) | ( , |) 2 | i B m x Y X p BY i p y x − ∈ = ∑ X The BICM capacity is given by BICM ind C I XY ≡ (;) Since BICM can be regarded as MLC with (Gray mapping and) parallel independent decoding (i.e., decoder at level i makes no use of decisions of other levels j ≠ i ), it is shown that [Wachsmann-Huber99] ( ( ) ) 1 BICM CM CM 1 0 1 2 i b m i b C CC = = = − ∑ ∑ X X where CM CA is the capacity (information rate) for coded modulation over a general constellation A. The BICM (或MLC/PDL) approach is simply a suboptimum approximation of an