mapper,which can be considered as a nonrecursive single-state encoder.So the iterative dec ding method for SCCC can be applied to BICM. oding(BICM-ID)was proposed by Li and Ritcey [Li9]for further improving the FED of Zehavi's BICM scheme.This FED improvement can be achieved with the aid of combining SP(set partitioning)-based constellation labeling,as in TCM,and by invoking soft-decision feedback from the decoder's output to the demodulator's input,in order to exchange soft-decision based information between them. The BICM-ID scheme using sof-decision feedback is shown in Fig.5.11.2.where soft-in soft-out(SISO)detector/decoder is used in the receiver modulo.Let C be a binary code. Assume that it is concatenated with an N-dim memoryless modulator over a signal set C of sizeM=2",through a bit interleaver and a one-to-one binary labeling map f:0,1).Denote the code sequence by c.The interleaved sequence (c)is segmented into m-bit blocks denoted by c=c,which are mapped into signal points x,=f(c,)with c,as the label of x,The signal x,are then transmitted over the channel at time t,resulting in the received signaly. Let x denote a signal point in A,and b(x)the ith bit of the label of x.With the use of iterative demodulation/decodin compute APPs forea label b at the receiver,the dema r can use the MAP algorithm to P=b1)APIW)xAP1m where =xExb(x)=b)=(x=f(c,)ex=b is the subset of all the signalsx whose label has the value b)in position i,and P(x)is the a priori probability of transmittingx At the first iteration,P(x)is initialized to be 1/M for all values ofx.对于第二次及以后各次迭代， P(x)=ΠP(c=b,(x) (with充分长的交织器) 考虑到交织/解交织，在图5.11.2中即为 Px)=ΠP(=b,(xI） Therefore. P=b1)=∑PIP(=bG)22 mapper, which can be considered as a nonrecursive single-state encoder. So the iterative decoding method for SCCC can be applied to BICM. BICM with iterative decoding (BICM-ID) was proposed by Li and Ritcey [Li98] for further improving the FED of Zehavi’s BICM scheme. This FED improvement can be achieved with the aid of combining SP(set partitioning)-based constellation labeling, as in TCM, and by invoking soft-decision feedback from the decoder’s output to the demodulator’s input, in order to exchange soft-decision based information between them. The BICM-ID scheme using soft-decision feedback is shown in Fig. 5.11.2, where soft-in soft-out (SISO) detector/decoder is used in the receiver modulo. Let C be a binary code. Assume that it is concatenated with an N-dim memoryless modulator over a signal set N X ⊆ C of size | | 2m X = M = , through a bit interleaver π and a one-to-one binary labeling map :{0,1}m f → X . Denote the code sequence by c. The interleaved sequence ( ) π c is segmented into m-bit blocks denoted by ( ) (0) (1) ( 1) , ,., m t tt t cc c − c = , which are mapped into signal points ( ) t t x f = c with ct as the label of xt. The signal xt are then transmitted over the channel at time t, resulting in the received signal yt. Let x denote a signal point in X, and ( ) i b x the ith bit of the label of x. With the use of iterative demodulation/decoding at the receiver, the demapper can use the MAP algorithm to compute APPs for each label bit of xt and deliver them to the decoder; i.e., ( ) () () ( ) | ( | ) ( | )() i i t t b b i t t tt tt t x x Pc b y Px y py x Px ∈ ∈ == ∝ ∑ ∑ X X , for i=1.,m where { } ( ) | () i b i X X =∈ = x bx b { } ( ) () | i tt t = x =∈ = f cb c X is the subset of all the signals x∈X whose label has the value {0,1} b∈ in position i, and P(xt) is the a priori probability of transmitting xt. At the first iteration, P(xt) is initialized to be 1/ M for all values of xt. 对于第二次及以后各次迭代， ( ) 1 ( ) 0 () () m j t t jt j Px Pc b x − = = = ∏ (with 充分长的交织器) 考虑到交织/解交织，在图 5.11.2 中即为 ( ) 1 ( ) 0 ( ) ( ); m j t t jt j Px Pv b x I − = = = ∏ Therefore, () ( ) ( ) 1 () ( ) 0 | ( | ) () i t b m i j t t t t t jt x j Pc b y Py x Pc b x − ∈ = == = ∑ ∏ X