0122229现代数字通信与编码理论 December 10,2011 XDU,Winter 2011 Lecture Notes Capacity-Approaching Coded-Modulation Schemes 5.9级联TCM TCM码可以按Tubo方式并行级联，也可以与其它码构成串行级联系统（例如，在 RS+TCM中做内码，在TCM+STBC中做外码)。 5.9.1TCM码的Symbol-Based Nonbinary)MAP译码算法 Consider a general trellis code.Let u=()be an information symbol sequence of length N.Each information symbol is assumed to be a binary m-tuple,i.e. =)"for =1.2.N.For convenience,we will denote u by its decimal representation,ie.,assume=,."-1.The m-bit symbols are fed into a TCM encoder,producing a sequence of N modulated symbols,x=(x),where xwithstanding for the signal constellation of size2".We assume that the symbols xx are transmitted over an AWGN channel.Let y=y=(y.y.)be the received sequence,where y(k=1,2.N)is the noisy observation of x if x is not punctured;otherwise,sety=*(implying no observation obtained). TCM yk Channel Symbol-based encoder MAP decoder Figure 5.9.1Atrellis coding system The received sequence is fed to the TCM decoder to produce the estimate of transmitted 2-ary information symbols.To minimize the probability of symbol errors,the symbol-based MAP decoder may be used.This decoder computes the APP for every 2"-ary information symbol;i.e.,P(=iy),for i=0,1,."-1,k=1,2.N Then it makes decisions according to the MAP criterion: ig =argmax P(u =ily 1 0122229 现代数字通信与编码理论 December 10, 2011 XDU, Winter 2011 Lecture Notes Capacity-Approaching Coded-Modulation Schemes 5.9 级联 TCM TCM 码可以按 Turbo 方式并行级联，也可以与其它码构成串行级联系统（例如，在 RS+TCM 中做内码，在 TCM+STBC 中做外码）。 5.9.1 TCM 码的(Symbol-Based Nonbinary) MAP 译码算法 Consider a general trellis code. Let u uu u = ( 1 2 , ,., N ) be an information symbol sequence of length N. Each information symbol is assumed to be a binary m-tuple, i.e., ( ) ,0 ,1 , 1 2 , ,., m k k k km uu u u = ∈ − F , for k=1,2,.N. For convenience, we will denote uk by its decimal representation; i.e., assume {0,1,.,2 1} m k u ∈ U = − . The m-bit symbols are fed into a TCM encoder, producing a sequence of N modulated symbols, ( ) 1 2 , ,., N x = x x x , where k x ∈X with X standing for the signal constellation of size | | 2n X = . We assume that the symbols xk are transmitted over an AWGN channel. Let 1 12 ( , ,., ) N N y y = = yy y be the received sequence, where k y (k=1,2,.N) is the noisy observation of k x if k x is not punctured; otherwise, set yk = ∗ (implying no observation obtained). ˆk u Figure 5.9.1 A trellis coding system The received sequence is fed to the TCM decoder to produce the estimate of transmitted 2m-ary information symbols. To minimize the probability of symbol errors, the symbol-based MAP decoder may be used. This decoder computes the APP for every 2m-ary information symbol; i.e., ( ) 1 | , for 0,1,.,2 1, 1,2,., N m Pu i i k N k = = −= y . Then it makes decisions according to the MAP criterion: ˆ arg max | ( 1 ) N k k i u Pu i ∈ = = y U