B(s)=1/2”s∈S (4.30) a(0) a4-(0)⊙ (0,0) 40,0) 0 ⊙B.(0) 1,0) \(0,2) a-① ② ② ②B(2) 图4.13立，(s)和B(s)的递推计算示意图.a,(0)=a4-(0)M(0,0)+a-()y,(L,0) andB(0)=B(O)ya+(0,0)+B(2)M(0,2) Note:The MAP algorithm is often called the BCJR algorithm or forward-backward algorithm. They are equivalent to the Baum-Welch algorithm used in Hidden Markov models. The MAP algorithm can be summarized as follows. ■Initialization a(S。=0)=1,a(S。=s)=0fors≠0 B(0)=1,(s≠0)=0 ■Forward recursion For k=1 to N,do 1)Fori=0.1.compute and store the branch metrics(s's)as in (4.21): 2)For seS,compute and store the forward metrics (s)as in (4.24) ■Backward recursion 4-244-24 ( ) 1/2 v N   s s    (4.30) 0 1 2 3 0 1 2 3 0 1 2 3 Sk-1 Sk Sk+1 yk (0,0) k  (0) k (0) k yk+1 (1,0) k  1(0,2) k   1(0,0) k   1(0) k 1(1) k 1 (0) k 1(2)  k 图 4.13 ~ ( ) ~   ( ) k k s s 和 的递推计算示意图. 1 1 (0) (0) (0,0) (1) (1,0) k k k kk        and 11 11 (0) (0) (0,0) (2) (0, 2)  k kk kk       Note: The MAP algorithm is often called the BCJR algorithm or forward-backward algorithm. They are equivalent to the Baum-Welch algorithm used in Hidden Markov models. The MAP algorithm can be summarized as follows.  Initialization 00 00   ( 0) 1, ( ) 0 for 0 S Ss s       N (0) 1, ( 0) 0 N      s    Forward recursion For k = 1 to N, do 1) For i = 0, 1, compute and store the branch metrics ( ', ) i k  s s as in (4.21); 2) For s  , compute and store the forward metrics ( ) k  s as in (4.24)  Backward recursion