By the total probability relationship p xj r1n sj l l

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Unformatted text preview: 2, · · · , M represent all the states over all stages. Let Sj be the set of states (0) at stage j that correspond to the zero symbol at stage j , xj . That is, for the (0) (1) (2) illustration in Figure 5(a), Sj = {Sj , Sj }. Similarly, (l) Kevin Buckley - 2007 (1) 14 let Sj be the set of states at stage j that correspond to the one symbol at stage j , (1) (1) (3) (4) xj , i.e. in Figure 5(a) Sj = {Sj , Sj }. Consider the a posterior probabilities (m) (APP’s) of the states at stage j , P (Sj /r1,N ); m = 1, 2, · · · , M . By the total probability relationship, P (xj /r1,N ) = Sj (l) (l) P (Sj /r1,N ) , (m) l = 0, 1 . (28) So, in terms of this trellis diagram representation, for each stage j we need the (m) P (Sj /r1,N ); m = 1, 2, · · · , M , the APP’s of the states. j = m−1 = m’ S = (0,0) (1) j=m j=0 1 2 3 4 5 6 ..... S = (0,1) (2) ..... ..... ..... (b) ..... S = (1,0) (3) ..... S = (1,1) (a) (4) Figure 5: (a) successive trellis diagram stages for a rate 1 , K = 3 convo...
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