# The solution to this symbol by symbol map problem

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Unformatted text preview: otation more common to BCJR algorithm description, we will denote the binary symbol (i.e .a bit) at (l) time j as xj which can take on values xj ; l = 0, 1. The symbol-by-symbol MAP problem statement is, for each and every information bit in the block xj ; j = 1, 2, · · · , N , max (l) xj P (xj /r1,N ) , (l) (27) (l) where P (xj /r1,N ) is the a posterior probability (APP) of the xj bit value, xj , given all the data r1,N . It is called “a posterior” because it is “after the data” is observed. The solution to this symbol-by-symbol MAP problem provides the minimum BER information bit estimates. Because of the memory in the convolutional encoder, the xj ’s are a statistically dependent of all the rj ; j = 1, 2, · · · , N , and all the data must be processed for each xj . Thus, to solve this optimization problem, for each xj , we need the (l) (l) P (xj /r1,N ); l = 0, 1. To calculate the P (xj /r1,N ); l = 0, 1, consider the trellis (m) representation illustrated below in Figure 5(a). Let Sj ; j = 0, , · · · , N ; m = (0) 1,...
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## This document was uploaded on 10/12/2009.

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