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Unformatted text preview: −1 ) , (m′ ) (35) so that priors on the information bits are incorporated into P (Sj /Sj −1 ). The resulting algorithm is the same (i.e. BCJR), and has the same forward/backward structure. Kevin Buckley - 2007 16 Upon completion of the BCJR algorithm (after the backward pass), for each stage (l) j , the information bit APP’s P (xj /r1,N ); l = 0, 1 are compared, and the output information bit corresponds to the maximum. The information bit APP’s provide additional information. Speciﬁcally, consider the Log Likelihood Ratios (LLRs), L(xj ) = loge P (xj /r1,N ) P (xj /r1,N )
(0) (1) ; j = 1, 2 , · · · , N . (40) L(xj ) >> 0 indicates that the xj = x1 output is highly reliable. Likewise, j L(xj ) << 0 indicates xj = x0 output is highly reliable. Conversely, L(xj ) close to j zero means that the output is not very reliable. L(xj ) is often called the reliability. As opposed to the Viterbi algorithm, which just provides ”hard” bit information (i.e. as the elements of the estimated sequence), this symbol-by-symbol MAP algorithm provides both hard and ”soft” A Posterior Probabilities (APP’s) of the bits, as well as the LLRs. This soft information, referred to as em extrinsic information, is vital for eﬀective iterative decoding. 2.6 A Comparison Between MLSE with Viterbi & Symbol-by-Symbol MAP with BCJR In this Subsection we use Monte Carlo simulations to co...
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This document was uploaded on 10/12/2009.
- Spring '09