Information Forwarding in LDPC Decoding for Markov Sources

Belief propagation decoding of binary LDPC codes combines three independent probability estimates, a-priori, intrinsic, and extrinsic information, iterations along the Tanner graph are estimating the value of the received bits, the likelihood of the values increasing with each iteration. The a-priori estimate of the information bits is a measure of the source statistics for generating bit values 0 and 1 (mapped to ±1), reflecting bias and redundancy in the information sequence itself. In this paper, we have modified the a-priori estimate to incorporate memory properties present in the transmitted information sequence resulting from a Markov source. We consider two principle alternatives for decoding. The first option is to use the Markov dependencies directly as further links between variable nodes in the Tanner graph of the LDPC code. The second alternative is to see the Markov source and the LDPC code as a serial concatenation asking for a Turbo iterative decoding between the two corresponding decoders. The latter comes with significant complexity compared to the direct embedding into the LDPC Tanner graph. Especially, one modification applying Jensen's inequality leads to a very low decoding complexity at no performance loss. The Turbo scheme's performance depends on the scheduling. Superior performance can be achieved with sufficient iterations in the LDPC decoder itself.