Reliability-Based Soft-Decision Decoding for Memory Channel

In this paper, we investigate the use of most reliable basis (MRB) based decoding algorithms for the Markov modulated Gaussian noise (MMGN) channel, with an interleaver used at the transmitter. The decoder first finds a most reliable column basis (MRCB), which is a common reliable basis for each row of the interleaver (each row of the interleaver is a codeword). Based on this common reliable basis, each row is decoded with a MRB based decoding algorithm. This new decoding method is denoted as joint column decoding (JCD). Simulation results show that this new method can achieve better performance than the straightforward MRB based decoding, where each codeword is decoded independently with a smaller complexity. An upper bound of the decoding error performance of JCD is derived based on the theory of order statistics and Markov chain.