This paper investigates the joint iterative decoding of low-density parity-check (LDPC) codes and channels with memory. Sequences of irregular LDPC codes are presented that achieve, under joint iterative decoding, the symmetric information rate of a class of channels with memory and erasure noise. This gives proof, for the first time, that joint iterative decoding can be information rate lossless with respect to maximumlikelihood decoding. These results build on previous capacityachieving code constructions for the binary erasure channel. A two state intersymbol-interference channel with erasure noise, known as the dicode erasure channel, is used as a concrete example throughout the paper.
Henry D. Pfister, Paul H. Siegel