Joint iterative decoding of LDPC codes for channels with memory and erasure noise

Abstract—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 informa-tion 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 maximum-likelihood decoding. These results build on previous capacity-achieving 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. Index Terms—joint iterative decoding, intersymbol interfer-ence, low-density parity-check codes, dicode erasure channel, symmetric information rate, capacity-achieving codes. I