Low-Density Parity-Check Codes for the Gilbert-Elliott Channel

In this paper, we review recent developments concerning the application of lowdensity parity-check (LDPC) codes to the Gilbert-Elliott (GE) channel. Firstly, we discuss the analysis of LDPC estimation-decoding in these channels using density evolution. We show that the required conditions of density evolution are satisfied in the GE channel, and that analysis demonstrates that large potential gains over the memoryless assumption. We also give results which mitigate the complexity of characterizing the GE parameter space using DE. Subsequently, we give a design tool for finding good degree sequences for irregular LDPC codes in the GE channel. The degree sequences obtained using this technique are the best available codes for the GE channel.