Channels with both random errors and burst erasures: Capacities, LDPC code thresholds, and code performances

We derive the capacities of a class of channels, either memoryless or indecomposable finite-state, that also suffer from bursts of erasures. For such channels, we analyze the performances of low-density parity-check (LDPC) codes and code ensembles under belief propagation (BP) decoding, using density evolution (DE) techniques. Although known LDPC codes perform well in non-erasure-affected channels, their performances are far from the capacities when both random errors and erasures are present. We show that enhancing the codes' erasure handling using published methods beats, in some instances, the BP thresholds. However, to achieve capacity, codes must be constructed to tackle both effects simultaneously.