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.