Upper bounds on the MAP threshold of iterative decoding systems with erasure noise

Following the work of Méasson, Montanari, and Urbanke, this paper considers the maximum a posteriori (MAP) decoding thresholds of three iterative decoding systems. First, irregular repeat-accumulate (IRA) and accumulate-repeat-accumulate (ARA) code ensembles are analyzed on the binary erasure channel (BEC). Next, the joint iterative decoding of LDPC codes is studied on the dicode erasure channel (DEC). The DEC is a two-state intersymbol-interference (ISI) channel with erasure noise, and it is the simplest example of an ISI channel with erasure noise. The MAP threshold bound for the joint decoder is based on a slight generalization of the EXIT area theorem.