Decoding with belief propagation

This chapter revisits the problem of decoding low density parity check (LDPC) codes. The maximum a posteriori probability (MAP) decoding of a bit is described as a statistical inference problem, and belief propagation is applied to its solution. The corresponding message passing procedure is analyzed in details, and the threshold noise level below which this ‘iterative decoding’ achieves perfect decoding is derived. The chapter ends with a general discussion of the relation between message passing and optimal (exact symbol MAP) decoding.