Description: The paper is about bounds for LDPC and LDGM codes under MAP. A new method for analyzing low density parity check (LDPC) codes and low density generator
matrix (LDGM) codes under bit maximum a posteriori probability (MAP) decoding is
introduced. The method is based on a rigorous approach to spin glasses developed by Francesco
Guerra. It allows to construct lower bounds on the entropy of the transmitted message conditional
to the received one. Based on heuristic statistical mechanics calculations, we conjecture
such bounds to be tight. The result holds for standard irregular ensembles when used over
binary input output symmetric channels.
The method is first developed for Tanner graph ensembles with Poisson left degree distribution.
It is then generalized to ‘multi-Poisson’ graphs, and, by a completion procedure, to
arbitrary degree distribution.
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boundsonLDPCandLDGM.pdf
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