The Mutual information of LDGM codes
Information Theory
2017-07-27 v2 math.IT
Probability
Abstract
We provide matching upper and lower bounds on the mutual information in noisy reconstruction of parity check codes and thereby prove a long-standing conjecture by Montanari [IEEE Transactions on Information Theory 2005]. Besides extending a prior concentration result of Abbe and Montanari [Theory of Computing 2015] to the case of odd check degrees, we precisely determine the conjectured formula for code ensembles of arbitrary degree distribution, thus capturing a broad class of capacity approaching codes.
Cite
@article{arxiv.1707.04413,
title = {The Mutual information of LDGM codes},
author = {Jan van den Brand and Nor Jaafari},
journal= {arXiv preprint arXiv:1707.04413},
year = {2017}
}