On concentration of measures for LDPC code ensembles
Igal Sason, R. Eshel · 2011
This work considers the concentration of measures for low-density parity-check (LDPC) code ensembles. The two results derived in this paper follow from Azuma's inequality for Doob martingales with bounded differences. The first result is a tightened concentration inequality for the conditional entropy (originally derived by Méasson et al.), and the second result is a concentration inequality for the cardinality of the fundamental systems of cycles of a bipartite graph from the ensemble.