ON UNIVERSAL LDPC CODES OVER MEMORYLESS SYMMETRIC CHANNELS

Igal Sason, Boaz Shuval

Published Jan 1, 2011• 1 citation

Abstract

A design of robust error-correcting codes that achieve reli able communication over various channels is of great theoretical and practical interest. Such codes are termed universal. This paper considers the universality of lowdensity parity-check (LDPC) code ensembles over families of memoryless binary-input output-symmetric (MBIOS) channels. Universality is considered both under belief-pr opagation (BP) and maximum-likelihood (ML) decoding. For the BP decoding case, we derive a density-evolution-based analytical method for designing LDPC code ensembles that are universal over various families of MBIOS channels. We also derive a necessary condition for universality of LDPC code ensembles under BP decoding; this condition is used to provide bounds on the universally achievable fraction of capacity. These results enable us to provide conditions for reliable / unreliable communications under BP decoding that are based on the Bhattacharyya parameter of the channel. For the ML decoding case, we prove that properly selected regular LDPC code ensembles are universally capacity-achieving for the set of equicapacity MBIOS channels and extend this result to punctured regular LDPC code ensembles. Index Terms Belief propagation (BP), Bhattacharyya parameter (B-parameter), density evolution (DE), linear programming (LP) bounds, low-density parity-check (LDPC) codes, maximum-likelihood (ML), memoryless binary-input outputsymmetric (MBIOS) channels, stability.

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