Pivoting algorithms for maximum likelihood decoding of LDPC codes over erasure channels

Authors:
Gianluigi Liva;Balazs Matuz;Enrico Paolini;Marco Chiani
Affiliations:
Deutsches Zentrum fur Luft- und Raumfahrt (DLR), Wessling, Germany;Deutsches Zentrum fur Luft- und Raumfahrt (DLR), Wessling, Germany;University of Bologna, Cesena FC, Italy;University of Bologna, Cesena FC, Italy
Venue:
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
Year:
2009

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Abstract

This paper investigates efficient maximum-likelihood (ML) decoding algorithms for low-density parity-check (LDPC) codes over erasure channels. In particular, enhancements to a previously proposed structured Gaussian elimination approach are presented. The improvements are achieved by developing a set of algorithms, here referred to as pivoting algorithms, aiming to limit the average number of reference variables (or pivots) from which the erased symbols can be recovered. Four pivoting algorithms are compared, which exhibit different trade-offs between the complexity of the pivoting phase and the average number of pivots. Numerical results on the performance of LDPC codes under ML erasure decoding complete the analysis, confirming that a near-optimum performance can be obtained with an affordable decoding complexity, up to very high data rates. For example, for one of the presented algorithms, a software implementation has been developed, which is capable to provide data rates above 1.5 Gbps on a commercial computing platform.