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IEEE International Symposium on Information Theory (ISIT)

Partially-regular LDPC codes with linear encoding complexity and improved thresholds

D. K. Zigangirov, Kamil Sh. Zigangirov, Daniel J. Costello

Published Jul 1, 2011• 0 citations
Publisher

Abstract

We consider an ensemble of systematic low-density parity-check (LDPC) codes of length N with linear encoding complexity, i.e., with complexity O(N). We call these codes partially-regular, since they can be considered as modifications of regular LDPC codes. Further, their iterative decoding thresholds on the binary erasure channel (BEC) are found to be significantly better than the thresholds of the corresponding regular LDPC codes.

DOI
10.1109/isit.2011.6034184

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In this paper, we are concerned with the finite-length analysis of low-density parity-check (LDPC) codes when used over the binary erasure channel (BEC). The main result is an expression for the exact average bit and block erasure probability for a given regular ensemble of LDPC codes when decoded iteratively. We also give expressions for upper bounds on the average bit and block erasure probability for regular LDPC ensembles and the standard random ensemble under maximum-likelihood (ML) decoding. Finally, we present what we consider to be the most important open problems in this area.
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