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Asymptotic enumeration methods for analyzing LDPC codes


Abstract:

We show how asymptotic estimates of powers of polynomials with nonnegative coefficients can be used in the analysis of low-density parity-check (LDPC) codes. In particula...Show More

Abstract:

We show how asymptotic estimates of powers of polynomials with nonnegative coefficients can be used in the analysis of low-density parity-check (LDPC) codes. In particular, we show how these estimates can be used to derive the asymptotic distance spectrum of both regular and irregular LDPC code ensembles. We then consider the binary erasure channel (BEC). Using these estimates we derive lower bounds on the error exponent, under iterative decoding, of LDPC codes used over the BEC. Both regular and irregular code structures are considered. These bounds are compared to the corresponding bounds when optimal (maximum-likelihood (ML)) decoding is applied.
Published in: IEEE Transactions on Information Theory ( Volume: 50, Issue: 6, June 2004)
Page(s): 1115 - 1131
Date of Publication: 01 June 2004

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