Finite-Length Analysis of Irregular Expurgated LDPC Codes under Finite Number of Iterations

Details Finite-Length Analysis of Irregular Expurgated LDPC Codes under Finite Number of Iterations Finite-Length Analysis of Irregular Expurgated LDPC Codes under Finite Number of Iterations

2009-01-15

arxiv.org/abs/0901.2204v2

Computer Science

Information Theory

5 pages, 3 figures, submitted to ISIT2009; revised

Scientific paper

Communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) codes and belief propagation (BP) decoding is considered. The average bit error probability of an irregular LDPC code ensemble after a fixed number of iterations converges to a limit, which is calculated via density evolution, as the blocklength $n$ tends to infinity. The difference between the bit error probability with blocklength $n$ and the large-blocklength limit behaves asymptotically like $\alpha/n$, where the coefficient $\alpha$ depends on the ensemble, the number of iterations and the erasure probability of the BEC\null. In [1], $\alpha$ is calculated for regular ensembles. In this paper, $\alpha$ for irregular expurgated ensembles is derived. It is demonstrated that convergence of numerical estimates of $\alpha$ to the analytic result is significantly fast for irregular unexpurgated ensembles.

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