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Electronics Letters

Density evolution for low-density parity-checkcodes under Max-Log-MAP decoding

X. Wei, Ali N. Akansu

Published Aug 30, 2001• 29 citations
Publisher

Abstract

A density evolution procedure for low-density parity-check (LDPC) codes under Max-Log-MAP decoding is presented. Using this technique, the precise convergence threshold for LDPC code could be easily derived.
DOI
10.1049/el:20010755

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We derive a new fast convergent Density Evolution algorithm for finding optimal rate Low-Density Parity-Check (LDPC) codes used over the binary erasure channel (BEC). The fast convergence property comes from the modified Density Evolution (DE), a numerical method for analyzing the behavior of iterative decoding convergence of a LDPC code. We have used the method of [16] for designing of a LDPC code with optimal rate. This has been done for a given parity check node degree distribution, erasure probability and specified DE constraint. The fast behavior of DE and found optimal rate with this method compare with the previous DE constraint.
In modern communication systems Low-Density Parity Check (LDPC) codes are widely used. It is because of their performance under iterative decoding, hardware-friendly structure and well-known construction methods. For one to construct good LDPC code Density Evolution (DE) can be used, it estimates the decoding threshold, that is it estimates performance of the code. LDPC codes can be further extended to Generalized LDPC (GLDPC) codes, where simple SPC code is replaced with some component code. With more complex structure common DE is no longer correct. This letter presents the upper bound for decoding error and, therefore, an upper bound of a iterative threshold (in dB). It will be shown that the Gaussian approximation gives an upper bound for a decoding error. As one of the results it means that EXIT-charts analysis also gives an upper bound for an iterative threshold for a GLDPC code.