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Physica A Statistical Mechanics and its Applications

Iterative decoding of LDPC codes: some bounds and properties

David Burshtein, Gadi Miller

Published Dec 1, 2001• 0 citations
Publisher
DOI
10.1016/s0378-4371(01)00438-1

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This paper deals with the Low-Density Parity-Check codes with the constituent Hamming codes (H-LDPC codes) and two different iterative hard-decision low-complexity decoding algorithms. Both algorithms are based on the same main idea: the decreasing of the syndrome weight on each step of the decoding algorithm. The first decoding algorithm uses the properties of the constituent Hamming code. The best known lower-bound on the guaranteed corrected errors fraction for the H-LDPC codes under the first decoding algorithm was obtained in 2011. The second decoding algorithm considers H-LDPC as the irregular LDPC code and uses the well-known majority decoding algorithm. The lower-bound on the guaranteed corrected errors fraction for H-LDPC code under the second decoding algorithm is introduced for the first time in this paper. Numerical results for the lower-bound, obtained in this paper for H-LDPC code under the second decoding algorithm, significantly exceed the numerical results for the best known lower-bounds, obtained previously for H-LDPC code under the first decoding algorithm.
This paper investigates decoding of low-density parity-check (LDPC) codes over the binary erasure channel (BEC). We study the iterative and maximum-likelihood (ML) decoding of LDPC codes on this channel. We derive bounds on the ML decoding of LDPC codes on the BEC. We then present an improved decoding algorithm. The proposed algorithm has almost the same complexity as the standard iterative decoding. However, it has better performance. Simulations show that we can decrease the error rate by several orders of magnitude using the proposed algorithm. We also provide some graph-theoretic properties of different decoding algorithms of LDPC codes over the BEC which we think are useful to better understand the LDPC decoding methods, in particular, for finite-length codes.
This paper deals with the irregular binary low-density parity-check (LDPC) codes and two iterative low-complexity decoding algorithms. The first one is the majority error-correcting decoding algorithm, and the second one is iterative erasure-correcting decoding algorithm. The lower bounds on correcting capabilities (the guaranteed corrected error and erasure fraction respectively) of irregular LDPC code under decoding (error and erasure correcting respectively) algorithms with low-complexity were represented. These lower bounds were obtained as a result of analysis of Tanner graph representation of irregular LDPC code. The numerical results, obtained at the end of the paper for proposed lower-bounds achieved similar results for the previously known best lower-bounds for regular LDPC codes and were represented for the first time for the irregular LDPC codes.