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ML and Near-ML Decoding of LDPC Codes Over the BEC: Bounds and Decoding Algorithms

Irina E. Bocharova, Boris D. Kudryashov, Vitaly Skachek +2 more

The performance of maximum-likelihood (ML) decoding on the binary erasure channel for finite-length low-density parity-check (LDPC) codes from two random ensembles is studied. The theoretical average spectrum of the Gallager ensemble is computed by using a recurrent procedure and compared to the empirically found average spectrum for the same ensemble as well as to the empirical average spectrum of the Richardson-Urbanke ensemble and spectra of selected codes from both ensembles. Distance properties of the random codes from the Gallager ensemble are discussed. A tightened union-type upper bound on the ML decoding error probability based on the precise coefficients of the average spectrum is presented. A new upper bound on the ML decoding performance of LDPC codes from the Gallager ensemble based on computing the rank of submatrices of the code parity-check matrix is derived. A new low-complexity near-ML decoding algorithm for quasi-cyclic LDPC codes is proposed and simulated. Its performance is compared to the upper bounds on the ML decoding performance.The performance of maximum-likelihood (ML) decoding on the binary erasure channel for finite-length low-density parity-check (LDPC) codes from two random ensembles is studied. The theoretical average spectrum of the Gallager ensemble is computed by using a recurrent procedure and compared to the empirically found average spectrum for the same ensemble as well as to the empirical average spectrum of the Richardson-Urbanke ensemble and spectra of selected codes from both ensembles. Distance properties of the random codes from the Gallager ensemble are discussed. A tightened union-type upper bound on the ML decoding error probability based on the precise coefficients of the average spectrum is presented. A new upper bound on the ML decoding performance of LDPC codes from the Gallager ensemble based on computing the rank of submatrices of the code parity-check matrix is derived. A new low-complexity near-ML decoding algorithm for quasi-cyclic LDPC codes is proposed and simulated. Its performance is compared to the upper bounds on the ML decoding performance.

arXiv:1709.01455Sep 5, 20171 citation

A construction of low-density parity-check codes

李铁楠, 单秀玲

Jan 1, 20132 citations

Two approaches to the analysis of low-density parity-check codes

Kamil Sh. Zigangirov, Michael Lentmaier, Dmitri V. Truhachev

We overview two approaches to the analysis of low-density parity-check (LDPC) codes: selected code approach and ensemble approach. As examples of application of the methods we consider Gallager's homogeneous LDPC codes and Berrou-Glavieux-Thitimajshima (BGT) turbo-codes.

IEEE International Symposium on Information Theory (ISIT)Jun 25, 20032 citations

LOW-DENSITY PARITY-CHECK CODES AND THE RELATED PERFORMANCE ANALYSIS METHODS

Xudong Ma

Series on coding theory and cryptologyFeb 1, 20100 citations

A NEW FAMILY OF LOW-DENSITY PARITY CHECK CODES WITH LARGE GIRTH AND LOW COMPLEXITY

Xu Xia, Yanping Li, Moon Ho Lee

한국통신학회 학술대회 및 강연회Apr 1, 20040 citations

Chained Gallager codes

Victor Zyablov, Florian Hug, Rolf Johannesson

The ensemble of regular Low-Density Parity-Check (LDPC) codes introduced by Gallager is considered. Using probabilistic arguments a lower bound on the normalized minimum distance is derived. A new code construction, called Chained Gallager codes, is introduced as the combination of two Gallager codes and its error correcting capabilities are studied.

Jan 1, 20091 citation

An Extension of Gallager Ensemble of Low Density Parity Check Codes

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