IEEE International Symposium on Information Theory (ISIT)

On the Erasure Correction Capability of LDPC Codes

D. K. Zigangirov, Kamil Sh. Zigangirov

Published Jul 1, 2006• 0 citations

Abstract

The erasure correcting capability of LDPC codes with parity-check matrices composed of permutation matrices is considered. A new lower bound for number of the iteratively correcting erasures for the Zyablov-Pinsker algorithm is given

DOI: 10.1109/isit.2006.261702

Related papers

Decoding of low-density codes with parity-check matrices composed of permutation matrices in an erasure channel

D. K. Zigangirov, Kamil Sh. Zigangirov

A lower bound for the number of iteratively correctable erasures is given, with application to the ensemble of LDPC codes with parity-check matrices composed of permutation matrices [1]. We assume that the Zyablov-Pinsker iterative decoding algorithm [2] is used. Its complexity is O ( N log N ), where N is the block length.

Problems of Information TransmissionJun 1, 20064 citations

On the error-correcting capability of LDPC codes

Kamil Sh. Zigangirov, A. E. Pusane, D. K. Zigangirov +1 more

We consider the ensemble of low-density parity-check (LDPC) codes introduced by Gallager [1]. The Zyablov-Pinsker majority-logic iterative algorithm [2] for decoding LDPC codes is analyzed on the binary symmetric channel. An analytical lower bound on the error-correcting capability τ max that grows linearly in the code block length is obtained.

Problems of Information TransmissionSep 1, 200811 citations

Erasure correction by low-density codes

Victor Zyablov, Pavel S. Rybin

We generalize the method for computing the number of errors correctable by a low-density parity-check (LDPC) code in a binary symmetric channel, which was proposed by V.V. Zyablov and M.S. Pinsker in 1975. This method is for the first time applied for computing the fraction of guaranteed correctable erasures for an LDPC code with a given constituent code used in an erasure channel. Unlike previously known combinatorial methods for computing the fraction of correctable erasures, this method is based on the theory of generating functions, which allows us to obtain more precise results and unify the computation method for various constituent codes of a regular LDPC code. We also show that there exist an LDPC code with a given constituent code which, when decoded with a low-complexity iterative algorithm, is capable of correcting any erasure pattern with a number of erasures that grows linearly with the code length. The number of decoding iterations, required to correct the erasures, is a logarithmic function of the code length. We make comparative analysis of various numerical results obtained by various computation methods for certain parameters of an LDPC code with a constituent single-parity-check or Hamming code.

Problems of Information TransmissionSep 1, 20096 citations

On the erasure-correcting capabilities of low-complexity decoded LDPC codes with constituent Hamming codes

Victor Zyablov, Maja Lončar, Rolf Johannesson +1 more

Low-density parity-check (LDPC) codes can be constructed using constituent block codes other than single parity-check (SPC) codes. This paper considers random LDPC codes with constituent Hamming codes and investigates their asymptotic performance over the binary erasure channel. It is shown that there exist Hamming code-based LDPC codes which, when decoded with a low-complexity iterative algorithm, are capable of correcting any erasure pattern with a number of erasures that grows linearly with the code length. The number of decoding iterations, required to correct the erasures, is a logarithmic function of the code length. The fraction of correctable erasures is computed numerically for various choices of code parameters.

Jan 1, 20086 citations

Correcting capabilities of binary irregular LDPC code under low-complexity iterative decoding algorithm

Pavel S. Rybin

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.

Journal of Communications Technology and ElectronicsDec 1, 20162 citations

Burst-Correction Decoding of Cyclic LDPC Codes

Shumei Song, Shu Lin, Khaled Abdel-Ghaffar

LDPC codes have excellent performance when iteratively decoded based on sparse parity-check matrices over both the AWGN channel and the erasure channel. In this paper, we propose a simple burst-correction decoding scheme for cyclic LDPC codes based on the same sparse circulant parity-check matrices used to perform iterative decoding. Although the proposed scheme may not achieve the full burst-correcting capability of the codes, it is rather simple and fast. We also show that the full burst-correcting capabilities of some codes constructed from Euclidean and projective geometries are very close to the Reiger upper bound

IEEE International Symposium on Information Theory (ISIT)Jul 1, 20064 citations