Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Problems of Information Transmission

On the error-correcting capability of LDPC codes

Kamil Sh. Zigangirov, A. E. Pusane, D. K. Zigangirov, Daniel J. Costello

Published Sep 1, 2008• 11 citations
Publisher

Abstract

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.

DOI
10.1134/s0032946008030046

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 Transmission•Jun 1, 2006•4 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 Transmission•Sep 1, 2009•6 citations

On the asymptotic performance of low-complexity decoded LDPC codes with constituent hamming codes

Victor Zyablov, Maja Lončar, Rolf Johannesson +1 more

Hamming code-based LDPC (H-LDPC) block codes are obtained by replacing single parity-check codes in Gallager’s LDPC codes with Hamming constituent codes. This paper investigates the asymptotic error-correcting capabilities of ensembles of random H-LDPC codes, used over the binary symmetric channel and decoded with a low-complexity hard-decision iterative decoding algorithm. The number of required decoding iterations is a logarithmic function of the code length. It is shown that there exist H-LDPC codes for which such an iterative decoding corrects any error pattern with a number of errors that grows linearly with the code length. For various choices of code parameters the results are supported by numerical examples.

International Symposium on Turbo Codes and Iterative Information Processing•Sep 1, 2008•5 citations

On the Erasure Correction Capability of LDPC Codes

D. K. Zigangirov, Kamil Sh. Zigangirov

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

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2006•0 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 Electronics•Dec 1, 2016•2 citations

Low-complexity error correction of Hamming-code-based LDPC codes

Victor Zyablov, Rolf Johannesson, Matea Lončar

Ensembles of binary random LDPC block codes constructed using Hamming codes as constituent codes are studied for communicating over the binary symmetric channel. These ensembles are known to contain codes that asymptotically almost meet the Gilbert-Varshamov bound. It is shown that in these ensembles there exist codes which can correct a number of errors that grows linearly with the code length, when decoded with a low-complexity iterative decoder, which requires a number of iterations that is a logarithmic function of the code length. The results are supported by numerical examples, for various choices of the code parameters.

Problems of Information Transmission•Jun 1, 2009•17 citations
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.
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.
Hamming code-based LDPC (H-LDPC) block codes are obtained by replacing single parity-check codes in Gallager’s LDPC codes with Hamming constituent codes. This paper investigates the asymptotic error-correcting capabilities of ensembles of random H-LDPC codes, used over the binary symmetric channel and decoded with a low-complexity hard-decision iterative decoding algorithm. The number of required decoding iterations is a logarithmic function of the code length. It is shown that there exist H-LDPC codes for which such an iterative decoding corrects any error pattern with a number of errors that grows linearly with the code length. For various choices of code parameters the results are supported by numerical examples.
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.
Ensembles of binary random LDPC block codes constructed using Hamming codes as constituent codes are studied for communicating over the binary symmetric channel. These ensembles are known to contain codes that asymptotically almost meet the Gilbert-Varshamov bound. It is shown that in these ensembles there exist codes which can correct a number of errors that grows linearly with the code length, when decoded with a low-complexity iterative decoder, which requires a number of iterations that is a logarithmic function of the code length. The results are supported by numerical examples, for various choices of the code parameters.