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

arXiv:cond-mat/9906011 · Physical Review Letters

Error-Correcting Codes That Nearly Saturate Shannon's Bound

Ido Kanter, David Saad

Published Sep 27, 1999• 60 citations
arXivHTMLPDF

Abstract

Gallager-type error-correcting codes that nearly saturate Shannon's bound are constructed using insight gained from mapping the problem onto that of an Ising spin system. The performance of the suggested codes is evaluated for different code rates for both finite and infinite message lengths.
DOI
10.1103/physrevlett.83.2660

Related papers

Finite-size effects and error-free communication in Gaussian channels

Ido Kanter, David Saad

The efficacy of a specially constructed Gallager-type error-correcting code to communication in a Gaussian channel is being examined. The construction is based on the introduction of complex matrices, used in both encoding and decoding, which comprise sub-matrices of cascading connection values. The finite size effects are estimated for comparing the results to the bounds set by Shannon. The critical noise level achieved for certain code-rates and infinitely large systems nearly saturates the bounds set by Shannon even when the connectivity used is low.

arXiv:cond-mat/9907424•Journal of Physics A Mathematical and General•Feb 22, 2000•18 citations

On the Hamming bound for nonbinary localized-error-correcting codes

Leonid Alexandrovich Bassalygo, M.S. Pinsker, Rudolf Ahlswede

Problems of Information Transmission•Jan 1, 1999•5 citations

Tighter decoding reliability bound for Gallager’s error-correcting code

Yoshiyuki Kabashima, Naoya Sazuka A, Kazutaka Nakamura +1 more

Statistical physics is employed to evaluate the performance of error-correcting codes in the case of finite message length for an ensemble of Gallager's error correcting codes. We follow Gallager's approach of upper bounding the average decoding error rate, but invoke the replica method to reproduce the tightest general bound to date, and to improve on the most accurate zero-error noise level threshold reported in the literature. The relation between the methods used and those presented in the information theory literature are explored.

arXiv:cond-mat/0010173•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Sep 21, 2001•28 citations

Construction of some new entanglement-assisted quantum error-correcting codes of large lengths

Meng Cao, Fuchuan Wei

Discrete Mathematics•Mar 19, 2024•5 citations

On Bounds for Quantum Error Correcting Codes over EJ-Integers

Eda Yıldız

•Sep 14, 2018•0 citations

Regular and Irregular Gallager-zype Error-Correcting Codes

Yoshiyuki Kabashima, Tatsuto Murayama, David Saad +1 more

The performance of regular and irregular Gallager-type error-correcting code is investigated via methods of statistical physics. The transmitted codeword comprises products of the original message bits selected by two randomly-constructed sparse matrices; the number of non-zero row/column elements in these matrices constitutes a family of codes. We show that Shannon's channel capacity may be saturated in equilibrium for many of the regular codes while slightly lower performance is obtained for others which may be of higher practical relevance. Decoding aspects are considered by employing the TAP approach which is identical to the commonly used belief-propagation-based decoding. We show that irregular codes may saturate Shannon's capacity but with improved dynamical properties.

neural information processing systems•Nov 29, 1999•1 citation
The efficacy of a specially constructed Gallager-type error-correcting code to communication in a Gaussian channel is being examined. The construction is based on the introduction of complex matrices, used in both encoding and decoding, which comprise sub-matrices of cascading connection values. The finite size effects are estimated for comparing the results to the bounds set by Shannon. The critical noise level achieved for certain code-rates and infinitely large systems nearly saturates the bounds set by Shannon even when the connectivity used is low.
Statistical physics is employed to evaluate the performance of error-correcting codes in the case of finite message length for an ensemble of Gallager's error correcting codes. We follow Gallager's approach of upper bounding the average decoding error rate, but invoke the replica method to reproduce the tightest general bound to date, and to improve on the most accurate zero-error noise level threshold reported in the literature. The relation between the methods used and those presented in the information theory literature are explored.
The performance of regular and irregular Gallager-type error-correcting code is investigated via methods of statistical physics. The transmitted codeword comprises products of the original message bits selected by two randomly-constructed sparse matrices; the number of non-zero row/column elements in these matrices constitutes a family of codes. We show that Shannon's channel capacity may be saturated in equilibrium for many of the regular codes while slightly lower performance is obtained for others which may be of higher practical relevance. Decoding aspects are considered by employing the TAP approach which is identical to the commonly used belief-propagation-based decoding. We show that irregular codes may saturate Shannon's capacity but with improved dynamical properties.