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

IEEE International Symposium on Information Theory (ISIT)

Potential-decoding, error correction beyond the half minimum distance for linear block codes

R. Lohnert

Published Nov 19, 2002• 0 citations
Publisher

Abstract

An error correction procedure for linear block codes is presented which corrects errors beyond the half minimum distance. The algorithm is based on minimizing a real valued function, called potential. Since the potential decreases monotonously with decreasing weight of the error vector, minimization of the potential can be done by local search.

DOI
10.1109/isit.1995.531154

Related papers

Hard- and soft-decision decoding beyond the half minimum distance---An algorithm for linear codes (Corresp.)

Martin Bossert, F. Hergert

A decoding algorithm for linear codes that uses the minimum weight words of the dual code as parity checks is defined. This algorithm is able to correct beyond the half minimum distance and has the capability of including soft-decision decoding. Results on applying this algorithm to quadratic residue (QR) codes, BCH codes, and the Golay codes (with and without soft-decision decoding) are presented.

IEEE Transactions on Information Theory•Sep 1, 1986•38 citations

Error-Correction Capability of Binary Linear Codes

Tor Helleseth, Torleiv Kløve, V.I. Levenshtein

The monotone structure of correctable and uncorrectable errors given by the complete decoding for a binary linear code is investigated. New bounds on the error-correction capability of linear codes beyond half the minimum distance are presented, both for the best codes and for arbitrary codes under some restrictions on their parameters. It is proved that some known codes of low rate are as good as the best codes in an asymptotic sense.

IEEE Transactions on Information Theory•Apr 1, 2005•30 citations

DECODING OF MATRIX-PRODUCT CODES

Fernando Hernando, Diego Ruano

We propose a decoding algorithm for the (u | u + v)-construction that decodes up to half of the minimum distance of the linear code. We extend this algorithm for a class of matrix-product codes in two different ways. In some cases, one can decode beyond the error-correction capability of the code.

arXiv:1107.1529•Journal of Algebra and Its Applications•Sep 1, 2012•26 citations

Computing the minimum distance of linear codes by the error impulse method

Claude Berrou, Sandrine Vaton, Michel Jézéquel +1 more

A new method for computing the minimum distances of linear error-correcting codes is proposed and justified. Unlike classical techniques that rely on exhaustive or partial enumeration of codewords, this new method is based on the ability of the Soft-In decoder to overcome Error Impulse input patterns. It is shown that the maximum magnitude of the Error Impulse that can be corrected by the decoder is directly related to the minimum distance. This leads to a very fast algorithm to obtain minimum distances of any linear code whatever the block size and the code rate considered. In particular, the method can be advantageously worked out for turbo-like concatenated codes.

Globecom•Mar 22, 2004•72 citations

Generalized minimum distance iterative decoding of Tanner codes

Saejoon Kim

In this letter, we present a linear-time decoding algorithm for Tanner codes that can correct errors up to close to half the minimum distance of the code. The algorithm is a simple generalization to the iterative decoding algorithm of expander codes proposed by Skachek and Roth (2003).

IEEE Communications Letters•Aug 1, 2005•1 citation

On decoding algorithms for binary linear block codes

Bruce L. Montgomery

This dissertation investigates the complexity of minimum-distance decoding (MDD) algorithms for general binary linear block codes, and also investigates the use of such codes in constructing error correcting/detecting codes that are effective against both random and unidirectional errors. A new MDD algorithm is proposed, and its complexity is analyzed and compared to that of other such algorithms. The question of whether all good codes satisfy certain properties required for efficient implementation of the algorithm is also considered. The performance of decoding algorithms, with the information bit error rate as the criterion instead of the block error rate, is also studied. New decoding rules which can yield lower information bit error rates than the MDD rule are proposed and evaluated. A new class of binary codes is developed which corrects random errors and detects all unidirectional errors. These codes are obtained by appending a suffix to each codeword of a linear block code. To evaluate the efficiency of the new codes, a thorough comparison with the best previously obtained codes is made.

•Jan 1, 1987•0 citations
An error correction procedure for linear block codes is presented which corrects errors beyond the half minimum distance. The algorithm is based on minimizing a real valued function, called potential. Since the potential decreases monotonously with decreasing weight of the error vector, minimization of the potential can be done by local search.
A new method for computing the minimum distances of linear error-correcting codes is proposed and justified. Unlike classical techniques that rely on exhaustive or partial enumeration of codewords, this new method is based on the ability of the Soft-In decoder to overcome Error Impulse input patterns. It is shown that the maximum magnitude of the Error Impulse that can be corrected by the decoder is directly related to the minimum distance. This leads to a very fast algorithm to obtain minimum distances of any linear code whatever the block size and the code rate considered. In particular, the method can be advantageously worked out for turbo-like concatenated codes.
This dissertation investigates the complexity of minimum-distance decoding (MDD) algorithms for general binary linear block codes, and also investigates the use of such codes in constructing error correcting/detecting codes that are effective against both random and unidirectional errors. A new MDD algorithm is proposed, and its complexity is analyzed and compared to that of other such algorithms. The question of whether all good codes satisfy certain properties required for efficient implementation of the algorithm is also considered. The performance of decoding algorithms, with the information bit error rate as the criterion instead of the block error rate, is also studied. New decoding rules which can yield lower information bit error rates than the MDD rule are proposed and evaluated. A new class of binary codes is developed which corrects random errors and detects all unidirectional errors. These codes are obtained by appending a suffix to each codeword of a linear block code. To evaluate the efficiency of the new codes, a thorough comparison with the best previously obtained codes is made.