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

The IMA volumes in mathematics and its applications

On the Effective Weights of Pseudocodewords for Codes Defined on Graphs with Cycles

G. David Forney, R. Koetter, Frank R. Kschischang, Alex Reznik

Published Jan 1, 2001• 120 citations
Publisher
DOI
10.1007/978-1-4613-0165-3_5

Related papers

Pseudocodeword-free criterion for codes with cycle-free Tanner graph

Wittawat Kositwattanarerk

Designs Codes and Cryptography•Mar 23, 2018•0 citations

On Iterative Decoding of Cycle Codes of Graphs

Gilles Zémor

The IMA volumes in mathematics and its applications•Jan 1, 2001•4 citations

Pseudocodeword-based Decoding of Quantum Color Codes

July X. Li, Joseph M. Renes, Pascal O. Vontobel

In previous work, we have shown that pseudocodewords can be used to characterize the behavior of decoders not only for classical codes but also for quantum stabilizer codes. With the insights obtained from this pseudocodewords-based analysis, we have also introduced a two-stage decoder based on pseudocodewords for quantum cycle codes that leads to improved decoding performance. In this paper, we consider quantum (stabilizer) color codes and propose a two-stage decoder that is a generalization of the pseudocodeword-based decoder for quantum cycle codes. Our decoder has local operations w.r.t. the underlying graphs, syndrome-weight-dependent computational complexity, and better decoding performance compared with previous approaches for quantum color codes.

arXiv:2010.10845•IEEE International Symposium on Information Theory (ISIT)•Jul 12, 2021•1 citation

Pseudocodeword-Free Criterion for Codes with Cycle-Free Tanner Graph

Wittawat Kositwattanarerk

Iterative decoding and linear programming decoding are guaranteed to converge to the maximum-likelihood codeword when the underlying Tanner graph is cycle-free. Therefore, cycles are usually seen as the culprit of low-density parity-check (LDPC) codes. In this paper, we argue in the context of graph cover pseudocodeword that, for a code that permits a cycle-free Tanner graph, cycles have no effect on error performance as long as they are a part of redundant rows. Specifically, we characterize all parity-check matrices that are pseudocodeword-free for such class of codes.

arXiv:1706.06648•Jun 20, 2017•0 citations

Design and performance of LDPC codes extended with parity-check symbols from a larger alphabet

Elisa Mo, M.A. Armand

This paper describes a method for constructing a certain class of LDPC codes over mixed integer residue rings. These codes are essentially extended LDPC codes where the additional redundant symbols come from a larger alphabet. In particular, we address the effects that zero divisors as edge weights in the Tanner graph of LDPC codes over Z, have, from the pseudocodeword perspective. First, we show that weighting certain edges of a Tanner graph with zero divisors of Z, can reduce the number of pseudocodewords arising from its finite degree covers. Second, we prove that in adding a redundant row to a given parity-check matrix, the smaller the number of zero divisors it contains, the more effective it is in constricting the corresponding fundamental polytope. Moreover, we argue that cycles of length four are not bad provided at least one of the four corresponding edge weights is a zero divisor. The culmination of these findings is a procedure for judiciously adding redundant check nodes to the Tanner graph representation of a mixed- alphabet code such that significant performance improvements under iterative decoding may be obtained.

International Conference on Information, Communications & Signal Processing (ICICS)•Jan 1, 2007•1 citation

Sequences of Bivariate Bicycle Codes from Covering Graphs

Anonymous

PRX Quantum•Aug 3, 2026•0 citations
In previous work, we have shown that pseudocodewords can be used to characterize the behavior of decoders not only for classical codes but also for quantum stabilizer codes. With the insights obtained from this pseudocodewords-based analysis, we have also introduced a two-stage decoder based on pseudocodewords for quantum cycle codes that leads to improved decoding performance. In this paper, we consider quantum (stabilizer) color codes and propose a two-stage decoder that is a generalization of the pseudocodeword-based decoder for quantum cycle codes. Our decoder has local operations w.r.t. the underlying graphs, syndrome-weight-dependent computational complexity, and better decoding performance compared with previous approaches for quantum color codes.
Iterative decoding and linear programming decoding are guaranteed to converge to the maximum-likelihood codeword when the underlying Tanner graph is cycle-free. Therefore, cycles are usually seen as the culprit of low-density parity-check (LDPC) codes. In this paper, we argue in the context of graph cover pseudocodeword that, for a code that permits a cycle-free Tanner graph, cycles have no effect on error performance as long as they are a part of redundant rows. Specifically, we characterize all parity-check matrices that are pseudocodeword-free for such class of codes.
This paper describes a method for constructing a certain class of LDPC codes over mixed integer residue rings. These codes are essentially extended LDPC codes where the additional redundant symbols come from a larger alphabet. In particular, we address the effects that zero divisors as edge weights in the Tanner graph of LDPC codes over Z, have, from the pseudocodeword perspective. First, we show that weighting certain edges of a Tanner graph with zero divisors of Z, can reduce the number of pseudocodewords arising from its finite degree covers. Second, we prove that in adding a redundant row to a given parity-check matrix, the smaller the number of zero divisors it contains, the more effective it is in constricting the corresponding fundamental polytope. Moreover, we argue that cycles of length four are not bad provided at least one of the four corresponding edge weights is a zero divisor. The culmination of these findings is a procedure for judiciously adding redundant check nodes to the Tanner graph representation of a mixed- alphabet code such that significant performance improvements under iterative decoding may be obtained.