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

Error Exponents of Low-Density Parity-Check Codes on the Binary Erasure Channel

Thierry Mora, Olivier Rivoire

Published Feb 26, 2015• 2 citations
OpenAlex

Abstract

Abstract — We introduce a thermodynamic (large deviation) formalism for computing error exponents in error-correcting codes. Within this framework, we apply the heuristic cavity method from statistical me-chanics to derive the average and typical error expo-nents of low-density parity-check (LDPC) codes on the binary erasure channel (BEC) under maximum-likelihood decoding. I.

Related papers

Error Exponents of Low-Density Parity-Check Codes on the Binary Erasure Channel

Thierry Mora, Olivier Rivoire

We introduce a thermodynamic (large deviation) formalism for computing error exponents in error-correcting codes. Within this framework, we apply the heuristic cavity method from statistical mechanics to derive the average and typical error exponents of low-density parity-check (LDPC) codes on the binary erasure channel (BEC) under maximum-likelihood decoding.

arXiv:cs/0605130•IEEE Information Theory Workshop (ITW)•Oct 1, 2006•1 citation

An Efficient Maximum-Likelihood Decoding of LDPC Codes Over the Binary Erasure Channel

David Burshtein, G. Miller

We propose an efficient maximum-likelihood (ML) decoding algorithm for decoding low-density parity-check (LDPC) codes over the binary-erasure channel (BEC). We also analyze the computational complexity of the proposed algorithm.

IEEE Transactions on Information Theory•Oct 26, 2004•97 citations

Finite-length analysis of low-density parity-check codes on the binary erasure channel

Changyan Di, D. Proietti, I. Emre Telatar +2 more

In this paper, we are concerned with the finite-length analysis of low-density parity-check (LDPC) codes when used over the binary erasure channel (BEC). The main result is an expression for the exact average bit and block erasure probability for a given regular ensemble of LDPC codes when decoded iteratively. We also give expressions for upper bounds on the average bit and block erasure probability for regular LDPC ensembles and the standard random ensemble under maximum-likelihood (ML) decoding. Finally, we present what we consider to be the most important open problems in this area.

IEEE Transactions on Information Theory•Jun 1, 2002•864 citations

On Decoding of Low-Density Parity-Check Codes Over the Binary Erasure Channel

Hossein Pishro-Nik, Faramarz Fekri

This paper investigates decoding of low-density parity-check (LDPC) codes over the binary erasure channel (BEC). We study the iterative and maximum-likelihood (ML) decoding of LDPC codes on this channel. We derive bounds on the ML decoding of LDPC codes on the BEC. We then present an improved decoding algorithm. The proposed algorithm has almost the same complexity as the standard iterative decoding. However, it has better performance. Simulations show that we can decrease the error rate by several orders of magnitude using the proposed algorithm. We also provide some graph-theoretic properties of different decoding algorithms of LDPC codes over the BEC which we think are useful to better understand the LDPC decoding methods, in particular, for finite-length codes.

IEEE Transactions on Information Theory•Mar 1, 2004•147 citations

Bounds on the maximum likelihood decoding error probability of low density parity check codes

G. Miller, D. Burshtein

We derive bounds on the error probability of ML decoded LDPC (low density parity check) codes, for any binary-input symmetric-output channel. For appropriately chosen ensembles of LDPC codes, reliable communication is possible up to channel capacity. The lower and upper bounds coincide asymptotically, indicating a polynomially decreasing ensemble averaged error probability. For ensembles with suitably chosen parameters, the error probability of almost all codes is exponentially decreasing. Furthermore, the error exponent can be set arbitrarily close to the standard random coding exponent.

IEEE International Symposium on Information Theory (ISIT)•Nov 7, 2002•7 citations

Upper Bound on Error Exponent of Regular LDPC Codes Transmitted Over the BEC

Idan Goldenberg, David Burshtein

The error performance of the ensemble of typical low-definition parity-check (LDPC ) codes transmitted over the binary erasure channel (BEC) is analyzed. In the past, lower bounds on the error exponents were derived. In this paper, a probabilistic upper bound on this error exponent is derived. This bound holds with some confidence level.

IEEE Transactions on Information Theory•May 19, 2009•4 citations
Abstract — We introduce a thermodynamic (large deviation) formalism for computing error exponents in error-correcting codes. Within this framework, we apply the heuristic cavity method from statistical me-chanics to derive the average and typical error expo-nents of low-density parity-check (LDPC) codes on the binary erasure channel (BEC) under maximum-likelihood decoding. I.
In this paper, we are concerned with the finite-length analysis of low-density parity-check (LDPC) codes when used over the binary erasure channel (BEC). The main result is an expression for the exact average bit and block erasure probability for a given regular ensemble of LDPC codes when decoded iteratively. We also give expressions for upper bounds on the average bit and block erasure probability for regular LDPC ensembles and the standard random ensemble under maximum-likelihood (ML) decoding. Finally, we present what we consider to be the most important open problems in this area.
This paper investigates decoding of low-density parity-check (LDPC) codes over the binary erasure channel (BEC). We study the iterative and maximum-likelihood (ML) decoding of LDPC codes on this channel. We derive bounds on the ML decoding of LDPC codes on the BEC. We then present an improved decoding algorithm. The proposed algorithm has almost the same complexity as the standard iterative decoding. However, it has better performance. Simulations show that we can decrease the error rate by several orders of magnitude using the proposed algorithm. We also provide some graph-theoretic properties of different decoding algorithms of LDPC codes over the BEC which we think are useful to better understand the LDPC decoding methods, in particular, for finite-length codes.
We derive bounds on the error probability of ML decoded LDPC (low density parity check) codes, for any binary-input symmetric-output channel. For appropriately chosen ensembles of LDPC codes, reliable communication is possible up to channel capacity. The lower and upper bounds coincide asymptotically, indicating a polynomially decreasing ensemble averaged error probability. For ensembles with suitably chosen parameters, the error probability of almost all codes is exponentially decreasing. Furthermore, the error exponent can be set arbitrarily close to the standard random coding exponent.