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)

Finite-length scaling of non-binary (c, d) LDPC codes for the BEC

Iryna Andriyanova, Kenta Kasai

Published Jun 1, 2010• 4 citations
Publisher

Abstract

This paper provides a performance analysis of the regular (c, d) LDPC code ensemble of codelength n with parity-check matrices defined over the general linear group GL(2m). The transmission is assumed to take place over the binary erasure channel with erasure probability ε. In this work, the scaling approximation of the block erasure rate is generalized to the non-binary case, and the scaling parameter α of the approximation is derived. The proposed estimation is then compared with numerical results, showing that it predicts well the slope of the block erasure rate vs. channel erasure probability.

DOI
10.1109/isit.2010.5513596

Related papers

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

Nonbinary spatially-coupled LDPC codes on the binary erasure channel

Amina Piemontese, Alexandre Graell i Amat, Giulio Colavolpe

We analyze the asymptotic performance of non-binary spatially-coupled low-density parity-check (SC-LDPC) codes built on the general linear group, when the transmission takes place over the binary erasure channel. We propose an efficient method to derive an upper bound to the maximum a posteriori probability (MAP) threshold for nonbinary LDPC codes, and observe that the MAP performance of regular LDPC codes improves with the alphabet size. We then consider nonbinary SC-LDPC codes. We show that the same threshold saturation effect experienced by binary SC-LDPC codes occurs for the nonbinary codes, hence we conjecture that the BP threshold for large termination length approaches the MAP threshold of the underlying regular ensemble.

arXiv:1209.5762•International Conference on Communications•Jun 1, 2013•13 citations

The Asymptotic Bit Error Probability of LDPC Codes for the Binary Erasure Channel with Finite Iteration Number

Ryuhei Mori, Kenta Kasai, Tomoharu Shibuya +1 more

We consider communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) code and belief propagation (BP) decoding. The bit error probability for infinite block length is known by density evolution and it is well known that a difference between the bit error probability at finite iteration number for finite block length $n$ and for infinite block length is asymptotically $α/n$, where $α$ is a specific constant depending on the degree distribution, the iteration number and the erasure probability. Our main result is to derive an efficient algorithm for calculating $α$ for regular ensembles. The approximation using $α$ is accurate for $(2,r)$-regular ensembles even in small block length.

arXiv:0801.0931•Jan 7, 2008•0 citations

Asymptotic bit error probability of LDPC codes for the binary erasure channel with finite number of iterations

Ryuhei Mori, Kenta Kasai, Tomoharu Shibuya +1 more

We consider communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) code and belief propagation (BP) decoding. Furthermore, a gap between the bit error probability after finite number of iterations for finite block length n and that for infinite block length is asymptotically α/n, where α denotes a speci..c constant determined by a degree distribution, a number of iterations and erasure probability. Our main result is to derive an ef..cient algorithm for calculating α for regular ensembles.

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2008•4 citations

Finite-length scaling of irregular LDPC code ensembles

Ala Eddine Kaddour Amraoui, Rudiger L. Urbanke, Andrea Montanari A

We investigate the finite-length scaling methodology for irregular LDPC code ensembles when transmission takes place over the binary erasure channel (BEC). We first show how the necessary computations, namely the covariance evolution and the computation of the finite-length shift, can be accomplished in the irregular case. We then investigate how the obtained approximation can be used to predict the performance of irregular code ensembles and to optimize the degree distributions for finite-length codes.

IEEE Information Theory Workshop (ITW)•Jan 1, 2005•22 citations

Analyzing the finite-length performance of generalized LDPC codes

Pablo M. Olmos, David G. M. Mitchell, Daniel J. Costello

In this paper, we analyze the performance of finite-length generalized LDPC (GLDPC) block codes constructed from protographs when transmission takes place over the binary erasure channel (BEC). A generalized peeling decoder is proposed and we derive a system of differential equations that gives the expected evolution of the graph degree distribution during decoding. We then show that the finite-length performance of a GLDPC code can be estimated by means of a simple scaling law, where a single scaling parameter represents the finite-length properties of the code. We also show that, as we consider stronger component codes, both the asymptotic threshold and the finite-length scaling parameter are improved.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2015•10 citations
This paper provides a performance analysis of the regular (c, d) LDPC code ensemble of codelength n with parity-check matrices defined over the general linear group GL(2m). The transmission is assumed to take place over the binary erasure channel with erasure probability ε. In this work, the scaling approximation of the block erasure rate is generalized to the non-binary case, and the scaling parameter α of the approximation is derived. The proposed estimation is then compared with numerical results, showing that it predicts well the slope of the block erasure rate vs. channel erasure probability.
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.
We analyze the asymptotic performance of non-binary spatially-coupled low-density parity-check (SC-LDPC) codes built on the general linear group, when the transmission takes place over the binary erasure channel. We propose an efficient method to derive an upper bound to the maximum a posteriori probability (MAP) threshold for nonbinary LDPC codes, and observe that the MAP performance of regular LDPC codes improves with the alphabet size. We then consider nonbinary SC-LDPC codes. We show that the same threshold saturation effect experienced by binary SC-LDPC codes occurs for the nonbinary codes, hence we conjecture that the BP threshold for large termination length approaches the MAP threshold of the underlying regular ensemble.
We consider communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) code and belief propagation (BP) decoding. The bit error probability for infinite block length is known by density evolution and it is well known that a difference between the bit error probability at finite iteration number for finite block length nnn and for infinite block length is asymptotically α/nα/nα/n, where ααα is a specific constant depending on the degree distribution, the iteration number and the erasure probability. Our main result is to derive an efficient algorithm for calculating ααα for regular ensembles. The approximation using ααα is accurate for (2,r)(2,r)(2,r)-regular ensembles even in small block length.
We consider communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) code and belief propagation (BP) decoding. Furthermore, a gap between the bit error probability after finite number of iterations for finite block length n and that for infinite block length is asymptotically α/n, where α denotes a speci..c constant determined by a degree distribution, a number of iterations and erasure probability. Our main result is to derive an ef..cient algorithm for calculating α for regular ensembles.
We investigate the finite-length scaling methodology for irregular LDPC code ensembles when transmission takes place over the binary erasure channel (BEC). We first show how the necessary computations, namely the covariance evolution and the computation of the finite-length shift, can be accomplished in the irregular case. We then investigate how the obtained approximation can be used to predict the performance of irregular code ensembles and to optimize the degree distributions for finite-length codes.
In this paper, we analyze the performance of finite-length generalized LDPC (GLDPC) block codes constructed from protographs when transmission takes place over the binary erasure channel (BEC). A generalized peeling decoder is proposed and we derive a system of differential equations that gives the expected evolution of the graph degree distribution during decoding. We then show that the finite-length performance of a GLDPC code can be estimated by means of a simple scaling law, where a single scaling parameter represents the finite-length properties of the code. We also show that, as we consider stronger component codes, both the asymptotic threshold and the finite-length scaling parameter are improved.