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:1211.6279

Optimal Rate Irregular LDPC Codes in Binary Erasure Channel

H. Tavakoli, M. Ahmadian, Mohammad Reza Peyghami

Published Nov 27, 2012• 1 citation
arXivHTMLPDF

Abstract

In this paper, we design the optimal rate capacity approaching irregular Low-Density Parity-Check code ensemble over Binary Erasure Channel, by using practical Semi-Definite Programming approach. Our method does not use any relaxation or any approximate solution unlike previous works. Our simulation results include two parts; first, we present some codes and their degree distribution functions that their rates are close to the capacity. Second, the maximum achievable rate behavior of codes in our method is illustrated through some figures.

DOI
10.48550/arxiv.1211.6279

Related papers

A family of LDPC codes for Binary Symmetric Channel with optimized rate

Hassan Tavakoli

In this paper, we present a family of irregular Low-Density Parity-Check (LDPC) code ensemble, which is designed for Binary Symmetric Channel (BSC) with maximum achievable rate. Our proposed method is based on solving the optimization problem of maximum achievable rate problem based on the related code-design conditions. In the proposed method, approximation is not used and optimization variables does not relaxed, which are used typically. Simulation results show some good codes close to the capacity.

Iranian Conference on Electrical Engineering•May 1, 2017•1 citation

An efficient complexity-optimizing LDPC code design for the binary erasure channel

Vahid Jamali, Yasser Karimian, Johannes B. Huber +1 more

The complexity-performance trade-off is a fundamental aspect of the design of low-density parity-check (LDPC) codes. In this paper, we consider LDPC codes for the binary erasure channel (BEC), use code rate for performance metric, and number of decoding iterations to achieve a certain residual erasure probability for complexity metric. The available complexity-optimizing problems in the literature for the BEC are either non-convex or belong to the class of semi-infinite problems which are computationally challenging to be solved. Hence, in this paper, we first propose a lower bound on the number of iterations for the BEC. Moreover, a simple but efficient utility function corresponding to the number of iterations is developed. Using this utility function, an optimization problem w.r.t. complexity is formulated to find complexity-optimized code degree distributions. We prove that the considered problem with the proposed utility function falls into the class of semi-definite programming (SDP) and thus, the global solution can be found efficiently using available SDP solvers. Numerical results reveal the superiority of the proposed code design compared to existing code designs from literature.

International Symposium on Turbo Codes and Iterative Information Processing•Aug 1, 2014•3 citations

On the Design of Fast Convergent LDPC Codes for the BEC: An Optimization Approach

Vahid Jamali, Yasser Karimian, Johannes B. Huber +1 more

The complexity-performance trade-off is a fundamental aspect of the design of low-density parity-check (LDPC) codes. In this paper, we consider LDPC codes for the binary erasure channel (BEC), use code rate for performance metric, and number of decoding iterations to achieve a certain residual erasure probability for complexity metric. We first propose a quite accurate approximation of the number of iterations for the BEC. Moreover, a simple but efficient utility function corresponding to the number of iterations is developed. Using the aforementioned approximation and the utility function, two optimization problems w.r.t. complexity are formulated to find the code degree distributions. We show that both optimization problems are convex. In particular, the problem with the proposed approximation belongs to the class of semi-infinite problems which are computationally challenging to be solved. However, the problem with the proposed utility function falls into the class of semi-definite programming (SDP) and thus, the global solution can be found efficiently using available SDP solvers. Numerical results reveal the superiority of the proposed code design compared to existing code designs from literature.

arXiv:1401.4337•IEEE Transactions on Communications•Dec 24, 2014•8 citations

Bounds on Achievable Rates of LDPC Codes Used Over the Binary Erasure Channel

Ohad Barak, David Burshtein, Meir Feder

We derive upper bounds on the maximum achievable rate of low-density parity-check (LDPC) codes used over the binary erasure channel (BEC) under Gallager's decoding algorithm, given their right-degree distribution. We demonstrate the bounds on the ensemble of right-regular LDPC codes and compare them with an explicit left-degree distribution constructed from the given right degree.

IEEE Transactions on Information Theory•Sep 28, 2004•20 citations

Performance of low-density parity-check codes with linear minimum distance

Hossein Pishro-Nik, Faramarz Fekri

This correspondence studies the performance of the iterative decoding of low-density parity-check (LDPC) code ensembles that have linear typical minimum distance and stopping set size. We first obtain a lower bound on the achievable rates of these ensembles over memoryless binary-input output-symmetric channels. We improve this bound for the binary erasure channel. We also introduce a method to construct the codes meeting the lower bound for the binary erasure channel. Then, we give upper bounds on the rate of LDPC codes with linear minimum distance when their right degree distribution is fixed. We compare these bounds to the previously derived upper bounds on the rate when there is no restriction on the code ensemble.

IEEE Transactions on Information Theory•Dec 28, 2005•13 citations

Design of LDPC codes for the q-ary partial erasure channel

Rami Cohen, Yuval Cassuto

In this paper, we discuss practical design of low-density parity-check (LDPC) codes for the q-ary partial erasure channel (QPEC). This channel is an extension of the binary erasure channel (BEC), where partial information on the output is available. We provide a linear programming (LP) optimization for the design of good degree distributions, and compare our code design results to codes obtained using an LP optimization formulated for the BEC. We show superior performance in terms of code rate and complexity, when designing an LDPC code for a desired decoding threshold.

IEEE Information Theory Workshop (ITW)•Apr 1, 2015•0 citations
In this paper, we design the optimal rate capacity approaching irregular Low-Density Parity-Check code ensemble over Binary Erasure Channel, by using practical Semi-Definite Programming approach. Our method does not use any relaxation or any approximate solution unlike previous works. Our simulation results include two parts; first, we present some codes and their degree distribution functions that their rates are close to the capacity. Second, the maximum achievable rate behavior of codes in our method is illustrated through some figures.
In this paper, we present a family of irregular Low-Density Parity-Check (LDPC) code ensemble, which is designed for Binary Symmetric Channel (BSC) with maximum achievable rate. Our proposed method is based on solving the optimization problem of maximum achievable rate problem based on the related code-design conditions. In the proposed method, approximation is not used and optimization variables does not relaxed, which are used typically. Simulation results show some good codes close to the capacity.
The complexity-performance trade-off is a fundamental aspect of the design of low-density parity-check (LDPC) codes. In this paper, we consider LDPC codes for the binary erasure channel (BEC), use code rate for performance metric, and number of decoding iterations to achieve a certain residual erasure probability for complexity metric. The available complexity-optimizing problems in the literature for the BEC are either non-convex or belong to the class of semi-infinite problems which are computationally challenging to be solved. Hence, in this paper, we first propose a lower bound on the number of iterations for the BEC. Moreover, a simple but efficient utility function corresponding to the number of iterations is developed. Using this utility function, an optimization problem w.r.t. complexity is formulated to find complexity-optimized code degree distributions. We prove that the considered problem with the proposed utility function falls into the class of semi-definite programming (SDP) and thus, the global solution can be found efficiently using available SDP solvers. Numerical results reveal the superiority of the proposed code design compared to existing code designs from literature.
The complexity-performance trade-off is a fundamental aspect of the design of low-density parity-check (LDPC) codes. In this paper, we consider LDPC codes for the binary erasure channel (BEC), use code rate for performance metric, and number of decoding iterations to achieve a certain residual erasure probability for complexity metric. We first propose a quite accurate approximation of the number of iterations for the BEC. Moreover, a simple but efficient utility function corresponding to the number of iterations is developed. Using the aforementioned approximation and the utility function, two optimization problems w.r.t. complexity are formulated to find the code degree distributions. We show that both optimization problems are convex. In particular, the problem with the proposed approximation belongs to the class of semi-infinite problems which are computationally challenging to be solved. However, the problem with the proposed utility function falls into the class of semi-definite programming (SDP) and thus, the global solution can be found efficiently using available SDP solvers. Numerical results reveal the superiority of the proposed code design compared to existing code designs from literature.
This correspondence studies the performance of the iterative decoding of low-density parity-check (LDPC) code ensembles that have linear typical minimum distance and stopping set size. We first obtain a lower bound on the achievable rates of these ensembles over memoryless binary-input output-symmetric channels. We improve this bound for the binary erasure channel. We also introduce a method to construct the codes meeting the lower bound for the binary erasure channel. Then, we give upper bounds on the rate of LDPC codes with linear minimum distance when their right degree distribution is fixed. We compare these bounds to the previously derived upper bounds on the rate when there is no restriction on the code ensemble.
In this paper, we discuss practical design of low-density parity-check (LDPC) codes for the q-ary partial erasure channel (QPEC). This channel is an extension of the binary erasure channel (BEC), where partial information on the output is available. We provide a linear programming (LP) optimization for the design of good degree distributions, and compare our code design results to codes obtained using an LP optimization formulated for the BEC. We show superior performance in terms of code rate and complexity, when designing an LDPC code for a desired decoding threshold.