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)

On the probabilistic computation algorithm for the minimum-size stopping sets of LDPC codes

Masanori Hirotomo, Yoshiho Konishi, Masakatu Morii

Published Jul 1, 2008• 9 citations
Publisher

Abstract

On the binary erasure channel, the performance of LDPC codes decoded by iterative algorithms is estimated by small-size stopping sets. We have proposed a probabilistic algorithm for computing the minimum size of stopping sets of LDPC codes. In this paper, we analyze the probability and the complexity of finding the minimum-size stopping sets, and give an error probability of determining the minimum size of stopping sets after processing our algorithm. Additionally, we show the numerical results of computing the minimum size of stopping sets of several LDPC codes. In these result, we could compute the minimum size of stopping sets with high reliability.

DOI
10.1109/isit.2008.4594995

Related papers

A probabilistic algorithm for finding the minimum-size stopping sets of LDPC codes

Masanori Hirotomo, Yoshiho Konishi, Masakatu Morii

On the binary erasure channel, the performance of LDPC codes decoded by iterative algorithms is dominated by small-size stopping sets, especially minimal stopping sets. In this paper, we propose a probabilistic algorithm for computing the minimum size of stopping sets of LDPC codes. In this algorithm, we generate efficiently small-size stopping sets by using the relation between small-size stopping sets and low-weight codewords. In numerical experiments, we could compute the minimum size of stopping sets of LDPC codes of length about 500, 1000 and 5000 with high reliability, and could find smaller stopping sets than that found by conventional methods.

IEEE Information Theory Workshop (ITW)•May 1, 2008•7 citations

On the probabilistic computation of the stopping redundancy of LDPC codes

Masanori Hirotomo, Yoshiho Konishi, Masakatu Morii

On the binary erasure channel (BEC), the performance of low-density parity-check (LDPC) codes decoded by iterative algorithms is estimated by the small stopping sets in the codes. The size of smallest stopping set is called the stopping distance. Since it depends on the structure of parity-check matrix for the code, we can construct the parity-check matrix by adding dependent rows so that the stopping distance is equal to the minimum distance. The stopping redundancy is defined as the smallest number of rows in such a parity-check matrix. In this paper, we propose a probabilistic algorithm for computing the stopping redundancy of LDPC codes. Additionally, we show numerical results of computing the stopping redundancy of (155,64), (504,252) and (1008,504) LDPC codes.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2009•1 citation

Finding Small Stopping Sets in the Tanner Graphs of LDPC Codes

Gerd Richter

The performance of low-density parity-check (LDPC) codes over the binary erasure channel for a low erasure probability is limited by small stopping sets. The frame error rate over the additive white Gaussian noise (AWGN) channel for a high signal-to-noise ratio is limited by small trapping sets and by the minimum distance of the LDPC code, which is equal to the codeword with the minimal Hamming weight. In this paper, we present a simple and fast algorithm based on the error impulse method to find small stopping sets in the Tanner graphs of LDPC codes. Since a codeword with small Hamming weight can be represented by a special stopping set, the algorithm can also be used to find the minimum distance of LDPC codes. Furthermore, we use the size of the small stopping sets and the minimum distance of the code to calculate asymptotic performance bounds for LDPC codes transmitted over the binary erasure and the AWGN channel, respectively and compare the bounds with simulations. 1

•Apr 3, 2006•27 citations

An Iterative Scheme of Stopping Set Enlargement in The Design of Short-Length Irregular LDPC Codes

Jingyu Kang, Pingyi Fan, Zhigang Cao

Abstract: Small stopping sets have been proved to be harmful to the error floor performance of a finite-length irregular low-density parity-check (LDPC) code over the binary erasure channel (BEC). On the additive white gaussian noise (AWGN) channel, small stopping sets are expected to have a similar effect. This paper proposes an algorithm that iteratively removes the small-stopping-set-inducing patterns from the graph of a randomly generated irregular LDPC code by means of node exchange, aiming at enlarging the average size of stopping sets in this code. Computer simulation results show that the short-length LDPC codes after our processing achieve a considerable performance improvement in the low-BER region compared to the randomly generated codes. Key words: Error floor, irregular LDPC codes, iterative processing, small stopping set 1

•Jan 1, 2005•1 citation

An Efficient Algorithm to Find All Small-Size Stopping Sets of Low-Density Parity-Check Matrices

Eirik Rosnes, Øyvind Ytrehus

In this work, we introduce an efficient algorithm to find all stopping sets, of size less than some threshold, of a fixed low-density parity-check (LDPC) matrix. The solution is inspired by the algorithm proposed by Rosnes and Ytrehus in 2005 to find an exhaustive list of all small-size turbo stopping sets in a turbo code. The efficiency of the proposed algorithm is demonstrated by several numerical examples. For instance, we have applied the algorithm to the well-known (3, 5)-regular (155, 64) Tanner code and found all stopping sets of size at most 18 in about 1 min on a standard desktop computer. Also, we have verified that the minimum stopping set size of the (4896, 2474) Ramanujan-Margulis code is indeed 24, and that the corresponding multiplicity is exactly 204. Furthermore, we have applied the algorithm to the IEEE 802.16e LDPC codes and determined the minimum stopping set size and the corresponding multiplicity exactly for these codes. Finally, as an application, we present a greedy algorithm to find a small number of redundant parity checks to add to the original parity-check matrix in order to remove all stopping sets in the corresponding Tanner graph of size less than the minimum distance. An extensive case study of the (155, 64) Tanner code illustrates the usefulness of the algorithm, and we present a 110 times 155 redundant parity-check matrix for this code with no stopping sets of size less than the minimum distance. Simulation results of iterative decoding on the binary erasure channel show performance improvements for low-to-medium erasure probabilities when this redundant parity-check matrix is used for decoding.

IEEE Transactions on Information Theory•Aug 24, 2009•63 citations

Approximate examination of trapping sets of LDPC codes using the probabilistic algorithm

Masanori Hirotomo, Yoshiho Konishi, Masakatu Morii

The performance of LDPC codes decoded by iterative algorithms depends on the structural properties of their underlying Tanner graphs. For general memoryless channels, error patterns dominating the bit and frame error probabilities at the error floor region are termed trapping sets. In this paper, we propose an effective method for finding small-size trapping sets of LDPC codes. In the proposed method, a probabilistic algorithm to find low-weight codewords is applied to finding small trapping sets of LDPC codes. Furthermore, we show numerical results of examining small trapping sets of (504, 252) and (1008, 504) LDPC codes.

International Symposium on Information Theory and its Applications•Dec 1, 2008•14 citations
On the binary erasure channel, the performance of LDPC codes decoded by iterative algorithms is estimated by small-size stopping sets. We have proposed a probabilistic algorithm for computing the minimum size of stopping sets of LDPC codes. In this paper, we analyze the probability and the complexity of finding the minimum-size stopping sets, and give an error probability of determining the minimum size of stopping sets after processing our algorithm. Additionally, we show the numerical results of computing the minimum size of stopping sets of several LDPC codes. In these result, we could compute the minimum size of stopping sets with high reliability.
On the binary erasure channel, the performance of LDPC codes decoded by iterative algorithms is dominated by small-size stopping sets, especially minimal stopping sets. In this paper, we propose a probabilistic algorithm for computing the minimum size of stopping sets of LDPC codes. In this algorithm, we generate efficiently small-size stopping sets by using the relation between small-size stopping sets and low-weight codewords. In numerical experiments, we could compute the minimum size of stopping sets of LDPC codes of length about 500, 1000 and 5000 with high reliability, and could find smaller stopping sets than that found by conventional methods.
On the binary erasure channel (BEC), the performance of low-density parity-check (LDPC) codes decoded by iterative algorithms is estimated by the small stopping sets in the codes. The size of smallest stopping set is called the stopping distance. Since it depends on the structure of parity-check matrix for the code, we can construct the parity-check matrix by adding dependent rows so that the stopping distance is equal to the minimum distance. The stopping redundancy is defined as the smallest number of rows in such a parity-check matrix. In this paper, we propose a probabilistic algorithm for computing the stopping redundancy of LDPC codes. Additionally, we show numerical results of computing the stopping redundancy of (155,64), (504,252) and (1008,504) LDPC codes.
The performance of low-density parity-check (LDPC) codes over the binary erasure channel for a low erasure probability is limited by small stopping sets. The frame error rate over the additive white Gaussian noise (AWGN) channel for a high signal-to-noise ratio is limited by small trapping sets and by the minimum distance of the LDPC code, which is equal to the codeword with the minimal Hamming weight. In this paper, we present a simple and fast algorithm based on the error impulse method to find small stopping sets in the Tanner graphs of LDPC codes. Since a codeword with small Hamming weight can be represented by a special stopping set, the algorithm can also be used to find the minimum distance of LDPC codes. Furthermore, we use the size of the small stopping sets and the minimum distance of the code to calculate asymptotic performance bounds for LDPC codes transmitted over the binary erasure and the AWGN channel, respectively and compare the bounds with simulations. 1
Abstract: Small stopping sets have been proved to be harmful to the error floor performance of a finite-length irregular low-density parity-check (LDPC) code over the binary erasure channel (BEC). On the additive white gaussian noise (AWGN) channel, small stopping sets are expected to have a similar effect. This paper proposes an algorithm that iteratively removes the small-stopping-set-inducing patterns from the graph of a randomly generated irregular LDPC code by means of node exchange, aiming at enlarging the average size of stopping sets in this code. Computer simulation results show that the short-length LDPC codes after our processing achieve a considerable performance improvement in the low-BER region compared to the randomly generated codes. Key words: Error floor, irregular LDPC codes, iterative processing, small stopping set 1
In this work, we introduce an efficient algorithm to find all stopping sets, of size less than some threshold, of a fixed low-density parity-check (LDPC) matrix. The solution is inspired by the algorithm proposed by Rosnes and Ytrehus in 2005 to find an exhaustive list of all small-size turbo stopping sets in a turbo code. The efficiency of the proposed algorithm is demonstrated by several numerical examples. For instance, we have applied the algorithm to the well-known (3, 5)-regular (155, 64) Tanner code and found all stopping sets of size at most 18 in about 1 min on a standard desktop computer. Also, we have verified that the minimum stopping set size of the (4896, 2474) Ramanujan-Margulis code is indeed 24, and that the corresponding multiplicity is exactly 204. Furthermore, we have applied the algorithm to the IEEE 802.16e LDPC codes and determined the minimum stopping set size and the corresponding multiplicity exactly for these codes. Finally, as an application, we present a greedy algorithm to find a small number of redundant parity checks to add to the original parity-check matrix in order to remove all stopping sets in the corresponding Tanner graph of size less than the minimum distance. An extensive case study of the (155, 64) Tanner code illustrates the usefulness of the algorithm, and we present a 110 times 155 redundant parity-check matrix for this code with no stopping sets of size less than the minimum distance. Simulation results of iterative decoding on the binary erasure channel show performance improvements for low-to-medium erasure probabilities when this redundant parity-check matrix is used for decoding.
The performance of LDPC codes decoded by iterative algorithms depends on the structural properties of their underlying Tanner graphs. For general memoryless channels, error patterns dominating the bit and frame error probabilities at the error floor region are termed trapping sets. In this paper, we propose an effective method for finding small-size trapping sets of LDPC codes. In the proposed method, a probabilistic algorithm to find low-weight codewords is applied to finding small trapping sets of LDPC codes. Furthermore, we show numerical results of examining small trapping sets of (504, 252) and (1008, 504) LDPC codes.