Threshold Values and Convergence Properties of Majority-Based Algorithms for Decoding Regular Low-Density Parity-Check Codes

Zarrinkhat, P.; Banihashemi, Amir H.

doi:10.1109/tcomm.2004.838738

Cited by 36 publications

(20 citation statements)

References 14 publications

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“…Codes 2-5 are taken from [10]. Codes 2, 3 and 5 have variable node and check node degrees (3,6), (4,36) and (3,6), respectively. Code 4 is constructed by the progressive-edge-growth (PEG) algorithm [11] and has a variable node degree 3.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Codes 7 and 8 both have variable node degree 5 and check node degree 6. Codes 7 and 8 are decoded by MB algorithm of order zero (MB0), while all the other codes are decoded by GA. For the degree distributions of Codes 7 and 8, MB0 has a better threshold than GA algorithm [3]. The Tanner graphs of the codes do not have cycles of length 4.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…No n FER P(J) + 5 lEilestEi(1 6)n-i + 5 pi, (3) i= J+I i=No+l algorithm, the complexity of enumerating cycles of length 1 for a length n LDPC code with variable node degree d, and check node degree d, is only 0 (rdd dc) F1), where [xl is the smallest integer which is greater than or equal to x. The complexity of Step 2 is thus negligible compared to that of Step 3 which contributes the most to the total computational complexity of Algorithm (1).…”

Section: Modified Estimation Equationsmentioning

confidence: 99%

“…In this paper, we focus on hard-decision iterative decoding algorithms. Examples of hard-decision iterative decoding algorithms are Gallager's algorithms A (GA) and B (GB) [1], their variants [2] and majority-based (MB) algorithms [3]. The main advantage of hard-decision algorithms is their simplicity which makes them fast and easy to implement.…”

Section: Introductionmentioning

confidence: 99%

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Error Rate Estimation of Finite-Length Low-Density Parity-Check Codes on Binary Symmetric Channels Using Cycle Enumeration

Xiao

Banihashemi

2007

2007 IEEE International Symposium on Information Theory

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The performance of low-density parity-check (LDPC) codes decoded by hard-decision iterative decoding algorithms can be accurately estimated if the weight J and the number IE of the smallest error patterns that cannot be corrected by the decoder are known. To obtain J and IEj , one would need to perform the direct enumeration of error patterns with weight i < J. The complexity of enumeration increases exponentially with J, essentially as ni, where n is the code block length. In this paper, we approximate J and IEj by enumerating and testing the error patterns that are subsets of short cycles in the code's Tanner graph. This reduces the computational complexity by several orders of magnitude compared to direct enumeration, making it possible to estimate the error rates for almost any practical LDPC code. To obtain the error rate estimates, we propose an algorithm that progressively improves the estimates as larger cycles are enumerated. Through a number of examples, we demonstrate that the proposed method can accurately estimate both the bit error rate (BER) and the frame error rate (FER) of regular and irregular LDPC codes decoded by a variety of hard-decision iterative decoding algorithms.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Simulation Resultsmentioning

confidence: 99%

Section: Modified Estimation Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Error Rate Estimation of Finite-Length Low-Density Parity-Check Codes on Binary Symmetric Channels Using Cycle Enumeration

Xiao

Banihashemi

2007

2007 IEEE International Symposium on Information Theory

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“…Such algorithms, which are referred to as hard-decision iterative algorithms, are the subject of this paper. Examples are the so-called Gallager algorithms A (GA) and B (GB) [1], [2], [3], their variants [4] and majoritybased (MB) algorithms [5].…”

Section: Introductionmentioning

confidence: 99%

Estimation of Bit and Frame Error Rates of Low-Density Parity-Check Codes on Binary Symmetric Channels

Xiao

Banihashemi

2007

2007 10th Canadian Workshop on Information Theory (CWIT)

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A method for estimating the performance of low-density parity-check (LDPC) codes decoded by hard-decision iterative decoding algorithms on binary symmetric channels (BSC) is proposed. Based on the enumeration of the smallest weight error patterns that cannot be all corrected by the decoder, this method estimates both the frame error rate (FER) and the bit error rate (BER) of a given LDPC code with very good precision for all crossover probabilities of practical interest. Through a number of examples, we show that the proposed method can be effectively applied to both regular and irregular LDPC codes and to a variety of hard-decision iterative decoding algorithms. Compared with the conventional Monte Carlo simulation, the proposed method has a much smaller computational complexity, particularly for lower error rates. Index TermsLow-density parity-check (LDPC) codes, finite length LDPC codes, iterative decoding, hard-decision decoding algorithms, binary symmetric channels (BSC), error floor.

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QC-LDPC Code-Based Cryptography

Baldi

2014

SpringerBriefs in Electrical and Computer Engineering

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The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein.

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Threshold Values and Convergence Properties of Majority-Based Algorithms for Decoding Regular Low-Density Parity-Check Codes

Cited by 36 publications

References 14 publications

Error Rate Estimation of Finite-Length Low-Density Parity-Check Codes on Binary Symmetric Channels Using Cycle Enumeration

Error Rate Estimation of Finite-Length Low-Density Parity-Check Codes on Binary Symmetric Channels Using Cycle Enumeration

Estimation of Bit and Frame Error Rates of Low-Density Parity-Check Codes on Binary Symmetric Channels

QC-LDPC Code-Based Cryptography

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