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

Applied science and technology

An improved PEG algorithm for construction of LDPC codes

WU Yu-ping

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

Progressive-edge-growth(PEG) algorithm is much effective for constructing LDPC codes with short and intermediate block lengths.However,the complexity of the codes produced by such algorithm is directly proportional to the square of code length,which hinders the development of LDPC code's implementation.To solve such a problem,this paper presents an improved PEG algorithm which can be encoded by the iterative encoding algorithm with linear coding complexity.The simulation results indicated that,for MSK modulation,the obvious advantage of the presented method is its low complexity in hardware implementation although the error-correcting capability of irregular LDPC codes constructed by the proposed methods is basically identical to that of the codes constructed by the PEG algorithm.

Related papers

A Kind of Improved PEG Algorithm of Q-Ary LDPC Codes

Ning Ning Tong, Dan Feng Zhao, Yu Ping Wu

Progressive-edge-growth (PEG) algorithm is one of the best known methods for constructing LDPC codes at short and intermediate block lengths, however, the codes directly designed by such algorithm has high encoding complexity, especially for q-ary LDPC codes, encoding complexity increases with the increase of q value rapidly, which hinder the development of q-ary LDPC code’s implementation seriously. To such problem, the paper presents a improved method based on PEG algorithm which can be encoded by the iterative encoding algorithm with the liner operation complexity. The simulation results indicate: Though the error correcting capability of irregular q-ary LDPC codes constructed by the proposed methods in the paper is basically identical with the codes constructed by the PEG algorithm, but the powerful advantage makes it be easily implemented by the hardware .

Applied Mechanics and Materials•Oct 1, 2011•1 citation

A Method for Constructing Quasi-Cycle Extension LDPC Codes with Low Encoding Complexity

Wei Li

Progressive-Edge-Growth(PEG) algorithm is an efficient method for constructing LDPC codes with short and intermediate block lengths.However,the complexity of codes produced directly by this algorithm is proportional to quadratic length of the codes,which restricts the implementation of the LDPC codes.To solve the problem,a method was proposed for constructing quasi-cycle extension LDPC codes with low encoding complexity and good error performance.Based on PEG algorithm,a base matrix with an approximate lower triangular was constructed,then all its elements were replaced by circulation permutations.The new method could eliminate the short cycles effectively without changing the degree distribution fraction of the basic matrix.The simulation results show that: compared with LDPC codes generated by PEG algorithm,the LDPC codes presented here have lower encoding complexity and better error performance,which is easy for implementation with hardware.

Electronics Optics & Control•Jan 1, 2012•1 citation

New PEG algorithm with low error floor for construction of irregular LDPC codes

Feijin Shi, Shuangshuang Han

The progressive-edge-growth (PEG) algorithm for constructing Tanner graphs with large girth by progressively establishing edges/connections between symbol nodes and check nodes in an edge-by-edge way is highly known to construct low-density parity-check (LDPC) codes at short block lengths for achieving good performance. This paper proposed an improved PEG construction for irregular codes, which heuristically selects good codes from random graphs for short block lengths. The simulation results are given to demonstrate that the proposed algorithm gians better BER performance for high signal-to-noise (SNR) ratios without performance loss for low-SNR region, i.e. low error floor.

IEEE International Conference on Computer and Communications (ICCC)•Oct 1, 2015•1 citation

Improved progressive edge-growth algorithm for fast encodable LDPC codes

Xueqin Jiang, Moon Ho Lee, Jinpeng Qi

The progressive edge-growth (PEG) algorithm is known to construct low-density parity-check (LDPC) codes at finite code lengths with large girths by establishing edges between symbol and check nodes in an edge-by-edge manner. The linear-encoding PEG (LPEG) algorithm, a simple variation of the PEG algorithm, can be applied to generate linear time encodable LDPC codes whose m parity bits p1, p2, ..., p m are computed recursively in m steps. In this article, we propose modifications of the LPEG algorithm to construct LDPC codes whose number of encoding steps is independent of the code length. The maximum degree of the symbol nodes in the Tanner graph is denoted by ; The m parity bits of the proposed LDPC codes are divided into subgroups and can be computed in only steps. Since , the number of encoding steps can be significantly reduced. It has also been proved that the PEG codes and the codes proposed in this article have similar lower bound on girth. Simulation results showed that the proposed codes perform very well over the AWGN channel with an iterative decoding.

EURASIP Journal on Wireless Communications and Networking•May 21, 2012•7 citations

An improved algorithm for constructing QC-LDPC codes based on the PEG algorithm

Zhiyong Fan, Weibo Zhang, Xingcheng Liu +1 more

The Progressive edge-growth (PEG) algorithm was proven to be a simple and effective approach in designing Low-density parity-check (LDPC) codes. However, the Tanner graph constructed with the PEG algorithm is non-structured, which leads to random distributions of the positions of 1's in the corresponding parity-check matrix. In this paper, an improved algorithm based on the PEG algorithm for constructing quasi-cyclic (QC) LDPC codes is proposed. The proposed algorithm can eliminate short cycles efficiently and gain low error-floors. What is more important, the proposed QC-LDPC codes construction method is hardware-friendly because of its quasi-cyclic structure. Our simulation results demonstrate that the codes constructed with the proposed algorithm has better performance than the PEG algorithm over the additive white Gaussian noise (AWGN) channel and Rayleigh flat fading channel.

International Conference on Communications and Networking in China (ChinaCom)•Aug 1, 2009•5 citations

Regular and irregular progressive edge-growth tanner graphs

Xiao-Yu Hu, Evangelos S. Eleftheriou, Donald M. Arnold

We propose a general method for constructing Tanner graphs having a large girth by establishing edges or connections between symbol and check nodes in an edge-by-edge manner, called progressive edge-growth (PEG) algorithm. Lower bounds on the girth of PEG Tanner graphs and on the minimum distance of the resulting low-density parity-check (LDPC) codes are derived in terms of parameters of the graphs. Simple variations of the PEG algorithm can also be applied to generate linear-time encodeable LDPC codes. Regular and irregular LDPC codes using PEG Tanner graphs and allowing symbol nodes to take values over GF(q) (q>2) are investigated. Simulation results show that the PEG algorithm is a powerful algorithm to generate good short-block-length LDPC codes.

IEEE Transactions on Information Theory•Jan 1, 2005•1,489 citations
Progressive-edge-growth(PEG) algorithm is much effective for constructing LDPC codes with short and intermediate block lengths.However,the complexity of the codes produced by such algorithm is directly proportional to the square of code length,which hinders the development of LDPC code's implementation.To solve such a problem,this paper presents an improved PEG algorithm which can be encoded by the iterative encoding algorithm with linear coding complexity.The simulation results indicated that,for MSK modulation,the obvious advantage of the presented method is its low complexity in hardware implementation although the error-correcting capability of irregular LDPC codes constructed by the proposed methods is basically identical to that of the codes constructed by the PEG algorithm.
Progressive-edge-growth (PEG) algorithm is one of the best known methods for constructing LDPC codes at short and intermediate block lengths, however, the codes directly designed by such algorithm has high encoding complexity, especially for q-ary LDPC codes, encoding complexity increases with the increase of q value rapidly, which hinder the development of q-ary LDPC code’s implementation seriously. To such problem, the paper presents a improved method based on PEG algorithm which can be encoded by the iterative encoding algorithm with the liner operation complexity. The simulation results indicate: Though the error correcting capability of irregular q-ary LDPC codes constructed by the proposed methods in the paper is basically identical with the codes constructed by the PEG algorithm, but the powerful advantage makes it be easily implemented by the hardware .
Progressive-Edge-Growth(PEG) algorithm is an efficient method for constructing LDPC codes with short and intermediate block lengths.However,the complexity of codes produced directly by this algorithm is proportional to quadratic length of the codes,which restricts the implementation of the LDPC codes.To solve the problem,a method was proposed for constructing quasi-cycle extension LDPC codes with low encoding complexity and good error performance.Based on PEG algorithm,a base matrix with an approximate lower triangular was constructed,then all its elements were replaced by circulation permutations.The new method could eliminate the short cycles effectively without changing the degree distribution fraction of the basic matrix.The simulation results show that: compared with LDPC codes generated by PEG algorithm,the LDPC codes presented here have lower encoding complexity and better error performance,which is easy for implementation with hardware.
The progressive-edge-growth (PEG) algorithm for constructing Tanner graphs with large girth by progressively establishing edges/connections between symbol nodes and check nodes in an edge-by-edge way is highly known to construct low-density parity-check (LDPC) codes at short block lengths for achieving good performance. This paper proposed an improved PEG construction for irregular codes, which heuristically selects good codes from random graphs for short block lengths. The simulation results are given to demonstrate that the proposed algorithm gians better BER performance for high signal-to-noise (SNR) ratios without performance loss for low-SNR region, i.e. low error floor.
The progressive edge-growth (PEG) algorithm is known to construct low-density parity-check (LDPC) codes at finite code lengths with large girths by establishing edges between symbol and check nodes in an edge-by-edge manner. The linear-encoding PEG (LPEG) algorithm, a simple variation of the PEG algorithm, can be applied to generate linear time encodable LDPC codes whose m parity bits p1, p2, ..., p m are computed recursively in m steps. In this article, we propose modifications of the LPEG algorithm to construct LDPC codes whose number of encoding steps is independent of the code length. The maximum degree of the symbol nodes in the Tanner graph is denoted by ; The m parity bits of the proposed LDPC codes are divided into subgroups and can be computed in only steps. Since , the number of encoding steps can be significantly reduced. It has also been proved that the PEG codes and the codes proposed in this article have similar lower bound on girth. Simulation results showed that the proposed codes perform very well over the AWGN channel with an iterative decoding.
The Progressive edge-growth (PEG) algorithm was proven to be a simple and effective approach in designing Low-density parity-check (LDPC) codes. However, the Tanner graph constructed with the PEG algorithm is non-structured, which leads to random distributions of the positions of 1's in the corresponding parity-check matrix. In this paper, an improved algorithm based on the PEG algorithm for constructing quasi-cyclic (QC) LDPC codes is proposed. The proposed algorithm can eliminate short cycles efficiently and gain low error-floors. What is more important, the proposed QC-LDPC codes construction method is hardware-friendly because of its quasi-cyclic structure. Our simulation results demonstrate that the codes constructed with the proposed algorithm has better performance than the PEG algorithm over the additive white Gaussian noise (AWGN) channel and Rayleigh flat fading channel.
We propose a general method for constructing Tanner graphs having a large girth by establishing edges or connections between symbol and check nodes in an edge-by-edge manner, called progressive edge-growth (PEG) algorithm. Lower bounds on the girth of PEG Tanner graphs and on the minimum distance of the resulting low-density parity-check (LDPC) codes are derived in terms of parameters of the graphs. Simple variations of the PEG algorithm can also be applied to generate linear-time encodeable LDPC codes. Regular and irregular LDPC codes using PEG Tanner graphs and allowing symbol nodes to take values over GF(q) (q>2) are investigated. Simulation results show that the PEG algorithm is a powerful algorithm to generate good short-block-length LDPC codes.