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)

A Method for Constructing LDPC Codes with Low Error Floor

Eran Sharon, Simon N. Litsyn

Published Jul 1, 2006• 4 citations
Publisher

Abstract

This paper describes a novel progressive edge growth (PEG) algorithm for constructing LDPC codes with minimized block error probability over the binary erasure channel (BEC). The constructed codes provide superior performance and lower error floor compared to codes generated by previously known algorithms. Furthermore, an upper bound on the expected block error probability in the error floor region of the generated code is derived

DOI
10.1109/isit.2006.262096

Related papers

Constructing LDPC codes by error minimization progressive edge growth

E. Sharon, Simon N. Litsyn

A novel approach to constructing Tanner graphs using progressive edge growth (PEG) is introduced. It yields LDPC codes providing minimized block error probability in Binary Erasure Channels (BEC). The constructed codes exhibit superior performance over codes generated by previously known algorithms, both for BEC and AWGN channels. Furthermore, an upper bound on the expected block error probability in the error floor region of the generated codes is derived. This allows analytical prediction of the codes' error floor performance. Finally, the method is generalized for generating simple in implementation LDPC codes based on lifted graphs.

IEEE Transactions on Communications•Mar 1, 2008•24 citations

An Improvement of the PEG Algorithm for LDPC Codes in the Waterfall Region

Gerd Richter

There exist many different algorithms to construct good low-density parity-check (LDPC) codes. To maximize the girth of the bipartite graph, which represents the LDPC code, the progressive edge-growth (PEG) algorithm was introduced. This construction methods leads for irregular LDPC codes to a lower error floor, but also to a performance loss in the waterfall region compared with randomly constructed LDPC codes. In this paper, we describe a modification of the PEG algorithm that improves the performance in the waterfall region. Furthermore, this modified PEG algorithm yields codes with lower error floors and a slightly better performance in the waterfall region than randomly constructed LDPC codes

IEEE EUROCON - International Conference on Computer as a Tool (EUROCON)•Jan 1, 2005•9 citations

Generating Good Finite Length LDPC Codes Based on Lifted Graphs

Eran Sharon, Simon N. Litsyn

A method for generating good finite length Low-Density Parity-Check (LDPC) codes based on lifted graphs is described.The codes are constructed using a progressive edge growth technique by taking into account the influence that every introduced edge has on the error floor and waterfall threshold of the code.The generated code can be tailored according to prescribed specification, achieving the desirable error floor versus waterfall threshold trade-off.For the constructed codes, an analytical upper bound on the expected block error probability of the code over the Binary Erasure Channel (BEC) in the error floor region and an asymptotic Density Evolution (DE) waterfall threshold are obtained.

•Sep 27, 2006•0 citations

A PEG Construction of Finite-Length LDPC Codes with Low Error Floor

Sina Khazraie, Reza Asvadi, Amir H. Banihashemi

The progressive-edge-growth (PEG) algorithm of Hu et al. is modified to improve the error floor performance of the constructed low-density parity-check (LDPC) codes. To improve the error floor, the original PEG algorithm is equipped with an efficient algorithm to find the dominant elementary trapping sets (ETS's) that are added to the Tanner graph of the under-construction code by the addition of each variable node and its adjacent edges. The aim is to select the edges, among the candidates available at each step of the original PEG algorithm, that prevent the creation of dominant ETS's. The proposed method is applicable to both regular and irregular variable node degree distributions. Simulation results are presented to demonstrate the superior ETS distribution and error floor performance of the constructed codes compared to similar codes constructed by the original and other modifications of the PEG algorithm.

IEEE Communications Letters•Jun 5, 2012•43 citations

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

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
This paper describes a novel progressive edge growth (PEG) algorithm for constructing LDPC codes with minimized block error probability over the binary erasure channel (BEC). The constructed codes provide superior performance and lower error floor compared to codes generated by previously known algorithms. Furthermore, an upper bound on the expected block error probability in the error floor region of the generated code is derived
A novel approach to constructing Tanner graphs using progressive edge growth (PEG) is introduced. It yields LDPC codes providing minimized block error probability in Binary Erasure Channels (BEC). The constructed codes exhibit superior performance over codes generated by previously known algorithms, both for BEC and AWGN channels. Furthermore, an upper bound on the expected block error probability in the error floor region of the generated codes is derived. This allows analytical prediction of the codes' error floor performance. Finally, the method is generalized for generating simple in implementation LDPC codes based on lifted graphs.
There exist many different algorithms to construct good low-density parity-check (LDPC) codes. To maximize the girth of the bipartite graph, which represents the LDPC code, the progressive edge-growth (PEG) algorithm was introduced. This construction methods leads for irregular LDPC codes to a lower error floor, but also to a performance loss in the waterfall region compared with randomly constructed LDPC codes. In this paper, we describe a modification of the PEG algorithm that improves the performance in the waterfall region. Furthermore, this modified PEG algorithm yields codes with lower error floors and a slightly better performance in the waterfall region than randomly constructed LDPC codes
A method for generating good finite length Low-Density Parity-Check (LDPC) codes based on lifted graphs is described.The codes are constructed using a progressive edge growth technique by taking into account the influence that every introduced edge has on the error floor and waterfall threshold of the code.The generated code can be tailored according to prescribed specification, achieving the desirable error floor versus waterfall threshold trade-off.For the constructed codes, an analytical upper bound on the expected block error probability of the code over the Binary Erasure Channel (BEC) in the error floor region and an asymptotic Density Evolution (DE) waterfall threshold are obtained.
The progressive-edge-growth (PEG) algorithm of Hu et al. is modified to improve the error floor performance of the constructed low-density parity-check (LDPC) codes. To improve the error floor, the original PEG algorithm is equipped with an efficient algorithm to find the dominant elementary trapping sets (ETS's) that are added to the Tanner graph of the under-construction code by the addition of each variable node and its adjacent edges. The aim is to select the edges, among the candidates available at each step of the original PEG algorithm, that prevent the creation of dominant ETS's. The proposed method is applicable to both regular and irregular variable node degree distributions. Simulation results are presented to demonstrate the superior ETS distribution and error floor performance of the constructed codes compared to similar codes constructed by the original and other modifications of the PEG algorithm.
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.
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.