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)

Irregular low-density parity-check code design based on integer lattices

Wataru Matsumoto, Hirotaka Imai

Published Jan 1, 2003• 1 citation
Publisher

Abstract

We propose an irregular low-density parity-check (LDPC) code design scheme by extension of a regular LDPC code using Latin square matrices of random sequence. Our scheme is a deterministic method that enables to easily design good irregular LDPC code for any code rate and degree distributions. We optimize LDPC codes by Gaussian approximation (GA) Chung, S-Y et al., (2001) method and construct irregular LDPC codes based on integer lattices Vasic, B et al., (2002).

DOI
10.1109/isit.2003.1228017

Related papers

A systematic construction of irregular low-density parity-check codes from combinatorial designs

S. Sankaranarayanan, Bane V. Vasic, Erozan M. Kurtas

In this paper, we propose an algorithm to design an irregular low-density parity-check (LDPC) code, with a given degree distribution pair, from a combinatorially constructed regular LDPC code. Richardson et al., (2001) showed that long LDPC codes from irregular bipartite graphs with carefully chosen degree distribution pair performed very close to the Shannon capacity limit. It is known that the cyclic or quasicyclic property of regular LDPC codes, constructed from combinatorial designs Colbourn, J et al., (1996), helps to simplify their encoding procedure and also facilitates a memory-efficient storage of the codes. The proposed algorithm involves splitting columns and rows of a regular LDPC code systematically in order to achieve an irregular code with a given distribution pair. Also, this algorithm is a useful alternative to random generation of irregular codes because it enables to exploit the structural properties of the regular code in efficiently storing the resultant irregular code.

IEEE International Symposium on Information Theory (ISIT)•Jan 1, 2003•5 citations

Construction of irregular LDPC codes based on Balanced Incomplete Block Designs

Siddarama R. Patil, Sant Saran Pathak

In this paper, we present a method to design irregular structured low-density parity-check (LDPC) codes based on balanced incomplete block designs (BIBD). The problem of designing irregular structured LDPC codes that have good overall error performance for a wide range of code rates and block sizes with attractive storage requirements is attempted. The proposed codes are well structured and unlike random codes can lend themselves to a very low-complexity implementation. The codes constructed by this method have the girth at least 6 and they perform well with the sum-product iterative decoding algorithm. Furthermore, the codes are compared with known random LDPC codes, in order to assess their relative achievable performance. The proposed LDPC codes demonstrate performance that is better than an average random LDPC code of similar block length, code rate and parity check matrix sparsity.

IEEE International Conference on Industrial and Information Systems (ICIIS)•Jan 1, 2007•0 citations

Regular and Irregular Quasi-Cyclic LDPC Codes

Xueqin Jiang, Moon Ho Lee, Jia Hou

This paper presents methods to the construction of regular and irregular low-density parity-check (LDPC) codes based on Euclidean geometries. Codes constructed by these methods are quasi-cyclic. The degree distributions of proposed LDPC codes can be optimized by the curve fitting approach in the extrinsic information transfer (EXIT) charts. Simulation results show that these codes perform very well with the iterative decoding.

IEEE Vehicular Technology Conference•May 1, 2011•0 citations

Low-density parity-check code based on binary sequence splitting

Zhu Li-yan

A new and simple approach to construct irregular low-density parity-check(LDPC)code based on the binary sequence splitting was proposed.Experimental results show that constructed irregular LDPC code with iterative decoding perform well over the AWGN channel and have a good code weight distribution with 4-cycle free.

Journal of Shandong University of Technology•Jan 1, 2007•0 citations

Irregular low-density parity-check lattices

Ihn-Jung Baik, Sae-Young Chung

We construct lattices with high coding gains based on nested low-density parity-check (LDPC) codes by Construction D′.We generalize the LDPC lattices [1] to have irregular degrees and call them irregular LDPC lattices. To construct good irregular LDPC lattices, we optimize the degree distributions by using density evolution and a modified sequential quadratic programming (SQP) and show our optimized irregular LDPC lattice has a threshold 0.48dB from the capacity, which is about 0.6dB better than the regular one in [1]. To construct a Tanner graph corresponding to LDPC lattices, we generalize the progressive-edge growth (PEG) algorithm and show a lower bound on the girth of the graph. Simulation is performed using the sum-product algorithm. Also, we compare the performance of joint decoding and multi-stage decoding [2] and show the advantage of joint decoding.

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2008•13 citations

A More Accurate One-Dimensional Analysis and Design of Irregular LDPC Codes

Masoud Ardakani, Frank R. Kschischang

We introduce a new one-dimensional (1-D) analysis of low-density parity-check (LDPC) codes on additive white Gaussian noise channels which is significantly more accurate than similar 1-D methods. Our method assumes a Gaussian distribution in message-passing decoding only for messages from variable nodes to check nodes. Compared to existing work, which makes a Gaussian assumption both for messages from check nodes and from variable nodes, our method offers a significantly more accurate estimate of convergence behavior and threshold of convergence. Similar to previous work, the problem of designing irregular LDPC codes reduces to a linear programming problem. However, our method allows irregular code design in a wider range of rates without any limit on the maximum variable-node degree. We use our method to design irregular LDPC codes with rates greater than 1/4 that perform within a few hundredths of a decibel from the Shannon limit. The designed codes perform almost as well as codes designed by density evolution.

IEEE Transactions on Communications•Dec 1, 2004•119 citations
We propose an irregular low-density parity-check (LDPC) code design scheme by extension of a regular LDPC code using Latin square matrices of random sequence. Our scheme is a deterministic method that enables to easily design good irregular LDPC code for any code rate and degree distributions. We optimize LDPC codes by Gaussian approximation (GA) Chung, S-Y et al., (2001) method and construct irregular LDPC codes based on integer lattices Vasic, B et al., (2002).
In this paper, we propose an algorithm to design an irregular low-density parity-check (LDPC) code, with a given degree distribution pair, from a combinatorially constructed regular LDPC code. Richardson et al., (2001) showed that long LDPC codes from irregular bipartite graphs with carefully chosen degree distribution pair performed very close to the Shannon capacity limit. It is known that the cyclic or quasicyclic property of regular LDPC codes, constructed from combinatorial designs Colbourn, J et al., (1996), helps to simplify their encoding procedure and also facilitates a memory-efficient storage of the codes. The proposed algorithm involves splitting columns and rows of a regular LDPC code systematically in order to achieve an irregular code with a given distribution pair. Also, this algorithm is a useful alternative to random generation of irregular codes because it enables to exploit the structural properties of the regular code in efficiently storing the resultant irregular code.
In this paper, we present a method to design irregular structured low-density parity-check (LDPC) codes based on balanced incomplete block designs (BIBD). The problem of designing irregular structured LDPC codes that have good overall error performance for a wide range of code rates and block sizes with attractive storage requirements is attempted. The proposed codes are well structured and unlike random codes can lend themselves to a very low-complexity implementation. The codes constructed by this method have the girth at least 6 and they perform well with the sum-product iterative decoding algorithm. Furthermore, the codes are compared with known random LDPC codes, in order to assess their relative achievable performance. The proposed LDPC codes demonstrate performance that is better than an average random LDPC code of similar block length, code rate and parity check matrix sparsity.
We construct lattices with high coding gains based on nested low-density parity-check (LDPC) codes by Construction D′.We generalize the LDPC lattices [1] to have irregular degrees and call them irregular LDPC lattices. To construct good irregular LDPC lattices, we optimize the degree distributions by using density evolution and a modified sequential quadratic programming (SQP) and show our optimized irregular LDPC lattice has a threshold 0.48dB from the capacity, which is about 0.6dB better than the regular one in [1]. To construct a Tanner graph corresponding to LDPC lattices, we generalize the progressive-edge growth (PEG) algorithm and show a lower bound on the girth of the graph. Simulation is performed using the sum-product algorithm. Also, we compare the performance of joint decoding and multi-stage decoding [2] and show the advantage of joint decoding.
We introduce a new one-dimensional (1-D) analysis of low-density parity-check (LDPC) codes on additive white Gaussian noise channels which is significantly more accurate than similar 1-D methods. Our method assumes a Gaussian distribution in message-passing decoding only for messages from variable nodes to check nodes. Compared to existing work, which makes a Gaussian assumption both for messages from check nodes and from variable nodes, our method offers a significantly more accurate estimate of convergence behavior and threshold of convergence. Similar to previous work, the problem of designing irregular LDPC codes reduces to a linear programming problem. However, our method allows irregular code design in a wider range of rates without any limit on the maximum variable-node degree. We use our method to design irregular LDPC codes with rates greater than 1/4 that perform within a few hundredths of a decibel from the Shannon limit. The designed codes perform almost as well as codes designed by density evolution.