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 codes from regular graphs

Pascal O. Vontobel, Hans‐Andrea Loeliger

Published Jun 25, 2003• 5 citations
Publisher

Abstract

It has been recognized that appropriately chosen irregular low-density parity-check (LDPC) codes have a remarkable performance advantage compared to regular LDPC codes and that their threshold is much better. Starting with regular graphs, we construct codes consisting of more sophisticated subcodes (compared to simple XORs) and show that performance gains can be achieved by optimizing the proportions of the high-degree bit nodes and the different subcodes being used.

DOI
10.1109/isit.2002.1023556

Related papers

Sufficient Conditions for a Regular LDPC Code Better than an Irregular LDPC Code

MiyamotoShinya, KasaiKenta, SakaniwaKohichi

Decoding performance of LDPC (Low-Density Parity-Check) codes is highly dependent on the degree distributions of the Tanner graphs which define the LDPC codes. We compare two LDPC code ensembles, o...

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Feb 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

Optimized decoding schedule for irregular LDPC codes

Xuwei Chen, Hui Ling Yu, Youyun Xu

Recently, the concept of layered decoding schedule for Low-Density Parity-Check codes has been introduced. But the advantage of layered decoding schedule for irregular LDPC codes is not as obvious as regular LDPC codes. The major drawback of the layered irregular LDPC codes versus the layered regular LDPC codes is its comparative low convergence decoding speed. Simulation results show that different bit node degrees of irregular LDPC codes significantly contribute to the decoding performance. The decoding performance of bit nodes with different degrees is of great difference. Bit nodes with small degrees always converge slower than larger ones. In this paper, we propose an optimized decoding schedule for irregular LDPC codes to accelerate the decoding convergence rate. Meanwhile, for the irregular LDPC decoder, the faster decoding speed means a higher throughput and almost the same error performance.

IET International Communication Conference on Wireless Mobile and Computing (CCWMC)•Jan 1, 2009•2 citations

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

Degree-Matched Check Node Decoding for Regular and Irregular LDPCs

Sheryl L. Howard, Christian B. Schlegel, Vincent Gaudet

This brief examines different parity-check node decoding algorithms for low-density parity-check (LDPC) codes, seeking to recoup the performance loss incurred by the min-sum approximation compared to sum-product decoding. Two degree-matched check node decoding approximations that depend on the check node degree dcare presented. Both have low complexity and can be applied to any degree distribution. Simulation results show near sum-product decoding performance for both degree-matched check node approximations for regular and irregular LDPCs

IEEE Transactions on Circuits and Systems II Analog and Digital Signal Processing•Oct 1, 2006•22 citations

Structured low-density parity-check codes

José M. F. Moura, Jin Lu, Haotian Zhang

This article describes the different methods to design regular low density parity-check (LDPC) codes with large girth. In graph terms, this corresponds to designing bipartite undirected regular graphs with large girth. Large girth speeds the convergence of iterative decoding and improves the performance at least in the high SNR range, by slowing down the onsetting of the error floor. We reviewed several existing constructions from exhaustive search to highly structured designs based on Euclidean and projective finite geometries and combinatorial designs. We describe GB and TS LDPC codes and compared the BER performance with large girth to the BER performance of random codes. These studies confirm that in the high SNR regime these codes with high girth exhibit better BER performance. The regularity of the codes provides additional advantages that we did not explore in this article like the simplicity of their hardware implementation and fast encoding.

IEEE Signal Processing Magazine•Jan 1, 2004•61 citations
It has been recognized that appropriately chosen irregular low-density parity-check (LDPC) codes have a remarkable performance advantage compared to regular LDPC codes and that their threshold is much better. Starting with regular graphs, we construct codes consisting of more sophisticated subcodes (compared to simple XORs) and show that performance gains can be achieved by optimizing the proportions of the high-degree bit nodes and the different subcodes being used.
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.
Recently, the concept of layered decoding schedule for Low-Density Parity-Check codes has been introduced. But the advantage of layered decoding schedule for irregular LDPC codes is not as obvious as regular LDPC codes. The major drawback of the layered irregular LDPC codes versus the layered regular LDPC codes is its comparative low convergence decoding speed. Simulation results show that different bit node degrees of irregular LDPC codes significantly contribute to the decoding performance. The decoding performance of bit nodes with different degrees is of great difference. Bit nodes with small degrees always converge slower than larger ones. In this paper, we propose an optimized decoding schedule for irregular LDPC codes to accelerate the decoding convergence rate. Meanwhile, for the irregular LDPC decoder, the faster decoding speed means a higher throughput and almost the same error performance.
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.
This brief examines different parity-check node decoding algorithms for low-density parity-check (LDPC) codes, seeking to recoup the performance loss incurred by the min-sum approximation compared to sum-product decoding. Two degree-matched check node decoding approximations that depend on the check node degree dcare presented. Both have low complexity and can be applied to any degree distribution. Simulation results show near sum-product decoding performance for both degree-matched check node approximations for regular and irregular LDPCs
This article describes the different methods to design regular low density parity-check (LDPC) codes with large girth. In graph terms, this corresponds to designing bipartite undirected regular graphs with large girth. Large girth speeds the convergence of iterative decoding and improves the performance at least in the high SNR range, by slowing down the onsetting of the error floor. We reviewed several existing constructions from exhaustive search to highly structured designs based on Euclidean and projective finite geometries and combinatorial designs. We describe GB and TS LDPC codes and compared the BER performance with large girth to the BER performance of random codes. These studies confirm that in the high SNR regime these codes with high girth exhibit better BER performance. The regularity of the codes provides additional advantages that we did not explore in this article like the simplicity of their hardware implementation and fast encoding.