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

Regular and Irregular Gallager-type Error-Correcting Codes

祥介 樺島, Yoshiyuki Kabashima

Published Jan 1, 2000• 0 citations
OpenAlex

Related papers

Typical performance of Gallager-type error-correcting codes

祥介 樺島, Yoshiyuki Kabashima

•Jan 1, 2000•0 citations

Tighter decoding reliability bound for Gallager's error-correcting code

祥介 樺島, YOSHIYUKI KABASHIMA

•Jan 1, 2001•0 citations

Regular and Irregular Gallager-zype Error-Correcting Codes

Yoshiyuki Kabashima, Tatsuto Murayama, David Saad +1 more

The performance of regular and irregular Gallager-type error-correcting code is investigated via methods of statistical physics. The transmitted codeword comprises products of the original message bits selected by two randomly-constructed sparse matrices; the number of non-zero row/column elements in these matrices constitutes a family of codes. We show that Shannon's channel capacity may be saturated in equilibrium for many of the regular codes while slightly lower performance is obtained for others which may be of higher practical relevance. Decoding aspects are considered by employing the TAP approach which is identical to the commonly used belief-propagation-based decoding. We show that irregular codes may saturate Shannon's capacity but with improved dynamical properties.

neural information processing systems•Nov 29, 1999•1 citation

One Class of Error-Correcting Codes

M. A. Karmazin

Soviet physics. Doklady•Jan 1, 1965•0 citations

Error correction capability of irregular LDPC codes under the Gallager a algorithm

Masakatu Morii, Hiroto Tamiya, Masanori Hirotomo

Many researchers have analyzed the error correction capability of LDPC codes for iterative decoding algorithms. However, it is difficult to show the error correction capability of LDPC codes for iterative decoding algorithms based on belief propagation theoretically. Chilappagari et al. reported the error correction capability of column-weight-three regular LDPC codes under the Gallager A algorithm since the behavior of the iterative decoding algorithm is easily analyzed. In this paper, we investigate the error correction capability of irregular LDPC codes. We also show relations between the decoding failures and 2-cycles of irregular LDPC codes under the Gallager A algorithm.

International Symposium on Information Theory and its Applications•Oct 1, 2016•2 citations

Further Results on the Error Correction Capability of Irregular LDPC Codes under the Gallager A Algorithm

Masanori Hirotomo, Hiroto Tamiya, Masakatu Mori

In this paper, we investigate the error correction capability of irregular LDPC codes. We have shown relationships between the decoding failure and the structures of the Tanner graph of irregular LDPC codes under the Gallager A algorithm. In this analysis, we focused on the structures of connecting degree-two variable nodes, called 2-cycle. In this paper, we present new structures of the subgraph which induces the decoding failure of irregular LDPC codes under the Gallager A algorithm. Furthermore, we analyze relationships between the newly found structures of subgraph and the decoding failure of irregular LDPC codes.

International Symposium on Information Theory and its Applications•Oct 1, 2018•0 citations
The performance of regular and irregular Gallager-type error-correcting code is investigated via methods of statistical physics. The transmitted codeword comprises products of the original message bits selected by two randomly-constructed sparse matrices; the number of non-zero row/column elements in these matrices constitutes a family of codes. We show that Shannon's channel capacity may be saturated in equilibrium for many of the regular codes while slightly lower performance is obtained for others which may be of higher practical relevance. Decoding aspects are considered by employing the TAP approach which is identical to the commonly used belief-propagation-based decoding. We show that irregular codes may saturate Shannon's capacity but with improved dynamical properties.
Many researchers have analyzed the error correction capability of LDPC codes for iterative decoding algorithms. However, it is difficult to show the error correction capability of LDPC codes for iterative decoding algorithms based on belief propagation theoretically. Chilappagari et al. reported the error correction capability of column-weight-three regular LDPC codes under the Gallager A algorithm since the behavior of the iterative decoding algorithm is easily analyzed. In this paper, we investigate the error correction capability of irregular LDPC codes. We also show relations between the decoding failures and 2-cycles of irregular LDPC codes under the Gallager A algorithm.
In this paper, we investigate the error correction capability of irregular LDPC codes. We have shown relationships between the decoding failure and the structures of the Tanner graph of irregular LDPC codes under the Gallager A algorithm. In this analysis, we focused on the structures of connecting degree-two variable nodes, called 2-cycle. In this paper, we present new structures of the subgraph which induces the decoding failure of irregular LDPC codes under the Gallager A algorithm. Furthermore, we analyze relationships between the newly found structures of subgraph and the decoding failure of irregular LDPC codes.