The DOI matches its Crossref record; 42 of the 42 references it cites were found in a registry or an index.
Low-density parity-check codes based on finite geometries: a rediscovery and new results
Abstract
This paper presents a geometric approach to the construction of low-density parity-check (LDPC) codes. Four classes of LDPC codes are constructed based on the lines and points of Euclidean and projective geometries over finite fields. Codes of these four classes have good minimum distances and their Tanner (1981) graphs have girth 6. Finite-geometry LDPC codes can be decoded in various ways, ranging from low to high decoding complexity and from reasonably good to very good performance. They perform very well with iterative decoding. Furthermore, they can be put in either cyclic or quasi-cyclic form. Consequently, their encoding can be achieved in linear time and implemented with simple feedback shift registers. This advantage is not shared by other LDPC codes in general and is important in practice. Finite-geometry LDPC codes can be extended and shortened in various ways to obtain other good LDPC codes. Several techniques of extension and shortening are presented. Long extended finite-geometry LDPC codes have been constructed and they achieve a performance only a few tenths of a decibel away from the Shannon theoretical limit with iterative decoding.
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Cites
(1988) · Cited by 16,582
Low-density parity-check codes
Gallager, R. (1962) · IEEE Transactions on Information Theory · doi:10.1109/tit.1962.1057683 · Cited by 10,602
Near Shannon limit error-correcting coding and decoding: Turbo-codes. 1
Berrou, C., Glavieux, A., & Thitimajshima, P. (2002) · Proceedings of ICC '93 - IEEE International Conference on Communications · doi:10.1109/icc.1993.397441 · Cited by 6,738
Factor graphs and the sum-product algorithm
Kschischang, F. R., Frey, B. J., & Loeliger, H.-A. (2001) · IEEE Transactions on Information Theory · doi:10.1109/18.910572 · Cited by 6,486 · cited 5×
“A detail exposition of the SPA can be found in [10], [17]–[20], [33].”
BackgroundMethodInfluentialOptimal decoding of linear codes for minimizing symbol error rate (Corresp.)
Bahl, L., Cocke, J., Jelinek, F., & Raviv, J. (1974) · IEEE Transactions on Information Theory · doi:10.1109/tit.1974.1055186 · Cited by 5,208
Optimal decoding of linear codes for minimizing symbol error rate
Bahl, L. R. (1974) · IEEE Transactions on Information Theory · Cited by 4,665
Low-Density Parity-Check Codes
Gallager, R. G. (1963) · The MIT Press eBooks · doi:10.7551/mitpress/4347.001.0001 · Cited by 4,401
Error control coding : fundamentals and applications
Lin, S., & Costello, D. J. (1983) · Medical Entomology and Zoology · Cited by 4,296
Self-citationNear Shannon limit error-correcting coding and decoding : Turbo-codes
Berrou, C. (1993) · International Conference on Communications · Cited by 4,264
Lauritzen, S. L., & Spiegelhalter, D. J. (1988) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1988.tb01721.x · Cited by 3,902
Cited by
Lan, L., Zeng, L., Tai, Y. Y., Chen, L., Lin, S., & Abdel-Ghaffar, K. (2007) · IEEE Transactions on Information Theory · doi:10.1109/tit.2007.899516 · Cited by 263
Self-citationCombinatorial Constructions of Low-Density Parity-Check Codes for Iterative Decoding
Vasic, B., & Milenkovic, O. (2004) · IEEE Transactions on Information Theory · doi:10.1109/tit.2004.828066 · Cited by 263
Channel Coding for DTTB System
(2015) · Digital Terrestrial Television Broadcasting · doi:10.1002/9781119084365.ch03
Metadata
- Authors
- Kou, Y., Lin, S., & Fossorier, M. P. C.
- Venue
- IEEE Transactions on Information Theory
- Published
- 2001
- Volume
- 47
- Issue
- 7
- Pages
- 2711-2736
- ISSN
- 0018-9448 (ISSN-L)
- OpenAlex
- W2114869758
- Cited by
- 1,302
- References
- 42
- FWCI
- 57.15
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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