The DOI matches its Crossref record; 27 of the 27 references it cites were found in a registry or an index.
Combinatorial Constructions of Low-Density Parity-Check Codes for Iterative Decoding
Open accessAbstract
This paper introduces several new combinatorial constructions of low-density parity-check (LDPC) codes, in contrast to the prevalent practice of using long, random-like codes. The proposed codes are well structured, and unlike random codes can lend themselves to a very low-complexity implementation. Constructions of regular Gallager codes based on cyclic difference families, cycle-invariant difference sets, and affine 1-configurations are introduced. Several constructions of difference families used for code design are presented, as well as bounds on the minimal distance of the codes based on the concept of a generalized Pasch configuration.
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Citations
Cites
A Mathematical Theory of Communication
Shannon, C. E. (1948) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1948.tb01338.x · Cited by 88,486
A Mathematical Theory of Communication
Shannon, C. E. (1948) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1948.tb00917.x · Cited by 48,949
(1988) · Cited by 16,582
The Theory of Error-Correcting Codes
(1977) · North-Holland Mathematical Library · doi:10.1016/s0924-6509(08)x7030-8 · Cited by 10,760
Low-density parity-check codes
Gallager, R. (1962) · IEEE Transactions on Information Theory · doi:10.1109/tit.1962.1057683 · Cited by 10,602
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 1×
“To visualize the decoding algorithm for LDPC codes, the parity-check matrix is represented as a bipartite graph with two types of vertices [8]–[10].”
MethodLow-Density Parity-Check Codes
Gallager, R. G. (1963) · The MIT Press eBooks · doi:10.7551/mitpress/4347.001.0001 · Cited by 4,401
Good error-correcting codes based on very sparse matrices
MacKay, D. J. C. (1999) · IEEE Transactions on Information Theory · doi:10.1109/18.748992 · Cited by 3,684
Design of capacity-approaching irregular low-density parity-check codes
Richardson, T. J., Shokrollahi, M. A., & Urbanke, R. L. (2001) · IEEE Transactions on Information Theory · doi:10.1109/18.910578 · Cited by 3,335
A recursive approach to low complexity codes
Tanner, R. (1981) · IEEE Transactions on Information Theory · doi:10.1109/tit.1981.1056404 · Cited by 3,138
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
Metadata
- Authors
- Vasic, B., & Milenkovic, O.
- Venue
- IEEE Transactions on Information Theory
- Published
- 2004-06
- Volume
- 50
- Issue
- 6
- Pages
- 1156-1176
- ISSN
- 0018-9448 (ISSN-L)
- OpenAlex
- W2119990840
- Cited by
- 263
- References
- 27
- FWCI
- 31.03
- Type
- journal article
- Language
- en
- Open access
- green
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