The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index.
A recursive approach to low complexity codes
Abstract
A method is described for constructing long error-correcting codes from one or more shorter error-correcting codes, referred to as subcodes, and a bipartite graph. A graph is shown which specifies carefully chosen subsets of the digits of the new codes that must be codewords in one of the shorter subcodes. Lower bounds to the rate and the minimum distance of the new code are derived in terms of the parameters of the graph and the subeodes. Both the encoders and decoders proposed are shown to take advantage of the code's explicit decomposition into subcodes to decompose and simplify the associated computational processes. Bounds on the performance of two specific decoding algorithms are established, and the asymptotic growth of the complexity of decoding for two types of codes and decoders is analyzed. The proposed decoders are able to make effective use of probabilistic information supplied by the channel receiver, e.g., reliability information, without greatly increasing the number of computations required. It is shown that choosing a transmission order for the digits that is appropriate for the graph and the subcodes can give the code excellent burst-error correction abilities. The construction principles
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Citations
Cites
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
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Low-Density Parity-Check Codes
Gallager, R. G. (1963) · The MIT Press eBooks · doi:10.7551/mitpress/4347.001.0001 · Cited by 4,401
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Biggs, N. L. (2008) · Springer Undergraduate Mathematics Series · doi:10.1007/978-1-84800-273-9_9 · Cited by 751
On Moore Graphs with Diameters 2 and 3
Hoffman, A. J., & Singleton, R. R. (1960) · IBM Journal of Research and Development · doi:10.1147/rd.45.0497 · Cited by 489
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Cited by
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
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
Information, Physics, and Computation
Mézard, M., & Montanari, A. (2009) · doi:10.1093/acprof:oso/9780198570837.001.0001 · Cited by 1,913
Low-density parity-check codes based on finite geometries: a rediscovery and new results
Kou, Y., Lin, S., & Fossorier, M. P. C. (2001) · IEEE Transactions on Information Theory · doi:10.1109/18.959255 · Cited by 1,302
Reduced complexity iterative decoding of low-density parity check codes based on belief propagation
Fossorier, M. P. C., Mihaljevic, M., & Imai, H. (1999) · IEEE Transactions on Communications · doi:10.1109/26.768759 · Cited by 1,041
Metadata
- Authors
- Tanner, R.
- Venue
- IEEE Transactions on Information Theory
- Published
- 1981-09
- Volume
- 27
- Issue
- 5
- Pages
- 533-547
- ISSN
- 0018-9448 (ISSN-L)
- 1557-9654
- OpenAlex
- W2133068391
- Cited by
- 3,138
- References
- 11
- FWCI
- 1.13
- Type
- journal article
- Language
- en
- Open access
- closed
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- Tanner, R. (1981). A recursive approach to low complexity codes. IEEE Transactions on Information Theory. https://doi.org/10.1109/tit.1981.1056404
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
