Years and Authors of Summarized Original Work
2002 and later; Feldman, Karger, Wainwright
Problem Definition
Error-correcting codes are fundamental tools used to transmit digital information over unreliable channels. Their study goes back to the work of Hamming and Shannon, who used them as the basis for the field of information theory. The problem of decoding the original information up to the full error-correcting potential of the system is often very complex, especially for modern codes that approach the theoretical limits of the communication channel.
LP decoding [4, 5, 8] refers to the application of linear programming (LP) relaxation to the problem of decoding an error-correcting code. Linear programming relaxation is a standard technique in approximation algorithms and operations research, and is central to the study of efficient algorithms to find good (albeit suboptimal) solutions to very difficult optimization problems [13]. LP decoders have tight combinatorial...
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Recommended Reading
Berlekamp E, McEliece R, van Tilborg H (1978) On the inherent intractability of certain coding problems. IEEE Trans Inf Theory 24:384–386
Berrou C, Glavieux A, Thitimajshima P (1993) Near Shannon limit error-correcting coding and decoding: turbo-codes. In: Proceedings of the IEEE international conference on communications (ICC), Geneva, 23–26 May 1993, pp 1064–1070
Boston N, Ganesan A, Koetter R, Pazos S, Vontobel P Papers on pseudocodewords. HP Labs, Palo Alto. http://www.pseudocodewords.info
Feldman J (2003) Decoding error-correcting codes via linear programming. Ph.D. thesis, Massachusetts Institute of Technology
Feldman J, Karger DR (2002) Decoding turbo-like codes via linear programming. In: Proceedings of the 43rd annual IEEE symposium on foundations of computer science (FOCS), Vancouver, 16–19 Nov 2002
Feldman J, Malkin T, Servedio RA, Stein C, Wainwright MJ (2004) LP decoding corrects a constant fraction of errors. In: Proceedings of the IEEE international symposium on information theory, Chicago, 27 June – 2 July 2004
Feldman J, Stein C (2005) LP decoding achieves capacity. In: Symposium on discrete algorithms (SODA '05), Vancouver, Jan 2005
Feldman J, Wainwright MJ, Karger DR (2003) Using linear programming to decode linear codes. In: 37th annual conference on information sciences and systems (CISS '03), Baltimore, 12–14 Mar 2003
Gallager R (1962) Low-density parity-check codes. IRE Trans Inf Theory (IT) 8:21–28
Koetter R, Vontobel P (2003) Graph covers and iterative decoding of finite-length codes. In: Proceedings of the 3rd international symposium on turbo codes and related topics, Brest, Sept 2003, pp 75–82
MacWilliams FJ, Sloane NJA (1981) The theory of error correcting codes. North-Holland, Amsterdam
Sipser M, Spielman D (1996) Expander codes. IEEE Trans Inf Theory 42:1710–1722
Vazirani VV (2003) Approximation algorithms. Springer, Berlin
Wainwright M, Jordan M (2003) Variational inference in graphical models: the view from the marginal polytope. In: Proceedings of the 41st Allerton conference on communications, control, and computing, Monticello Oct 2003
Wiberg N (1996) Codes and decoding on general graphs. Ph.D. thesis, Linkoping University
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Feldman, J. (2016). LP Decoding. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_216
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