Keywords and Synonyms
Decoding ; Error correction
Problem Definition
In order to ensure the integrity of data in the presence of errors, an error-correcting code is used to encode data into a redundant form (called a codeword). It is natural to view both the original data (or message) as well as the associated codeword as strings over a finite alphabet. Therefore, an error-correcting code C is defined by an injective encoding map \( { E: \Sigma^k \rightarrow \Sigma^n } \), where k is called the message length, and n the block length. The codeword, being a redundant form of the message, will be longer than the message. The rate of an error-correcting code is defined as the ratio k/n of the length of the message to the length of the codeword. The rate is a quantity in the interval \( { (0,1] } \), and is a measure of the redundancy introduced by the code. Let R(C) denote the rate of a code C.
The redundancy built into a codeword enables detection and hopefully also correction of any...
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Guruswami, V.: List Decoding of Error-Correcting Codes. Lecture Notes in Computer Science, vol. 3282. Springer, Berlin (2004)
Guruswami, V., Rudra, A.: Explicit codes achieving list decoding capacity: Error-correction with optimal redundancy. IEEE Trans. Inform. Theor. 54(1), 135–150 (2008)
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Guruswami, V., Sudan, M.: Improved decoding of Reed–Solomon and algebraic-geometric codes. IEEE Trans. Inf. Theory. 45(6), 1757–1767 (1999)
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Peterson, W.W.: Encoding and error-correction procedures for Bose-Chaudhuri codes. IEEE Trans. Inf. Theory. 6, 459–470 (1960)
Sudan, M.: Decoding of Reed–Solomon codes beyond the error-correction bound. J. Complex. 13(1), 180–193 (1997)
Sudan, M.: List decoding: Algorithms and applications. SIGACT News. 31(1), 16–27 (2000)
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© 2008 Springer-Verlag
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Guruswami, V. (2008). Decoding Reed–Solomon Codes. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_101
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