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. (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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