Berlekamp–Welch algorithm
Error-correcting algorithm / From Wikipedia, the free encyclopedia
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The Berlekamp–Welch algorithm, also known as the Welch–Berlekamp algorithm, is named for Elwyn R. Berlekamp and Lloyd R. Welch. This is a decoder algorithm that efficiently corrects errors in Reed–Solomon codes for an RS(n, k), code based on the Reed Solomon original view where a message is used as coefficients of a polynomial or used with Lagrange interpolation to generate the polynomial of degree < k for inputs and then is applied to to create an encoded codeword .
The goal of the decoder is to recover the original encoding polynomial , using the known inputs and received codeword with possible errors. It also computes an error polynomial where corresponding to errors in the received codeword.