A modified algorithm for correction of errors and erasures in Reed Solomon decoders

Decoders for t-error correcting RS codes sometimes incorporate also the ability to recover erasures. The option of controlling erasures can be viewed as a way of sending more information to the decoder about the actual received signal. An elegant method of correcting any patterns of epsilon errors and e erasures has been suggested by Berlekamp. Using Berlekamp's algorithm, some authors have shown how to derive the combined error and erasure locator polynomial. The present authors describe how it is possible to find the error-locator polynomial and the erasure-locator polynomial in an independent way, so that the computational complexity can be reduced. While the erasure-locator polynomial can easily be computed from the knowledge of erasure locations, the error-locator polynomial is obtained using the Berlekamp's algorithm with a particular change in the initial conditions.<
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