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 ε 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