Decoding of Reed Solomon Codes beyond the Error-Correction Bound

Decoding of Reed Solomon Codes beyond the Error-Correction Bound

We present a randomized algorithm which takes as input n distinct points {(xi, yi)}i=1 from F × F (where F is a field) and integer parameters t and d and returns a list of all univariate polynomials f over F in the variable x of degree at most d which agree with the given set of points in at least t places (i.e., yi = f(xi) for at least t values of i), provided t = Ω( √ nd). The running time is...

Decoding of Reed Solomon codes beyond the error-correction bound

Decoding Reed Solomon Codes beyond the Error-Correction Diameter

We describe a new algorithm for the decoding of Reed Solomon codes. This algorithm was originally described in [12]. While the algorithm presented in this article is the same, the presentation is somewhat di erent. In particular we derive more precise bounds on the performance of the algorithm and show the following: For an [n; n; (1 )n]q Reed Solomon code, the algorithm in [12] corrects ( ( ) ...

Error Correction beyond the Conventional Error Bound for Reed–solomon Codes

A modification of Blahut procedure is proposed for error correction beyond the conventional error bound for ReedSolomon codes. An effective method is offered for the searching of unknown discrepancies needed for analytical continuation of the Berlekamp-Massey algorithm through two additional iterations. This reduces the search time by 2(q-1)n/((n+t+1)(nt)) times compared to Blahut procedure. An...

Reed-Solomon Error Correction

he main aim of this paper is to give some essential background to the theory of Reed Solomon codes and the previous survey literature of the Reed Solomon error correction method using various algorithm.Reed Solomon codes have shown to be the best compromise between efficiency and complexity. These are cyclic codes and are used for the detection and correction of burst errors. Galois field is us...