VLSI Architecture of Euclideanized BM Algorithm for Reed-Solomon Code

In 1988, Eastman showed that the Euclideanized Berlekamp-Massey (BM) algorithm can be used to eliminate the calculation of discrepancies and the divisions of the finite field elements to find the errata locator polynomial in a Reed-Solomon (RS) decoder. However, the separate computations of the errata locator and the errata evaluator polynomials are still needed in Eastman's decoder. In this paper, a modified decoding algorithm based on the idea of Eastman is presented. It is derived to solve the errata locator and the errata evaluator polynomials simultaneously without performing the operations of polynomial division and field element inversion. Moreover, the weights used to represent the discrepancies at each iteration can be directly extracted from the coefficient. Therefore, the proposed algorithm saves many controlling circuits and provides a modular VLSI architecture with parallel. As a consequence, it is simple and easy to implement. And the decoding complexity of the algorithm proposed by Eastman can be further reduced.