High-speed Reed-Solomon decoder for correcting errors and erasures

Abstract

A Reed-Solomon decoder for errorsand-erasures correction, based on a new algebraic decoding algorithm, is presented. This high-speed decoder requires only n clock cycles for decoding each received n-symbol block. A serial structure that requires very few multipliers and provides a general expression to calculate the coefficients of the erasure-locator polynomial is also presented. A (15, 11) RS decoder and its shortened version (7, 3) RS decoder are used as design examples to illustrate the operating procedure of the new decoding algorithm.