Finite field polynomial processing module for error control coding

TL;DR: In this article, a single polynomial arithmetic operation over finite fields is provided in an error correcting system for correcting Reed-Solomon codewords with mixtures of errors and erasures in an optical disk storage.

Abstract: A single module for performing polynomial arithmetic operations over finite fields is provided in an error correcting system for correcting Reed-Solomon codewords with mixtures of errors and erasures in an optical disk storage. The module comprises two-dimensional register arrays, which serve as a working area to store initial data and intermediate results of the polynomial operations. A set of multiplier-adder units performs multiplication and addition operations under the data supplied from the register arrays based on finite field arithmetic over the Galois field GF(2 8 ). A set of multiplexers routes the input data to the corresponding multiplier-adder units depending on the polynomial functions to be performed. In response to initial condition signals, a control system determines what polynomial functions are to be performed by the polynomial processing module and supplies the module with control signals to provide the data control in the register arrays and selection of the multiplexers.