A systolic array architecture for implementing a fast parallel decoding algorithm of one-point AG codes

Abstract

Previously we proposed a fast parallel decoding algorithm for general one-point algebraic geometric (AG) codes with a systolic array architecture. But, designing the detailed structure of the systolic array and scheduling the relevant procedures remained to be given explicitly, because the proper discontinuities (i.e., gaps) accompanied with a pole-order (nongap) sequence make the problem very complicated. Based on a version of the fast decoding algorithm expressed in terms of matrices with univariate polynomials as entities, we present a method of complete scheduling on a revised architecture of systolic array for implementing this algorithm in parallel. For the size m of input data, i.e. the syndrome, and the first nongap /spl rho/, the time complexity is O(m) and the space complexity is O(/spl rho//sup 2/ m), where the time complexity O(/spl rho/m/sup 2/) was required by the serial algorithm.