A Noise Stability Study of the Algorithm of Optimal Symbol-by-Symbol Reception of Signals Corresponding to Parity Check Codes in Non-Binary Fields

Abstract

In this paper, we consider an algorithm for optimal symbol-by-symbol reception of signal constructions based on block error-correcting codes in non-binary fields. The basis of the developed symbol-by-symbol algorithm is shown to be the spectral transformation in the Walsh-Hadamard basis. The resulting complexity of the developed reception algorithm is shown to be determined by the dimension of the dual code, which determines the perspective of its application for block error-correcting codes with a high code rate. The simulation results of the developed reception algorithm for the purpose of studying the noise stability for signals based on parity check codes are presented.