Nonlinear Turbo Codes Based On Quasigroup String Processing

Abstract

Use of quasigroup transformations to build error-correcting codes was first proposed by GligorosNi, MarNovsNi, and Kocarev [1]. However, their decoding algorithm was based on the exponential-time minimum-distance decoding algorithm, in which the brute-force search for the error pattern is confined in blocNs of 16 bits and upper-bounded to two or three errors per blocN. We point out that any quasigroupbased error-correcting code, designed so far, can be modeled as finite state machine, thus it can be decoded in polynomial time with the well-Nnown Viterbi algorithm or the MAP decoding algorithm. In order to improve the error-correcting capability of quasigroup codes, in this paper we build an error-correcting system based on the Turbo-code design principles. We present the error-correcting capabilities of our Turbo-code system over the Gaussian channel.