Decoding complement-closed codes with coordinate-disjoint decomposition

Abstract

This paper presents a multilayer neural net decoder for a group of linear block codes with complement-closedness (cc) property. Many well known linear block codes such as Hamming and Golay all into this group. A method called coordinate-disjoint decomposition (cdd) is introduced, and it is shown that this method leads to a minimised decoder structure. Coordinate-disjoint decomposition of Hamming (2r – 1, 2r – r – 1) and extended Hamming (2r, 2r – r – 1) codes, Golay (24, 12)ode, as well as quadratic residue (32, 16) code are illustrated, together with their corresponding decoder structures.