Multi-rate convolutional codes using common nonlinear generators for memory order four

This paper presents sets of convolutional codes with memory order four which have maximal free distance and have common nonlinear generating functions. Every code in a set has at least one feedforward coding equation that is nonlinear over a binary Galois field. Each set has convolutional codes with rates one-half, one-third, and one-fourth. In each set, the generators of the rate one-third code include all the generators of the rate one-half code. In each set, the generators of the rate one-fourth code include all the generators of the rate one-third code. This commonality yields multi-rate code implementations with minimum logic. The focus is nonlinear convolutional codes that achieve Heller-Griesmer bound on maximum free distance.