Some optimal partial-unit-memory codes

Abstract

A class of time-invariant binary convolutional codes is defined, called partial-unit-memory codes. These codes are optimal in the sense of having maximum free distance for given values of R, k (the number of encoder inputs), and mu (the number of encoder memory cells). Optimal codes are given for rates R = 1/4, 1/3, 1/2, and 2/3, with mu not greater than 4 and k not greater than mu + 3, whenever such a code is better than previously known codes. An infinite class of optimal partial-unit-memory codes is also constructed based on equidistant block codes.