Some optimal partial-unit-memory codes (Corresp.)

Abstract

A new 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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R, k</tex> (the number of encoder inputs), and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\mu</tex> (the number of encoder memory cells). New optimal codes are given for rates <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R=l/4, 1/3, 1/2, \and 2/3</tex> with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\mu \leq 4 \and k \leq \mu + \3</tex> , whenever such a code is better than previously known An infinite class of optimal partial-unit-memory codes is also constructed based on equidistant block codes.