Construction of Convolution Codes by Suboptimization

A procedure for suboptimizing the choice of convolution codes is described. It is known that random convolution codes that have been passed through a binary symmetric channel, or a binary erasure channel, have a low probability of error and are easily decoded, but no practical procedure for finding the optimum convolution code for long code lengths is known. A convolution code is defined by its generator. It is proved that by sequentially choosing the generator digits, one can obtain a code whose probability of error decreases as fast as, or faster than, the usual upper bound for a random code. Little effort is required for suboptimizing the choice of the first few generator digits. This effort increases exponentially with the choice of successive generator digits. For a rate of transmission equal to 1/2, and the given procedure, a code of length 50 is the approximate limit, with the use of the digital computers that are available at present.