Large scale geometric programming: An application in coding theory

An algorithm is presented that solves the initial vector problem for group codes for the Gaussian channel. The Gaussian channel is a communications model in which messages are represented by vectors in R and transmitted over a noisy channel. In this paper, the set of messages, called a code, is generated by a group of permutation matrices and the problem of finding the code with the largest minimum distance between codewords for a particular permutation group is called the initial vector problem. This problem is an especially large scale nonlinear programming problem. We transform it to a generalized geometric programming problem and use the double condensation method to develop an algorithm for its solution.