The lattice theory of information

Abstract

The word "information" has been given many different meanings by various writers in the general field of information theory. It is likely that at least a number of these will prove sufficiently useful in certain applications to deserve further study and permanent recognition. It is hardly to be expected that a single concept of information would satisfactorily account for the numerous possible applications of this general field. The present note outlines a new approach to information theory which is aimed specifically at the analysis of certain communication problems in which there exist a number of information sources simultaneously in operation. A typical example is that of a simple communication channel with a feedback path from the receiving point to the transmitting point. The problem is to make use of the feedback information for improving forward transmission, and to determine the forward channel capacity when the best possible use is made of this feedback information. Another more general problem is that of a communication system consisting of a large number of transmitting and receiving points with some type of interconnection network between the various points. The problem here is to formulate the best systems design whereby, in some sense, the best overall use of the available facilities is made. While the analysis sketched here has not yet proceeded to the point or a complete solution of these problems, partial answers have been found and it is believed that a complete solution may be possible.