The utility of a communication channel and applications to suboptimal information handling procedures

This paper demonstrates the applicability of the functional equations of dynamic programming to information theory problems. Yielding the same results as those obtainable by Shannon's equations, the functional equations can be modified also to consider the many restrictions enforced upon information systems by the real world. A result of the application of functional equations to systems operating under suboptimum conditions is that the information rate of a system is dependent upon the manner in which the information is used. The Kelly concept-the gain of a gambler who wagers his capital on the outcome of a communication channel — is used to determine the information rate of the channel. The mathematical analysis follows the stochastic multistage decision process technique of Bellman and Kalaba. Together with some extensions by the author, the Kelly-Bellman-Kalaba model of communication is repeated. The models are analyzed for the optimum case and examined for various suboptimum conditions. The gambler's betting policy is analogous to information usage; restrictions upon this policy affect the information rate of the system. They can require that the policy which is best under optimum conditions be replaced by other policies which, although inferior in the ideal case, are better able to compensate for the restrictions. A null zone reception system first analyzed by Bloom and others is reanalyzed to provide a concrete example of the latitude of operation allowed by the functional equation approach. Bloom's analysis assumed that the system operates under optimum conditions. His results are duplicated, and their expression indicates their alteration by suboptimum conditions. An appendix expresses the results of this paper in the form used by Bloom.