Communication Systems Which Minimize Coding Noise

THE MODEL Shannon's theory of communication, shows how to defeat noise introduced in a communication medium by restricting the repertoire of transmitted signals to a discrete set.1 If the messages to be transmitted are not already in an appropriately discrete form, noise in the medium is then eliminated only at the expense of noise, here called coding noise, caused by the failure of the restricted family of available signals to represent faithfully the full family of possible messages. The amount of coding noise introduced is of course subject to control by design. This paper considers one aspect of the problem of minimizing coding noise. Noise in the medium is not considered. The paper limits attention to systems in which the random process representing the message is a discrete-time or sampled-data process. The sampling noise caused by creating such a process out of a continuous-time process is not considered. 8091 3102 T H E BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 19(59 The problem of selecting a coding scheme that maximizes the rate of communication over a noisy channel is not considered. Rather, the paper starts at the point that a coding scheme has been found, that is optimum according a fairly general criterion of fidelity. What is then shown is that the transmitter and receiver--encoder and decoder--of the system are of a special form. A Q-coded communication system is defined by a discrete set Q and by three jointly distributed random processes, {.r,, , qn , yn | n = 0, ± 1 , d=2, · · ·}.