Communication systems which minimize coding noise

The problem of minimizing coding or quantizing noise in a communication system is posed in a general setting. It is shown that if the messages to be transmitted are sample sequences drawn from a discrete-time random process meeting a certain simply stated criterion of “randomness” and if there exists a quantized communication system which is optimal in that it introduces a minimum amount of coding noise, then this optimal system can be realized using a transmitter of special form. Specifically, the optimum transmitter is one which quantizes each message sample according to a scheme that depends only upon the quantized material already transmitted, rather than upon the (unquantized) material that has been previously offered for transmission. It follows that only digital storage is required at the transmitter or receiver. If the receiver is limited, a priori, to have only a given finite amount of storage, and if the system is optimum within this constraint, the transmitter need have only the same amount of storage.