ON COMMUNICATION OF ANALOG DATA FROM A BOUNDED SOURCE SPACE

We consider the problem of the transmission of discrete‐time analog data with a variety of fidelity criteria. The outputs of the analog source are assumed to belong to a bounded set. Bounds on the minimum achievable average distortion for memoryless sources are derived both for the case where the coding delay is infinite (an extension of the Shannon Theory) and also for some cases where the coding delay is finite. Several examples are given, for which the upper and lower bounds coincide. Further, we discuss the case where the assumption of the existence of a probabilistic model for the source is dropped. We adopt as our fidelity criterion the supremum over all possible source‐output n‐sequences x, of the conditional expectation of the distortion given x (“guaranteed distortion”). The Shannon Theory is not directly applicable in determining the minimum guaranteed distortion. We do obtain results for two important cases. Some generalizations and applications are also discussed. © 1969 The Bell System Technical Journal