AN APPLICATION OF RATE-DISTORTION THEORY TO A CONVERSE TO CODING THEOREM

A lower bound to the information rate R(D) for a discrete memoryless source with a fidelity criterion is presented for the case in which the distortion matrix contains the same set of entries, perhaps permuted, in each column. A necessary and sufficient condition for R(D) to equal this bound is given. In particular, if the smallest column element is zero and occurs once in each row, then there is a range of D, 0≤ D ≤ Dt, in which equality holds. These results are then applied to the special case of dil = 1 - δij, for which the average distortion is just the probability of in-correctly reproducing the source output. We show how to construct R(D) for this case, from which one can solve for the minimum achievable probability of error when transmitting over a channel of known capacity. © 1969, IEEE. All Rights Reserved.