New fidelity criteria for discrete-time source encoding

A probabilistic approach to the source encoding problem requires the specification of a fidelity criterion which measures the degradation of the source output produced by the encoding transformation. Historically, the fidelity criteria generated by difference-type distortion measures have received by far the widest acceptance, due in part to their analytical tractability. This paper introduces two new fidelity criteria for discrete-time sources. These are designated as the mean incoherence(MIC) and the mean log-coherence (MLC). Both criteria are functionals of the magnitude-squared coherence between the source output and its reproduction, and thus do not admit a recognizable time-domain distortion measure representation. Interesting features of these fidelity criteria are indicated, and comparisons are made with the classical mean-squared error (MSE) fidelity criterion. The rate-distortion functions for a stationary Gaussian source subject to constraints on either the MIC or MLC are derived, and the corresponding optimum encoder behavior is described. Finally, the applications where these new fidelity criteria may be advantageous over the MSE criterion are discussed.