مرکز منطقه ای اطلاع رساني علوم و فناوري - Information rates of stationary ergodic finite-alphabet sources

Abstract :

The generalized Shannon lower bound to the rate-distortion function $R(D)$ for stationary sources with memory is extended to a wide class of distortion measures involving no symmetry conditions. The lower bound $R_{L} (D)$ is a reasonably simple function of the entropy and marginal probabilities of the source and the per-letter distortion measure. Sufficient conditions only slightly less general than necessary conditions are given for the existence of a strictly positive cutoff distortion $D_c$ such that $R(D) = R_{L} (D)$ for $D \\leq D_c$ . The sufficient conditions are the most general to date and include all previously known examples. This provides a nearly complete resolution of the question of when the Shannon-type lower bound to the rate-distortion function of a source with memory is tight. The results are applied to generalize earlier results for balanced distortion measures and Markov sources to nonbalanced distortion measures and wide-sense Markov sources. As a special case, it is shown that $D_c > 0$ for all finite-alphabet autoregressive sources. As an example, $R_{L} (D)$ is evaluated for the first-order ternary autoregressive source for a balanced (Hamming) and a nonbalanced (modular distance) distortion measure. A simple lower bound to $D_c$ is derived for this example.