High-resolution rate-distortion theory

Rate-distortion theory and high-resolution (asymptotic) quantization theory are two complementary theories of quantization. Shannon´s rate-distortion theory assumes a given rate (or distortion level) and asymptotically large dimension in order to determine the optimal performance theoretically attainable (OPTA) by any lossy source code. On the other hand, high-resolution quantization theory investigates the performance of codes with a fixed dimension and asymptotically large rate (or small distortion). High-resolution rate-distortion theory combines these two approaches to provide analytic approximations at high-rates to the OPTA function for a given coding problem. The goal of this paper is to relate high-resolution rate-distortion theory to the two competing theories of lossy coding and to survey recent developments in this area