| Hi-index | 754.84 |
Let R(·) be the rate-distortion function. Assume that we want to describe a source with distortion no larger than Δ1 . From the rate-distortion theory we know that we need to do so at a rate R1 no smaller than R(Δ1) [bits/symbol]. If it turns out that a more accurate description at distortion Δ2, Δ2<Δ1 , is desirable, one can transmit additional information at some rate ΔR. What is the minimal value for ΔR? More generally, which are the achievable (R1, R2) pairs for which, with high probability, one can describe the source at rate R1 and incur distortion not exceeding Δ1 and refine this description at a rate R2-R1 obtaining a final distortion not exceeding Δ2? The achievable region containing those pairs is characterized. An interpretation of Equitz and Cover's Markov condition is given. The Markov condition characterizes those cases for which (R(Δ1), R(Δ2)) is an achievable pair