Complexity and rate-distortion tradeoff via successive refinement

We demonstrate how successive refinement ideas can be used in point-to-point lossy compression problems in order to reduce complexity. We show two examples, the binary-Hamming and quadratic-Gaussian cases, in which a layered code construction results in a low complexity scheme that attains optimal performance. For example, when the number of layers grows with the block length n, we show how to design an O(n^log(n)) algorithm that asymptotically achieves the rate distortion bound. We then show that with the same scheme, used with a fixed number of layers, successive refinement is achieved in the classical sense, and at the same time the second order performance (i.e. dispersion) is also tight.