Mismatched codebooks and the role of entropy-coding in lossy data compression

This paper describe a random coding model for universal quantization. The universal quantizer consists of a (typically) mismatched random codebook followed by optimal entropy-coding. We precisely characterize the rate gain due to entropy-coding and show that it may be arbitrarily large. In the special case of entropy-coded i.i.d. Gaussian codebooks with large variance, we draw a novel connection with the compression performance of entropy-coded dithered lattice quantization. Our main tools are large deviations techniques that allow us to prove an almost sure version of the conditional limit theorem.