Excess-Distortion Exponents for Successive Refinement Using Gaussian Codebooks

This paper is eligible for the Jack Keil Wolf ISIT Student Paper Award. We derive achievability results on large deviations for mismatched successive refinement where one uses random i.i.d. Gaussian codebooks and minimum Euclidean distance encoding to compress an arbitrary memoryless source. Specifically, we consider both separate and joint excess-distortion criterion and derive achievable error exponents for both cases. Under the mismatched coding scheme, we show that the exponent of the joint excess-distortion probability equals the exponent of one of the separate excess-distortion probabilities, depending on the compression rate of the second encoder only. When specialized to a Gaussian memoryless source (GMS), we obtain the first achievable error exponent region. However, in contrast to the second-order asymptotics and to the large deviations for mismatched rate-distortion, the specialized result for GMS is not optimal. Further investigations are required to close the gap.