Achievable Refined Asymptotics for Successive Refinement Using Gaussian Codebooks

We study the mismatched successive refinement problem where one uses Gaussian codebooks to compress an arbitrary memoryless source with minimum Euclidean distance encoding under quadratic distortion measure. Specifically, we derive achievable refined asymptotics both joint excess-distortion probability (JEP) and separate probabilities (SEP) criteria. For second-order moderate deviations asymptotics, consider two types of codebooks: spherical codebook each codeword is drawn independently uniformly from surface a sphere i.i.d. component distribution. establish rate-region JEP show that SEP any satisfying mild moment conditions strongly successively refinable. When specialized (GMS), our results provide alternative achievability proof specific code design. SEP, same constant achievable. large only since has better performance than in this regime for layer rate-distortion (Zhou, Tan, Motani, TIT, 2019). exponents specialize GMS, which appears be novel result independent interest.