Excess Distortion In Lossy Compression: Beyond One-Shot Analysis

The problem of finite-blocklength lossy compression under an excess-distortion constraint is considered. If the blocklength constraint comes from the length of the source sequence itself, the excess rate needed above the rate-distortion function decays inversely proportional to the square root of the blocklength, according to second-order (dispersion) analysis. We consider a different case, where the source emits a long sequence, but shorter sub-sequences are considered for reasons such as delay, complexity and smoothness of the reconstruction fidelity. We analyze the redundancy of the rate with respect to different constraints. We show that the rate redundancy with respect to the processing blocklength, i.e. the dimension of the quantizer used, decays much faster than the dispersion analysis suggests. Thus, one may use much shorter source codes without sacrificing second-order performance.