Lossy compression with a short processing block: Asymptotic analysis

Finite-blocklength analysis of lossy compression can have a variety of different motivations. First, the source sequence itself may be short. Second, delay and complexity constraints may require processing of short source blocks. And finally, user experience may require low distortion when averaging over short blocks, which we term fidelity blocks. Existing work on the subject has largely coupled these issues, i.e., a source block is compressed taking into account the statistics of the distortion averaged over that block (usually the excess-distortion probability). For short source sequences, this coupling indeed makes sense. In this work, however, we instead consider the case of a long source sequence, whose compression performance is set by the interplay between the comparatively shorter processing and fidelity blocklengths. We focus on asymptotic analysis of the excess rate needed to ensure a given excess-distortion probability, for processing blocks that are shorter than the fidelity ones. Our main result is that the second-order performance (dispersion) is relatively unaffected by choosing a processing blocklength considerably shorter than the fidelity blocklength. Thus, one may use lower dimensional quantizers than existing work would otherwise suggest without sacrificing significant performance.