Ordered and Disordered Source Coding

The separation of the information in a vector into order (a permutation) and value (a multiset) is studied. We formulate rate-distortion problems in which order is irrelevant, for which we give conclusive results in cases where the set size approaches infinity. Conversely, we present a distortion measure on partial orders and source coding techniques based on partial orders. Multiple partial orders can be mutually refining, leading to a form of permutation coding for multiple descriptions. Permutation coding of a harmonic frame expansion gives lowcomplexity vector quantizers with low-rate performance superior to that of entropy-constrained scalar quantization.