The redundancy of universal fixed rate source coding

Given an independently and identically distributed (i.i.d) source X={X_t}_t=1^∞ with finite source and reproduction alphabets A and B, we are concerned with efficient universal block coding of X subject to a fidelity criterion. Let p be the generic distribution on A of X; p is unknown and regarded as a parameter vector ranging over all distributions on the source alphabet A. Universal lossy source coding theory assures that there exists a sequence of universal block codes (either at a fixed rate level or at a fixed distortion level) for the class of memoryless sources. However, the theory does not tell us how efficient universal block coding with a block length n can be, that is, how close the performance of a universal nth order block code, which is the best in some sense, can be to the distortion rate function d(p,R) (or the rate distortion function R(p,d)) of each memoryless source p. The purpose of this paper is to investigate this question. Namely, we analyze the redundancy of universal lossy source coding