Random coding strategies for minimum entropy

Abstract

This paper proves that there exists a fixed random coding strategy for block coding a memoryless information source to achieve the absolute epsilon entropy of the source. That is, the strategy can be chosen independent of the block length. The principal new tool is an easy result on the semicontinuity of the relative entropy functional of one probability distribution with respect to another. The theorem generalizes a result from rate-distortion theory to the 'zero-infinity' case.