New Non-Asymptotic Bounds on Numbers of Codewords for the Fixed-Length Lossy Compression

Abstract

In this paper, we deal with the fixed-length lossy compression, where a fixed-length sequence emitted from the information source is encoded into a codeword, and the source sequence is reproduced from the codeword with a certain distortion. We give lower and upper bounds on the minimum number of codewords such that the probability of exceeding a given distortion level is less than a given probability. These bounds are characterized by using the α-mutual information of order infinity. Further, for i.i.d. binary sources, we provide numerical examples of tight upper bounds which are computable in polynomial time in the blocklength.