Entropy and Average Cost of AUH Codes

Abstract

Abstract-In this paper we address the class of anti-uniform Huffman (AUH) codes, named also unary codes, for sources with finite and infinite alphabet, respectively. Geometric, quasi-geometric, Fibonacci, exponential, Poisson, and negative binomial distributions lead to anti -uniform sources for some ranges of their parameters. Huffman coding of these sources results in AUH codes. We prove that as result of this encoding, in general, sources with memory are obtained. For these sources we attach the graph and determine the transition matrix between states, the state probabilities and the entropy. If c 0 and c 1 denote the costs for storing or transmission of symbols "0" and "1", respectively, we compute the average cost for these AUH codes.