Infinite anti-uniform sources

In this paper we consider the class of anti-uniform Huffman (AUH) codes for sources with infinite alphabet. Poisson, negative binomial, geometric and exponential distributions lead to infinite anti-uniform sources for some ranges of their parameters. Huffman coding of these sources results in AUH codes. We prove that as a result of this encoding, we obtain sources with memory. For these sources we attach the graph and derive the transition matrix between states, the state probabilities and the entropy. If c₀ and c₁ denote the costs for storing or transmission of symbols “0” and “1”, respectively, we compute the average cost for these AUH codes.