M-ary anti-uniform Huffman codes for infinite sources with geometric distribution

In this paper we consider the class of generalized anti-uniform Huffman (AUH) codes for sources with infinite alphabet and geometric distribution. This distribution leads to infinite anti-uniform sources for some ranges of its parameters. Huffman coding of these sources results in AUH codes. We perform a generalization of binary Huffman encoding, using a, M-letter code alphabet and prove that as a result of this encoding, sources with memory are obtained. For these sources we attach the graph and derive the transition probabilities between states, as well as the state probabilities. The entropy and the average cost for AUH codes are derived.