Embedding discrete memoryless channels on compact and minimal surfaces

The aim of this paper is to identify the geometric and algebraic structures associated to discrete memoryless channels. The procedure employed to achieve this goal is based on the following steps: knowing the graph associated to the discrete memoryless channel, 1) determine the set of surfaces in which the graph is embedded; 2) establish the set of algebraic structures inherited by the surfaces through the first homology group; and 3) identify the regular tessellations which may be used in the design of modulators and quantizers.