A revisit to the Muroga method of computing channel capacity

The Muroga method is an algebraic method of computing the capacity of discrete memoryless channels. Shannon interpreted the method geometrically. However, in the process, he ignored the meaning of the intermediate vector x, although which played a key computational role in Muroga´s work. Although Shannon´s view was inherited thereafter, by Gallager, and Csiszsár and Körner, the algebra of Muroga was not. We revisit the original Muroga method, and while following Shannon´s view, will give a geometry of Muroga´s algebraic computation. This view enables new applications. One class of application is directly related to the capacity computation; We first give a sensitivity analysis of the capacity. Next, we give a capacity computation algorithm for the channels which have more input symbols than the output symbols. The other class of application is the universal noiseless source coding, in particular, the universal expected redundancy. For the latter, we propose a new (Muroga) upper bound and a stochastic complexity bound.