On Closed Form Capacities of Discrete Memoryless Channels

摘要

While capacities of discrete memoryless channels are well studied, it is still not possible to obtain a closed form expression of the capacity for an arbitrary discrete memoryless channel. This paper shows an elementary technique based on Karush-Kuhn-Tucker (KKT) conditions to obtain a closed form expression for a good upper bound of an arbitrary discrete memoryless channel. Furthermore, using this technique, we are able to obtain the closed form expressions for the capacities of channels whose channel matrices satisfy a number of conditions.