On Bounds and Closed Form Expressions for Capacities of Discrete Memoryless Channels with Invertible Positive Matrices

While capacities of discrete memoryless channels are well studied, it is still not possible to obtain a closed form expression for the capacity of an arbitrary discrete memoryless channel. This paper describes an elementary technique based on Karush-Kuhn-Tucker (KKT) conditions to obtain (1) a good upper bound of a discrete memoryless channel having an invertible positive channel matrix and (2) a closed form expression for the capacity if the channel matrix satisfies certain conditions related to its singular value and its Gershgorin’s disk.

Major Advisor: Thinh Nguyen
Committee: Bella Bose
Committee: Raviv Raich
Committee: Jinsub Kim
GCR: William H. Warnes