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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 disk