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While capacities of discrete memoryless channels are well studied, it isstill not possible to obtain a closed-form expression for the capacity of anarbitrary discrete memoryless channel. This paper describes an elementarytechnique based on Karush Kuhn Tucker (KKT) conditions to obtain (1) a goodupper bound of a discrete memoryless channel having an invertible positivechannel matrix and (2) a closed-form expression for the capacity if the channelmatrix satisfies certain conditions related to its singular value and itsGershgorin disk.

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