We study the problem of computing the capacity of a discrete memoryless channel under uncertainty affecting the channel law matrix, and possibly with a constraint on the average cost of the input distribution. The problem has been formulated in the literature as a max-min problem. We use the robust optimization methodology to convert the max-min problem to a standard convex optimization problem. For small-sized problems, and for many types of uncertainty, such a problem can be solved in principle using interior point methods (IPMs). However, for large-scale problems, IPMs are not practical. Here, we suggest an O(1/T) first-order algorithm based on [1] which is applied directly to the max-min problem.

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Keywords Channel capacity, convex optimization, duality
Persistent URL dx.doi.org/10.1109/TIT.2018.2821674, hdl.handle.net/1765/112708
Series ERIM Top-Core Articles
Journal IEEE Transactions on Information Theory
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Postek, K.S, & Ben-Tal, A. (Aharon). (2018). Computing the Channel Capacity of a Communication System Affected by Uncertain Transition Probabilities. IEEE Transactions on Information Theory, 64(10), 6803–6815. doi:10.1109/TIT.2018.2821674