Capacity-Achieving Input Distribution of the Additive Uniform Noise Channel with Peak Amplitude and Cost Constraint

Jonas Stapmanns, Catarina Dias, Luke Eilers, Jean-Pascal Pfister

Abstract: Under which condition is quantization optimal? We address this question in the context of the additive uniform noise channel under peak amplitude and cost constraints. We compute analytically the capacity-achieving input distribution as a function of the noise level, the average cost constraint, and the exponent of the cost function. We found that when the cost function is concave, the capacity-achieving input distribution is discrete, whereas when the cost function is convex and the cost constraint is active, the support of the capacity-achieving input distribution spans the entire interval.

External IDs:dblp:conf/isit/StapmannsDEP25