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On the capacity of some deterministic non-linear channels subject to additive white Gaussian noise

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2 Author(s)
Abou-Faycal, I. ; Dept. of Elec. & Comp. Eng., American Univ. of Beirut, Beirut, Lebanon ; Fahs, J.

We consider a variety of memoryless discrete-time noisy communication channels where the noise is modeled as an additive white Gaussian noise process, and where the input of the channel is distorted according to a deterministic function f(X) of the form i) f(X) = αXn ii) f(X) = α|X|n iii) f(X) = α|X|1/q iv) f(X) = αsgn(X)|X|1/q, for all α ϵ R*, n ϵ N*{1}. Subject to an average power constraint, we study the capacity-achieving input distributions of these classes of channels and prove them to be discrete except for the linear case f(X) = αX, where the optimal input is Gaussian distributed. Furthermore, we prove that these optimal input distributions have a finite number of mass points for classes iii) and iv). The results are reached through the development of a methodology and tools that are based on standard decompositions in a Hilbert space with the Hermite Polynomials as a basis, and we conjecture that these bases are natural candidates for general information-theoretic studies of the capacity of channels affected by additive white Gaussian noise.

Published in:

Telecommunications (ICT), 2010 IEEE 17th International Conference on

Date of Conference:

4-7 April 2010