Capacity Approximation of Continuous Channels by Discrete Inputs

Malcolm Egan (1, 2, 3) , Samir Perlaza (2, 4, 3)

1 INSA - Institut National des Sciences Appliquées
2 SOCRATE - Software and Cognitive radio for telecommunications
3 MARACAS - Modèle et algorithmes pour des systèmes de communication fiables
4 Princeton University

In this paper, discrete approximations of the capacity are introduced where the input distribution is constrained to be discrete in addition to any other constraints on the input. For point-to-point memoryless additive noise channels, rates of convergence to the capacity of the original channel are established for a wide range of channels for which the capacity is finite. These results are obtained by viewing discrete approximations as a capacity sensitivity problem, where capacity losses are studied when there are perturbations in any of the parameters describing the channel. In particular, it is shown that the discrete approximation converges arbitrarily close to the channel capacity at rate O(∆), where ∆ is the discretization level of the approximation. Examples of channels where this rate of convergence holds are also given, including additive Cauchy and inverse Gaussian noise channels.

Domaines: Théorie de l'information [cs.IT]; Théorie de l'information et codage [math.IT]

Malcolm Egan, Samir Perlaza. Capacity Approximation of Continuous Channels by Discrete Inputs. CISS 2018 - 52nd Annual Conference on Information Sciences and Systems, Mar 2018, Princeton, United States. pp.1-6, ⟨10.1109/CISS.2018.8362269⟩. ⟨hal-01686036⟩