A Kashin Approach to the Capacity of the Discrete Amplitude Constrained Gaussian Channel

Brendan Farrell (1) , Peter Jung (2)

1 Technische Universität Berlin - Heinrich-Hertz Lehrstuhl, Technische Universität Berlin
2 MCI - Fraunhofer German-Sino Lab for Mobile Communications

We derive an explicit lower bound on the capacity of the discrete amplitude–constrained Gaussian channel by proving the existence of tight frames that permit redundant vector representations with small coefficients. Our method encodes the information in subspaces that are optimal in terms of the power to amplitude ratio. In a recent paper, Lyubarskii and Vershynin discuss how the work of Kashin (1977) implies the existence of such representations, and they term them Kashin respresentations. We use this work from frame theory to address the relationship between signal redundancy, peak–to–average power ratio and achievable data rates.

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

Brendan Farrell, Peter Jung. A Kashin Approach to the Capacity of the Discrete Amplitude Constrained Gaussian Channel. SAMPTA'09, May 2009, Marseille, France. Special Session on Sampling and Communication. ⟨hal-00451439⟩