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

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.