Almost universal codes for fading wiretap channels

We consider a fading wiretap channel model where the transmitter has only statistical channel state information, and the legitimate receiver and eavesdropper have perfect channel state information. We propose a sequence of non-random lattice codes which achieve strong secrecy and semantic security over ergodic fading channels. The construction is almost universal in the sense that it achieves the same constant gap to secrecy capacity over Gaussian and ergodic fading models.Comment: 5 pages, to be submitted to IEEE International Symposium on Information Theory (ISIT) 201

Nonasymptotic Probability Bounds for Fading Channels Exploiting Dedekind Zeta Functions

In this paper, new probability bounds are derived for algebraic lattice codes. This is done by using the Dedekind zeta functions of the algebraic number fields involved in the lattice constructions. In particular, it is shown how to upper bound the error performance of a finite constellation on a Rayleigh fading channel and the probability of an eavesdropper's correct decision in a wiretap channel. As a byproduct, an estimate of the number of elements with a certain algebraic norm within a finite hyper-cube is derived. While this type of estimates have been, to some extent, considered in algebraic number theory before, they are now brought into novel practice in the context of fading channel communications. Hence, the interest here is in small-dimensional lattices and finite constellations rather than in the asymptotic behavior

Probability Estimates for Fading and Wiretap Channels from Ideal Class Zeta Functions

In this paper, new probability estimates are derived for ideal lattice codes from totally real number fields using ideal class Dedekind zeta functions. In contrast to previous work on the subject, it is not assumed that the ideal in question is principal. In particular, it is shown that the corresponding inverse norm sum depends not only on the regulator and discriminant of the number field, but also on the values of the ideal class Dedekind zeta functions. Along the way, we derive an estimate of the number of elements in a given ideal with a certain algebraic norm within a finite hypercube. We provide several examples which measure the accuracy and predictive ability of our theorems.Comment: 24 pages. Extends our earlier arxiv submission arxiv.1303.347

Achieving capacity and security in wireless communications with lattice codes

Based on lattice Gaussian distributions and ideal lattices, we present a unified framework of lattice coding to achieve the channel capacity and secrecy capacity of wireless channels in the presence of Gaussian noise. The standard additive white Gaussian-noise (AWGN) channel, block fading channel, and multi-input multi-output (MIMO) fading channel are considered, which form a hierarchy of increasingly challenging problems in coding theory. To achieve channel capacity, we apply Gaussian shaping to a suitably defined good lattice for channel coding. To achieve secrecy capacity, we use a secrecy-good lattice nested with a coding lattice