Almost universal codes for MIMO wiretap channels

Despite several works on secrecy coding for fading and MIMO wiretap channels from an error probability perspective, the construction of information theoretically secure codes over such channels remains as an open problem. In this paper, we consider a fading wiretap channel model where the transmitter has only partial statistical channel state information. We extend the flatness factor criterion from the Gaussian wiretap channel to fading and MIMO wiretap channels, and propose concrete lattice codes with a vanishing flatness factor to achieve information theoretic security. These codes are built from algebraic number fields with constant root discriminant for the singleantenna fading wiretap channel, and from division algebras centered at such number fields for the MIMO wiretap channel, respectively. The proposed lattice codes achieve strong secrecy and semantic security over any ergodic stationary fading/MIMO wiretap channel with sufficiently fast decay of time correlations, for all secrecy rates R < Cb−Ce−κ, where Cb and Ce are Bob and Eve’s channel capacities respectively, and κ is an explicit constant gap. Moreover, these codes are almost universal in the sense that a fixed code is good for secrecy for a wide range of fading models. Index Terms algebraic number theory, division algebras, fading wiretap channel, information theoretic security, lattice coding, MIMO wiretap channel, statistical CSIT.