Semantically Secure Lattice Codes for Compound MIMO Channels

Abstract

We consider compound multi-input multi-output (MIMO) wiretap channels where minimal channel state information at the transmitter (CSIT) is assumed. Code construction is given for the special case of isotropic mutual information, which serves as a conservative strategy for general cases. Using the flatness factor for MIMO channels, we propose lattice codes universally achieving the secrecy capacity of compound MIMO wiretap channels up to a constant gap (measured in nats) that is equal to the number of transmit antennas. The proposed approach improves upon existing works on secrecy coding for MIMO wiretap channels from an error probability perspective, and establishes information theoretic security (in fact semantic security). We also give an algebraic construction to reduce the code design complexity, as well as the decoding complexity of the legitimate receiver. Thanks to the algebraic structures of number fields and division algebras, our code construction for compound MIMO wiretap channels can be reduced to that for Gaussian wiretap channels, up to some additional gap to secrecy capacity.

An Approximation of Theta Functions with Applications to Communications

“…We refer to [4] for the complex alternative. 2 Assume that K > 1 transmitters want to communicate to a single destination, aided BARREAL, DAMIR, FREIJ-HOLLANTI, AND HOLLANTI Relay 1 . .…”

“…From an applications perspective, it has been recently shown that code design in various areas of wireless communications and cryptography can profit from studying the theta series of certain involved lattices, e.g., for wiretap code design [1,2], dither avoidance in lattice noise quantization [3], or compute-and-forward relaying [4]. Compute-and-forward relaying is a promising physical layer network coding protocol proposed in the award-winning paper [4] and exploits the natural effects of interference by decoding linear combinations of the transmitted messages at the intermediate relays to achieve high computation rates.…”