Almost universal codes for MIMO wiretap channels
Laura Luzzi, Roope Vehkalahti, Cong Ling

TL;DR
This paper develops universal lattice codes for MIMO wiretap channels with fading, achieving strong secrecy and semantic security across various fading models using algebraic number theory and a new flatness factor criterion.
Contribution
It introduces a new design criterion based on the flatness factor for fading MIMO wiretap channels and constructs universal lattice codes satisfying this criterion.
Findings
Codes achieve strong secrecy and semantic security.
Proposed codes are nearly universal across different fading models.
Achievable rates are close to the difference of capacities with a constant gap.
Abstract
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 an open problem. In this paper, we consider a fading wiretap channel model where the transmitter has only partial statistical channel state information. Our channel model includes static channels, i.i.d. block fading channels, and ergodic stationary fading with fast decay of large deviations for the eavesdropper's channel. We extend the flatness factor criterion from the Gaussian wiretap channel to fading and MIMO wiretap channels, and establish a simple design criterion where the normalized product distance / minimum determinant of the lattice and its dual should be maximized simultaneously. Moreover, we propose concrete lattice codes satisfying this design criterion, which are built…
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Taxonomy
TopicsCooperative Communication and Network Coding · Wireless Communication Security Techniques · Coding theory and cryptography
