Log In Sign Up

Formally Unimodular Packings for the Gaussian Wiretap Channel

by   Maiara F. Bollauf, et al.

This paper introduces the family of lattice-like packings, which generalizes lattices, consisting of packings possessing periodicity and geometric uniformity. The subfamily of formally unimodular (lattice-like) packings is further investigated. It can be seen as a generalization of the unimodular and isodual lattices, and the Construction A formally unimodular packings obtained from formally self-dual codes are presented. Recently, lattice coding for the Gaussian wiretap channel has been considered. A measure called secrecy function was proposed to characterize the eavesdropper's probability of correctly decoding. The aim is to determine the global maximum value of the secrecy function, called (strong) secrecy gain. We further apply lattice-like packings to coset coding for the Gaussian wiretap channel and show that the family of formally unimodular packings shares the same secrecy function behavior as unimodular and isodual lattices. We propose a universal approach to determine the secrecy gain of a Construction A formally unimodular packing obtained from a formally self-dual code. From the weight distribution of a code, we provide a necessary condition for a formally self-dual code such that its Construction A formally unimodular packing is secrecy-optimal. Finally, we demonstrate that formally unimodular packings/lattices can achieve higher secrecy gain than the best-known unimodular lattices.


page 1

page 2

page 3

page 4


The Secrecy Gain of Formally Unimodular Lattices on the Gaussian Wiretap Channel

We consider lattice coding for the Gaussian wiretap channel, where the c...

On the Secrecy Gain of Formally Unimodular Construction A_4 Lattices

Lattice coding for the Gaussian wiretap channel is considered, where the...

Construction C^ from Self-Dual Codes

Construction C^ was recently introduced as a generalization of the multi...

Semantically Secure Lattice Codes for Compound MIMO Channels

We consider code construction for compound multi-input multi-output (MIM...

Explicit Codes for the Wiretap Channel: A Unified Design Framework

A construction of explicit codes for the wiretap channel is proposed. Ap...

On isodual double Toeplitz codes

Double Toeplitz (shortly DT) codes are introduced here as a generalizati...

Multilevel constructions: coding, packing and geometric uniformity

Lattice and special nonlattice multilevel constellations constructed fro...