Well-rounded lattices for reliability and security in Rayleigh fading SISO channels

  title={Well-rounded lattices for reliability and security in Rayleigh fading SISO channels},
  author={Oliver Wilhelm Gnilke and Ha Thanh Nguyen Tran and Alex Karrila and Camilla Hollanti},
  journal={2016 IEEE Information Theory Workshop (ITW)},
For many wiretap channel models asymptotically optimal coding schemes are known, but less effort has been put into actual realizations of wiretap codes for practical parameters. Bounds on the mutual information and error probability when using coset coding on a Rayleigh fading channel were recently established by Oggier and Belfiore, and the results in this paper build on their work. However, instead of using their ultimate inverse norm sum approximation, a more precise expression for the… 

Figures and Tables from this paper

Well-Rounded Lattices: Towards Optimal Coset Codes for Gaussian and Fading Wiretap Channels
It is concluded that the minimization of the (average) flatness factor of the eavesdropper’s lattice leads to the study of well-rounded lattices, which are shown to be among the optimal in order to achieve these minima.
Well-rounded lattices for coset coding in MIMO wiretap channels
It is shown through extensive simulations that sublattices of the well-known Alamouti code and Golden code which meet the design criteria perform better than scalar multiples of the code lattice for the same parameters.
On Analytical and Geometric Lattice Design Criteria for Wiretap Coset Codes
It is concluded that in the Gaussian channel, the security boils down to the sphere packing density of the eavesdropper's lattice, whereas in the Rayleigh fading channel a full-diversity well-rounded lattice with a dense sphere packing will provide the best secrecy.
Information bounds and flatness factor approximation for fading wiretap MIMO channels
The design of secure lattice coset codes for general wireless channels with fading and Gaussian noise is studied and it is shown how the average flatness factor can be approximated numerically.
Analysis of Some Well-Rounded Lattices in Wiretap Channels
This paper studies various well-rounded lattices, including the best sphere packings, and analyzes their shortest vector lengths, minimum product distances, and flatness factors, with the goal of acquiring a better understanding of the role of these invarients regarding secure communications.
Lattice Codes for Physical Layer Communications
This thesis consists of several articles considering lattice code design for four different communication settings relevant in modern wireless communications.
Well-rounded algebraic lattices in odd prime dimension
Well-rounded lattices have been considered in coding theory, in approaches to MIMO, and SISO wiretap channels. Algebraic lattices have been used to obtain dense lattices and in applications to
On Communication for Distributed Babai Point Computation
A communication-efficient distributed protocol for computing the Babai point, an approximate nearest point for a random vector ${\bf X}\in\mathbb{R}^n$ in a given lattice is presented and it is suggested that for uniform distributions, the error probability becomes large with the dimension of the lattice, for lattices with good packing densities.
This paper investigates the well-roundedness of lattices coming from polynomials with integer coefficients and real roots in Euclidean space.
Well-Rounded Lattices via Polynomials
This paper investigates when lattices coming from polynomials with integer coefficients are well-rounded, a topic of recent studies with applications in wiretap channels and in cryptography.


Lattice Codes for the Wiretap Gaussian Channel: Construction and Analysis
We consider the Gaussian wiretap channel, where two legitimate players Alice and Bob communicate over an additive white Gaussian noise (AWGN) channel, while Eve is eavesdropping, also through an AWGN
Semantically Secure Lattice Codes for the Gaussian Wiretap Channel
This work proposes a new scheme of wiretap lattice coding that achieves semantic security and strong secrecy over the Gaussian wiretap channel and introduces the notion of secrecy-good lattices, and proposes the flatness factor as a design criterion of such lattices.
A comparison of skewed and orthogonal lattices in Gaussian wiretap channels
It is rigorously shown that, albeit offering simple bit labeling, orthogonal nested lattices are suboptimal for coset coding in terms of both the legitimate receiver's and the eavesdropper's probabilities.
Almost universal codes for fading wiretap channels
This work proposes a sequence of non-random lattice codes which achieve strong secrecy and semantic security over ergodic fading channels and achieves the same constant gap to secrecy capacity over Gaussian and er godic fading models.
Probability estimates for fading and wiretap channels from ideal class zeta functions
New probability estimates are derived for ideal lattice codes from totally real number fields using ideal class Dedekind zeta functions and 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 classdedekindZeta functions.
Algebraic Number Theory and Code Design for Rayleigh Fading Channels
The aim of this work is to provide both an overview on algebraic lattice code designs for Rayleigh fading channels, as well as a tutorial introduction to algebraic number theory.
Lattice Code Design for the Rayleigh Fading Wiretap Channel
  • J. BelfioreF. Oggier
  • Computer Science
    2011 IEEE International Conference on Communications Workshops (ICC)
  • 2011
A criterion of design of both the fine and coarse lattice when used on a Rayleigh fading wiretap channel is presented.
Reducing complexity with less than minimum delay space-time lattice codes
This paper studies the possibility of reducing the complexity, while holding on to a high code rate, by reducing the length of codes by letting go of the assumption of full diversity and studying the achievable diversity-multiplexing gain trade-off.
Inverse Determinant Sums and Connections Between Fading Channel Information Theory and Algebra
It is proven that the growth of the inverse determinant sum of a division algebra-based space-time code is completely determined by the growthof the unit group, and the approach reveals an interesting and tight relation between diversity-multiplexing gain tradeoff and point counting in Lie groups.
Integer Space-Time Block Codes for Practical MIMO Systems
It is shown that the reduction in the number of processor bits is significant for small MIMO channels, while the reduction of the PAPR is significant in comparison with the well known full-rate algebraic STBCs.