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

@article{Gnilke2016WellroundedLF, 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)}, year={2016}, pages={359-363} }

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…

## 14 Citations

Well-Rounded Lattices: Towards Optimal Coset Codes for Gaussian and Fading Wiretap Channels

- Computer ScienceIEEE Transactions on Information Theory
- 2021

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

- Computer Science2016 26th International Telecommunication Networks and Applications Conference (ITNAC)
- 2016

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

- Computer ScienceArXiv
- 2016

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

- Computer Science2016 26th International Telecommunication Networks and Applications Conference (ITNAC)
- 2016

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

- Computer Science2018 IEEE 19th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)
- 2018

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

- Computer ScienceArXiv
- 2017

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

- MathematicsArchiv der Mathematik
- 2018

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

- Computer ScienceIEEE Transactions on Information Theory
- 2021

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.

WELL-ROUNDED LATTICES VIA POLYNOMIALS WITH REAL ROOTS

- Computer Science, Mathematics
- 2020

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

- Mathematics, Computer ScienceArXiv
- 2019

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.

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