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

Mohamed Taoufiq Damir; Alex Karrila; Laia Amoros; Oliver W. Gnilke; David Karpuk; Camilla Hollanti

doi:10.1109/TIT.2021.3059749

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

Mohamed Taoufiq Damir, Alex Karrila, Laia Amoros, Oliver W. Gnilke, David Karpuk, Camilla Hollanti

Mathematics

Research output: Contribution to journal › Article › Scientific › peer-review

6 Citations (Scopus)

Abstract

The design of lattice coset codes for wiretap channels is considered. Bounds on the eavesdropper's correct decoding probability and information leakage are first revisited. From these bounds, it is explicit that both the information leakage and error probability are controlled by the average flatness factor of the eavesdropper's lattice, which we further interpret geometrically. 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. Constructions of some well-rounded lattices are also provided.

Original language	English
Article number	9354828
Pages (from-to)	3645-3663
Journal	IEEE Transactions on Information Theory
Volume	67
Issue number	6
DOIs	https://doi.org/10.1109/TIT.2021.3059749
Publication status	Published - Jun 2021
MoE publication type	A1 Journal article-refereed

Keywords

Fading channels
Error probability
Lattices
Minimization
Decoding
MIMO communication
Coset codes
flatness factor
information theoretic security
lattices
multiple-input multiple-output (MIMO) channels
number fields
physical layer security
Rayleigh fast-fading channels
single-input single-output (SISO) channels
well-rounded lattices
wiretap channels

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10.1109/TIT.2021.3059749

https://arxiv.org/abs/1609.07723Licence: Unknown
https://urn.fi/URN:NBN:fi-fe202201148643

Cite this

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title = "Well-Rounded Lattices: Towards Optimal Coset Codes for Gaussian and Fading Wiretap Channels",

abstract = "The design of lattice coset codes for wiretap channels is considered. Bounds on the eavesdropper's correct decoding probability and information leakage are first revisited. From these bounds, it is explicit that both the information leakage and error probability are controlled by the average flatness factor of the eavesdropper's lattice, which we further interpret geometrically. 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. Constructions of some well-rounded lattices are also provided.",

keywords = "Fading channels, Error probability, Lattices, Minimization, Decoding, MIMO communication, Coset codes, flatness factor, information theoretic security, lattices, multiple-input multiple-output (MIMO) channels, number fields, physical layer security, Rayleigh fast-fading channels, single-input single-output (SISO) channels, well-rounded lattices, wiretap channels",

author = "Damir, {Mohamed Taoufiq} and Alex Karrila and Laia Amoros and Gnilke, {Oliver W.} and David Karpuk and Camilla Hollanti",

year = "2021",

month = jun,

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language = "English",

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pages = "3645--3663",

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publisher = "Institute of Electrical and Electronics Engineers",

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T1 - Well-Rounded Lattices: Towards Optimal Coset Codes for Gaussian and Fading Wiretap Channels

AU - Damir, Mohamed Taoufiq

AU - Karrila, Alex

AU - Amoros, Laia

AU - Gnilke, Oliver W.

AU - Karpuk, David

AU - Hollanti, Camilla

PY - 2021/6

Y1 - 2021/6

N2 - The design of lattice coset codes for wiretap channels is considered. Bounds on the eavesdropper's correct decoding probability and information leakage are first revisited. From these bounds, it is explicit that both the information leakage and error probability are controlled by the average flatness factor of the eavesdropper's lattice, which we further interpret geometrically. 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. Constructions of some well-rounded lattices are also provided.

AB - The design of lattice coset codes for wiretap channels is considered. Bounds on the eavesdropper's correct decoding probability and information leakage are first revisited. From these bounds, it is explicit that both the information leakage and error probability are controlled by the average flatness factor of the eavesdropper's lattice, which we further interpret geometrically. 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. Constructions of some well-rounded lattices are also provided.

KW - Fading channels

KW - Error probability

KW - Lattices

KW - Minimization

KW - Decoding

KW - MIMO communication

KW - Coset codes

KW - flatness factor

KW - information theoretic security

KW - lattices

KW - multiple-input multiple-output (MIMO) channels

KW - number fields

KW - physical layer security

KW - Rayleigh fast-fading channels

KW - single-input single-output (SISO) channels

KW - well-rounded lattices

KW - wiretap channels

U2 - 10.1109/TIT.2021.3059749

DO - 10.1109/TIT.2021.3059749

M3 - Article

SN - 0018-9448

VL - 67

SP - 3645

EP - 3663

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 6

M1 - 9354828

ER -

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

Abstract

Keywords

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