TY - GEN
T1 - Analysis of Some Well-Rounded Lattices in Wiretap Channels
AU - Taoufiq Damir, Mohamed
AU - Gnilke, Oliver
AU - Amoros, Laia
AU - Hollanti, Camilla
PY - 2018/8/24
Y1 - 2018/8/24
N2 - Recently, various criteria for constructing wiretap lattice coset codes have been proposed, most prominently the minimization of the so-called flatness factor. However, these criteria are not constructive per se. As explicit constructions, well-rounded lattices have been proposed as possible minimizers of the flatness factor, but no rigorous proof has been given. In this paper, we study various well-rounded lattices, including the best sphere packings, and analyze 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. Simulations are carried out in dimensions four and eight, yielding the conclusion that the best sphere packing does not necessarily yield the best performance, not even when compared to other well-rounded lattices having the same superlattice. This motivates further study and construction of well-rounded lattices for physical laver security.
AB - Recently, various criteria for constructing wiretap lattice coset codes have been proposed, most prominently the minimization of the so-called flatness factor. However, these criteria are not constructive per se. As explicit constructions, well-rounded lattices have been proposed as possible minimizers of the flatness factor, but no rigorous proof has been given. In this paper, we study various well-rounded lattices, including the best sphere packings, and analyze 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. Simulations are carried out in dimensions four and eight, yielding the conclusion that the best sphere packing does not necessarily yield the best performance, not even when compared to other well-rounded lattices having the same superlattice. This motivates further study and construction of well-rounded lattices for physical laver security.
KW - Algebraic number fields
KW - coset coding
KW - ideals
KW - single-input single-output (SISO) channels
KW - sphere packings
KW - well-rounded lattices
KW - wiretap channels
UR - http://www.scopus.com/inward/record.url?scp=85053471135&partnerID=8YFLogxK
U2 - 10.1109/SPAWC.2018.8445937
DO - 10.1109/SPAWC.2018.8445937
M3 - Article in proceeding
AN - SCOPUS:85053471135
SN - 9781538635124
T3 - IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)
BT - 2018 IEEE 19th International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2018
PB - IEEE Signal Processing Society
T2 - 19th IEEE International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2018
Y2 - 25 June 2018 through 28 June 2018
ER -