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A Classification of Unimodular Lattice Wiretap Codes in Small Dimensions

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2 Author(s)
Fuchun Lin ; Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore ; Frédérique Oggier

Lattice coding over a Gaussian wiretap channel, where an eavesdropper listens to transmissions between a transmitter and a legitimate receiver, is considered. A new lattice invariant called the secrecy gain is used as a code design criterion for wiretap lattice codes since it was shown to characterize the confusion that a chosen lattice can cause at the eavesdropper: the higher the secrecy gain of the lattice, the more confusion. In this paper, secrecy gains of extremal odd unimodular lattices as well as unimodular lattices in dimension n, 16 ≤ n ≤ 23, are computed, covering the four extremal odd unimodular lattices and all the 111 nonextremal unimodular lattices (both odd and even), providing thus a classification of the best wiretap lattice codes coming from unimodular lattices in dimension n, 8 <; n ≤ 23. Finally, to permit lattice encoding via Construction A, the corresponding error correction codes of the best lattices are determined.

Published in:

IEEE Transactions on Information Theory  (Volume:59 ,  Issue: 6 )