2012/01/18 by Fuchun Lin, Lin, Fuchun, Frédérique Oggier +1 · 2 citations
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT) #Wireless Communication Security Techniques #cs.IT #math.IT #math.NT
paper · pdf · doi:10.48550/arxiv.1201.3688
10 pages
arxiv created 2012/01/18 · openalex publication_date 2012/01/18 · arxiv updated 2012/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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, a formula for the secrecy gain of unimodular lattices is derived. Secrecy gains of extremal odd unimodular lattices as well as unimodular lattices in dimension n, 16 ≤ n ≤ 23 are computed, covering the 4 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 are determined.