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Systematic and optimal cyclotomic lattices and diagonal space-time block code designs

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4 Author(s)
Genyuan Wang ; Dept. of Electr. & Comput. Eng., Univ. of Delaware, Newark, DE, USA ; Huiyong Liao ; Haiquan Wang ; Xiang-Gen Xia

In this correspondence, a new and systematic design of cyclotomic lattices with full diversity is proposed by using some algebraic number theory. This design provides infinitely many full diversity cyclotomic lattices for a given lattice size. Based on the packing theory and the concrete form of the design, optimal cyclotomic lattices are presented by minimizing the mean transmission signal power for a given minimum (diversity) product (or equivalently maximizing the minimum product for a given mean transmission signal power). The newly proposed cyclotomic lattices can be applied to both space-time code designs for multi-antenna systems and linear precode design for signal space diversity in single antenna systems over fast Rayleigh fading channels. Although there are some cyclotomic lattices/space-time codes existing in the literature, most of them are not optimal.

Published in:

IEEE Transactions on Information Theory  (Volume:50 ,  Issue: 12 )