Projects per year
Abstract
Computing the theta series of an arbitrary lattice, and more specifically a related quantity known as the flatness factor, has been recently shown to be important for lattice code design in various wireless communication setups. However, the theta series is in general not known in closed form, excluding a small set of very special lattices. In this article, motivated by the practical applications as well as the mathematical problem itself, a simple approximation of the theta series of a lattice is derived. A rigorous analysis of its accuracy is provided. In relation to this, maximumlikelihood decoding in the context of computeandforward relaying is studied. Following previous work, it is shown that the related metric can exhibit a flat behavior, which can be characterized by the flatness factor of the decoding function. Contrary to common belief, we note that the decoding metric can be rewritten as a sum over a random lattice only when at most two sources are considered. Using a particular matrix decomposition, a link between the random lattice and the code lattice employed at the transmitter is established, which leads to an explicit criterion for code design, in contrast to implicit criteria derived previously. Finally, candidate lattices are examined with respect to the proposed criterion using the derived theta series approximation.
Original language  English 

Pages (fromto)  471501 
Number of pages  31 
Journal  SIAM Journal on Applied Algebra and Geometry 
Volume  4 
Issue number  4 
DOIs  
Publication status  Published  2021 
MoE publication type  A1 Journal articlerefereed 
Keywords
 Arbitrary lattices
 Computeandforward protocol
 Flatness factor
 Geometry of lattices
 Lattice codes
 Theta series approximation
 Wireless communications
 Wiretap channels
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Projects
 3 Finished

Numbertheoretic and combinatorial tools for private and secure cloud services
Hollanti, C., Westerbäck, T., Arabi Kakavandfaramani, M., Grezet, M. & Damir, M.
01/07/2016 → 30/06/2018
Project: Academy of Finland: Other research funding

Applied algebra in communications technology
Hollanti, C., Gnilke, O. & Greferath, M.
01/09/2014 → 31/08/2019
Project: Academy of Finland: Other research funding

Applied Algebra and Number Theory in Robust and Secure Wireless Cloud Storage Systems
Gnilke, O., Hollanti, C., Amoros Carafi, L., Kuznetsova, O., Milione, P. & Westerbäck, T.
01/09/2014 → 31/08/2018
Project: Academy of Finland: Other research funding