Projekteja vuodessa
Abstrakti
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.
Alkuperäiskieli  Englanti 

Sivut  471501 
Sivumäärä  31 
Julkaisu  SIAM Journal on Applied Algebra and Geometry 
Vuosikerta  4 
Numero  4 
DOI  pysyväislinkit  
Tila  Julkaistu  2021 
OKMjulkaisutyyppi  A1 Julkaistu artikkeli, soviteltu 
Sormenjälki Sukella tutkimusaiheisiin 'An approximation of theta functions with applications to communications'. Ne muodostavat yhdessä ainutlaatuisen sormenjäljen.
Projektit
 3 Päättynyt

Lukuteoreettisia ja kombinatorisia työkaluja yksityisiin ja turvallisiin pilvipalveluihin
Hollanti, C., Westerbäck, T., Arabi Kakavandfaramani, M., Grezet, M. & Damir, M.
01/07/2016 → 30/06/2018
Projekti: Academy of Finland: Other research funding

Sovellettu algebra tietoliikenneteknologiassa
Hollanti, C., Gnilke, O. & Greferath, M.
01/09/2014 → 31/08/2019
Projekti: Academy of Finland: Other research funding

Sovellettu algebra ja lukuteoria kestävien ja turvallisten langattomien pilvitallennussysteemien suunnittelussa
Gnilke, O., Hollanti, C., Amoros Carafi, L., Kuznetsova, O., Milione, P. & Westerbäck, T.
01/09/2014 → 31/08/2018
Projekti: Academy of Finland: Other research funding