Enabling multiplication in lattice codes via Construction A
Date of Issue2013
Information Theory Workshop (2013 : Sevilla, Spain)
School of Physical and Mathematical Sciences
As a first step towards distributed computations in a wireless network, we introduce ideal lattices, that is lattices built over an ideal of a ring of integers in a number field, as a tool for constructing lattice codes at the physical layer. These lattices are not only additive groups as all lattices, but they are also equipped with a multiplication, which enables polynomial operations at each node of the wireless network. In this paper, we show how some of these ideal lattices can be constructed from polynomial codes (generalization of cyclic codes) via Construction A, and illustrate how these lattices enable multiplication.
© Institute of Electrical and Electronics Engineers (IEEE). This is the author created version of a work that has been peer reviewed and accepted for publication by 2013 IEEE Information Theory Workshop (ITW), Institute of Electrical and Electronics Engineers (IEEE). It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [DOI: http://dx.doi.org/10.1109/ITW.2013.6691274].