Lattice network coding over Euclidean Domains

• Main Authors: Vázquez-Castro, M. A., Oggier, Frédérique
• Other Authors: School of Physical and Mathematical Sciences
• Format: Conference or Workshop Item
• Language: English
• Published: 2014
• Subjects: DRNTU::Science::Mathematics
• Online Access: https://hdl.handle.net/10356/97292; http://hdl.handle.net/10220/24384; http://ieeexplore.ieee.org.ezlibproxy1.ntu.edu.sg/xpl/login.jsp?tp=&arnumber=6952389&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D6952389
• Institution: Nanyang Technological University

We propose a novel approach to design and analyse lattice-based network coding. The underlying alphabets are carved from (quadratic imaginary) Euclidean domains with a known Euclidean division algorithm, due to their inherent algorithmical ability to capture analog network coding computations. These alphabets are used to embed linear p-ary codes of length n, p a prime, into n-dimensional Euclidean ambient spaces, via a variation of the so-called Construction A of lattices from linear codes. A study case over one such Euclidean domain is presented and the nominal coding gain of lattices obtained from p-ary Hamming codes is computed for any prime p such that p ≡ 1 (mod 4).