2010/05/15 by Chen Feng, Danilo Silva, Frank R. Kschischang · 234 citations
Computer Science · Engineering · Mathematics · #Advanced Wireless Communication Technologies #Algebraic number #Algorithm #Artificial intelligence #Coding (social sciences) #Computer network #Computer science #Cooperative Communication and Network Coding #Decoding methods #Encoding (memory) #Gaussian #Lattice (music) #Linear network coding #Mathematics #Relay #Theoretical computer science #Topology (electrical circuits) #Wireless Communication Security Techniques #cs.IT #math.IT
paper · pdf · doi:10.1109/tit.2013.2274264
published in IEEE Transactions on Information Theory 59(11), 7576-7596 (Institute of Electrical and Electronics Engineers) · 5 pages, 3 figures, accepted to IEEE Int. Symp. Information Theory, 2010
arxiv created 2010/05/15 · openalex publication_date 2013/08/16 · arxiv updated 2016/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The problem of designing physical-layer network coding (PNC) schemes via nested lattices is considered. Building on the compute-and-forward (C&F) relaying strategy of Nazer and Gastpar, who demonstrated its asymptotic gain using information-theoretic tools, an algebraic approach is taken to show its potential in practical, nonasymptotic, settings. A general framework is developed for studying nested-lattice-based PNC schemes-called lattice network coding (LNC) schemes for short-by making a direct connection between C&F and module theory. In particular, a generic LNC scheme is presented that makes no assumptions on the underlying nested lattice code. C&F is reinterpreted in this framework, and several generalized constructions of LNC schemes are given. The generic LNC scheme naturally leads to a linear network coding channel over modules, based on which noncoherent network coding can be achieved. Next, performance/complexity tradeoffs of LNC schemes are studied, with a particular focus on hypercube-shaped LNC schemes. The error probability of this class of LNC schemes is largely determined by the minimum intercoset distances of the underlying nested lattice code. Several illustrative hypercube-shaped LNC schemes are designed based on Constructions A and D, showing that nominal coding gains of 3 to 7.5 dB can be obtained with reasonable decoding complexity. Finally, the possibility of decoding multiple linear combinations is considered and related to the shortest independent vectors problem. A notion of dominant solutions is developed together with a suitable lattice-reduction-based algorithm.