Algebraic Approach to Physical-Layer Network Coding

Details Algebraic Approach to Physical-Layer Network Coding Algebraic Approach to Physical-Layer Network Coding

2011-08-08

arxiv.org/abs/1108.1695v1

Computer Science

Information Theory

Submitted to IEEE Transactions on Information Theory, July 21, 2011

Scientific paper

The problem of designing physical-layer network coding (PNC) schemes via lattice partitions 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, non-asymptotic, settings. A general framework is developed for studying lattice-partition-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 lattice partition. C&F is re-interpreted in this framework, and several generalized constructions of LNC schemes are given based on the generic LNC scheme. Next, the error performance of LNC schemes is analyzed, with a particular focus on hypercube-shaped LNC schemes. The error probability of this class of LNC schemes is related to certain geometric parameters of the underlying lattice partitions, resulting in design criteria both for choosing receiver parameters and for optimizing lattice partitions. These design criteria lead to explicit algorithms for choosing receiver parameters that are closely related to sphere-decoding and lattice-reduction algorithms. These design criteria also lead to several specific methods for optimizing lattice partitions, and examples are provided showing that 3 to 5 dB performance improvement over some baseline LNC schemes is easily obtained with reasonable decoding complexity.

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