Design of lattice network codes based on Construction D

Abstract

Physical-layer network coding (PNC) takes advantage of signal interference to transmit linearly combined data from multiple nodes. Nazer and Gastpar introduced the use of nested lattice codes to network coding by demonstrating that linear combination according to channel dependent integer coefficients provides an effective coding scheme. Feng et al. presented an algebraic approach for this strategy based on modules. They developed practical design guidelines, especially for Construction A. This paper intends to show the same possibilities for lattices built with the multilevel Construction D. We know from Feng et al. that Construction D achieves higher coding gains than A and also that multilevel codes can construct large modulations from simple level codes. We present a multi-stage decoder with a modified Viterbi metric for lattice decoding. Simulation results verify the scheme's feasibility for a 64-QAM with effective rate of 5 bits per complex dimension (b/cdim) and for a 16-QAM with effective rate of 3 b/cdim.