Binary subchannel decomposition of lattice-based multiple access schemes

Abstract

Lattice codes used under the Compute-and-Forward paradigm suggest an alternative strategy for the standard Gaussian multiple-access channel (MAC). It has been proven that decoding an integer linear combination of the transmitted codewords enables higher data rates compared to decoding the messages individually. Recent work of Gasptar et al. proposed a new multiple access channel technique that they called Compute- and-Forward Multiple Access Channel (CFMA). The authors proved that, in the case of a two-user MAC and without time sharing, the entire capacity region is achieved using CFMA and a single-user decoder for signal to noise ratios above 1 + √2. Throughout this paper, we will work within the Compute- and-Forward framework. The strategy relies on lattice codes, here we will construct lattices using a multi-level coding based construction called construction D. To decode the lattice points, a multi-stage decoder (MSD) should be implemented at the receiver part. In this paper, we propose a new decoding strategy that helps to perform the standard MSD algorithm in a less complex way. The new technique is called Binary Subchannel Decomposition (BSCD). Since, we make use of MSD, we need at each level of the decoder to compute soft-inputs: Log-Likelihood ratios. However the calculations are very complex since we must compute infinite sums of exponentials at each stage. Hereinafter we give efficient LLR approximation for multi-stage decoders. Simulation results about the performance of BSCD are included and compared to the performance of the standard multi-stage decoder.