Low Complexity Coefficient Selection Algorithms for Compute-and-Forward

Compute-and-Forward (C&F) has been proved to be an efficient approach for multiuser, multihop wireless networks. It allows intermediate relays to infer and forward linear combinations of the transmitted messages, in order to achieve high computation rate. The coefficient selection for each relay is a shortest vector problem (SVP). The most common solutions for such a problem are exhaustive search and the Lenstra-LenstraLovsz (LLL) lattice reduction. The former has a high complexity and the latter proves to be suboptimal for large numbers of users. In this paper, we propose two novel algorithms, of which one can be regarded as a simplified version of the exhaustive search, while the other one selects the coefficients iteratively. Numerical results reveal that both methods achieve the same computation rate as the exhaustive search with much lower complexity. Both outperform the LLL algorithm (especially with a large number of users), and the complexities are lower than the LLL except in the very high SNR region.