Cloud Compute-and-Forward with Relay Cooperation

We study a cloud network with M distributed receiving antennas and L users, which transmit their messages towards a centralized decoder (CD), where M>=L. We consider that the cloud network applies the Compute-and-Forward (C&F) protocol, where L antennas/relays are selected to decode integer equations of the transmitted messages. In this work, we focus on the best relay selection and the optimization of the Physical-Layer Network Coding (PNC) at the relays, aiming at the throughput maximization of the network. Existing literature optimizes PNC with respect to the maximization of the minimum rate among users. The proposed strategy maximizes the sum rate of the users allowing nonsymmetric rates, while the optimal solution is explored with the aid of the Pareto frontier. The problem of relay selection is matched to a coalition formation game, where the relays and the CD cooperate in order to maximize their profit. Efficient coalition formation algorithms are proposed, which perform joint relay selection and PNC optimization. Simulation results show that a considerable improvement is achieved compared to existing results, both in terms of the network sum rate and the players' profits.Comment: Submitted to IEEE Transactions on Wireless Communication

Algebraic Approach to Physical-Layer Network Coding

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, non-asymptotic, 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 re-interpreted 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 non-coherent 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 inter-coset distances of the underlying nested lattice code. Several illustrative hypercube-shaped LNC schemes are designed based on Construction 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.Comment: Submitted to IEEE Transactions on Information Theory, July 21, 2011. Revised version submitted Sept. 17, 2012. Final version submitted July 3, 201