Abstract-In this paper we study the capacity region of the multi-pair bidirectional (or two-way) wireless relay network, in which a relay node facilitates the communication between multiple pairs of users. This network is a generalization of the well known bidirectional relay channel, where we have only one pair of users. We examine this problem in the context of the deterministic channel interaction model, which eliminates the channel noise and allows us to focus on the interaction between signals. We characterize the capacity region of this network when the relay is operating at either full-duplex mode or half-duplex mode (with non adaptive listen-transmit scheduling). In both cases we show that the cut-set upper bound is tight and, quite interestingly, the capacity region is achieved by a simple equationforwarding strategy.
Abstract-We show that girth can be used to certify that sparse compressed sensing matrices have good sparse approximation guarantees. This allows us to present the first deterministic measurement matrix constructions that have an optimal number of measurements for 1/ 1 approximation. Our techniques are coding theoretic and rely on a recent connection of compressed sensing to LP relaxations for channel decoding.
Abstract-We introduce a novel algorithm for decoding binary linear codes by linear programming. We build on the LP decoding algorithm of Feldman et al. and introduce a post-processing step that solves a second linear program that reweights the objective function based on the outcome of the original LP decoder output. Our analysis shows that for some LDPC ensembles we can improve the provable threshold guarantees compared to standard LP decoding. We also show significant empirical performance gains for the reweighted LP decoding algorithm with very small additional computational complexity.
The proliferation of mobile applications and ser vices involving group communications has increased the need for efficient wireless multicasting solutions in next generation broadband access networks. The availability of antenna arrays at the base stations makes adaptive beamforming especially attractive for multicasting; with beamforming, the received signal strength at the clients can be significantly improved. However, the problem of designing optimal transmit beamformers for multicast applications is challenging, mainly due to its non-convex nature.In this work, we design efficient transmit beamformers for wireless link layer multicasting where instantaneous channel state information is available at the transmitter. In addressing the non convexity of the problem, we design non-iterative, near-optimal beamforming algorithms based on the optimality conditions derived from its Lagrangian formulation. We show that for real channels, e.g, where Pulse Amplitude Modulation (PAM) is used, the optimal solution can be obtained. To address the effectiveness of the proposed solution for the complex channel, we also derive an upper bound on the multicast rate based on the dual formulation of the problem. Evaluations reveal that our algorithms deliver a performance that is close to the upper bound, while significantly improving the multicast rate over state of the art solutions.
Matrix rank minimization (RM) problems recently gained extensive attention due to numerous applications in machine learning, system identification and graphical models. In RM problem, one aims to find the matrix with the lowest rank that satisfies a set of linear constraints. The existing algorithms include nuclear norm minimization (NNM) and singular value thresholding. Thus far, most of the attention has been on i.i.d. Gaussian measurement operators. In this work, we introduce a new class of measurement operators, and a novel recovery algorithm, which is notably faster than NNM.The proposed operators are based on what we refer to as subspace expanders, which are inspired by the well known expander graphs based measurement matrices in compressed sensing. We show that given an n × n PSD matrix of rank r, it can be uniquely recovered from a minimal sampling of O(nr) measurements using the proposed structures, and the recovery algorithm can be cast as matrix inversion after a few initial processing steps.
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