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In this paper, a single-hop single-relay system with a direct link between the source and the destination is considered when the relay operates in the half-duplex mode. Motivated by the concept of signal space diversity, this paper introduces signal space cooperation, in which cooperation between the source and the relay is achieved using a novel constellation design approach. In this approach, the original constellation is expanded so that each member of the new constellation inherits its components from at least two members of the original constellation. The expanded constellation enables the relay to extract the required information in order to cooperate in the relay phase, and it helps the destination to effectively combine received signals during the broadcast phase and the relay phase. The analytical study of the proposed scheme leads to the development of two design criteria for the constellation expansion approach. The proposed design criteria aim at maximizing the relay role in the cooperative scheme by increasing the performance of the source-relay link. In this way, the source and the relay can effectively cooperate in order to maximize the overall performance of the system. The signal space cooperative scheme can be used for any constellation size without incurring significant complexity overhead to the system. Numerical results depict superior performance in comparison with other cooperative schemes such as the adaptive decode and forward and the distributed turbo code schemes.

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In this paper, learning of tree-structured Gaussian graphical models from distributed data is addressed. In our model, samples are stored in a set of distributed machines where each machine has access to only a subset of features. A central machine is then responsible for learning the structure based on received messages from the other nodes. We present a set of communication efficient strategies, which are theoretically proved to convey sufficient information for reliable learning of the structure. In particular, our analyses show that even if each machine sends only the signs of its local data samples to the central node, the tree structure can still be recovered with high accuracy. Our simulation results on both synthetic and real-world datasets show that our strategies achieve a desired accuracy in inferring the underlying structure, while spending a small budget on communication. Index Terms-Structure learning, Chow-Liu algorithm, Gaussian Graphical Model.!