This paper considers the competitive resource allocation problem in Multiple-Input Multiple-Output (MIMO) interfering channels, when users maximize their energy efficiency. Considering each transmitter-receiver pair as a selfish player, conditions on the existence and uniqueness of the Nash equilibrium of the underlying noncooperative game are obtained. A decentralized asynchronous algorithm is proven to converge towards this equilibrium under the same conditions. Two frameworks are considered for the analysis of this game. On the one hand, the game is rephrased as a Quasi-Variational Inequality (QVI). On the other hand, the best response of the players is analyzed in light of the contraction mappings. For this problem, the contraction approach is shown to lead to tighter results than the QVI one. When specializing the obtained results to OFDM networks, the obtained conditions appear to significantly outperform state-of-the-art works, and to lead to much simpler decentralized algorithms. Numerical results finally assess the obtained conditions in different settings.
The emerging large-scale and data-hungry algorithms require the computations to be delegated from a central server to several worker nodes. One major challenge in the distributed computations is to tackle delays and failures caused by the stragglers. To address this challenge, introducing efficient amount of redundant computations via distributed coded computation has received significant attention. Recent approaches in this area have mainly focused on introducing minimum computational redundancies to tolerate certain number of stragglers. To the best of our knowledge, the current literature lacks a unified end-to-end design in a heterogeneous setting where the workers can vary in their computation and communication capabilities. The contribution of this paper is to devise a novel framework for joint scheduling-coding, in a setting where the workers and the arrival of stream computational jobs are based on stochastic models. In our initial joint scheme, we propose a systematic framework that illustrates how to select a set of workers and how to split the computational load among the selected workers based on their differences in order to minimize the average in-order job execution delay. Through simulations, we demonstrate that the performance of our framework is dramatically better than the performance of naive method that splits the computational load uniformly among the workers, and it is close to the ideal performance.
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