Gaussian Half-Duplex Relay Networks: Improved Constant Gap and Connections With the Assignment Problem
Gaussian Half-Duplex Relay Networks: Improved Constant Gap and Connections With the Assignment Problem
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高斯半双工中继网络：改进的恒定间隙和连接与分配问题
DOI：
10.1109/tit.2014.2314636
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发表时间：
2013
影响因子：
2.5
通讯作者：
U. Salim
中科院分区：
文献类型：
--
作者：
Martina Cardone;Daniela Tuninetti;R. Knopp;U. Salim
本文考虑一个高斯中继网络，其中一个源在N个半双工中继的帮助下向一个目标发送消息。通过噪声网络编码，可以将容量的信息理论切集上限控制在1.96（N+2）位以内，从而减小了先前已知的间隙。这个间隙是高斯半双工组播网络中更为普遍的常数间隙结果的一个特例。然后证明了该网络的广义自由度是一个线性规划的解，其中线性不等式约束的系数是若干线性规划的解，这些线性规划被称为图论中的分配问题，存在有效的数值算法。研究了最优调度，即中继的2N个可能收发配置状态的最优值，并将菱形网络的已知结果推广到一般中继网络。结果表明，对于N=2个继电器，在2N=4种可能状态中，只有N+1=3种状态具有严格正的概率，并且足以表征在恒定间隙内的容量。大量实验结果表明，对于N≤8的一般N中继网络，最优调度至多有N+1个状态，且严格为正概率。作为菱形网络猜想的扩展，我们推测这一结果适用于任何半双工中继网络和任何数量的中继。最后，对N=2个中继的网络进行了详细的研究，以说明选择最佳中继并非最优的信道条件，并突出了多个中继导致的速率增益的性质。
This paper considers a Gaussian relay network where a source transmits a message to a destination with the help of N half-duplex relays. The information theoretic cut-set upper bound to the capacity is shown to be achieved to within 1.96(N+2) bits by noisy network coding, thereby reducing the previously known gap. This gap is obtained as a special case of a more general constant gap result for Gaussian half-duplex multicast networks. It is then shown that the generalized degrees-of-freedom of this network is the solution of a linear program, where the coefficients of the linear inequality constraints are proved to be the solution of several linear programs referred as the assignment problem in graph theory, for which efficient numerical algorithms exist. The optimal schedule, that is, the optimal value of the 2N possible transmit-receive configuration states for the relays, is investigated and known results for diamond networks are extended to general relay networks. It is shown, for the case of N=2 relays, that only N+1=3 out of the 2N=4 possible states have a strictly positive probability and suffice to characterize the capacity to within a constant gap. Extensive experimental results show that, for a general N -relay network with N≤8 , the optimal schedule has at most N+1 states with a strictly positive probability. As an extension of a conjecture presented for diamond networks, it is conjectured that this result holds for any half-duplex relay network and any number of relays. Finally, a network with N=2 relays is studied in detail to illustrate the channel conditions under which selecting the best relay is not optimal, and to highlight the nature of the rate gain due to multiple relays.