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首页> 外文期刊>IEEE Transactions on Information Theory >Gaussian Half-Duplex Relay Networks: Improved Constant Gap and Connections With the Assignment Problem
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Gaussian Half-Duplex Relay Networks: Improved Constant Gap and Connections With the Assignment Problem

机译：高斯半双工中继网络：改进的恒定间隙和分配问题的连接

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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 $2^{N}$ 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 $2^{N}=4$ 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 $Nleq 8$ , the optimal schedule has at most $N+1$ states with a strictly positive probab- lity. 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.
机译：本文考虑了一个高斯中继网络，其中源借助$ N $半双工中继将消息发送到目的地。通过有噪声的网络编码，可以证明在容量上的信息理论割集上限达到了$ 1.96（N + 2）$位，从而减少了先前已知的差距。对于高斯半双工多播网络，此间隙作为更通用的恒定间隙结果的特例获得。然后表明，该网络的广义自由度是线性程序的解，其中线性不等式约束的系数被证明是几种线性程序的解，在图论中称为分配问题，为此，存在有效的数值算法。研究了最佳调度，即中继的$ 2 ^ {N} $可能的发射-接收配置状态的最佳值，并将菱形网络的已知结果扩展到通用中继网络。对于$ N = 2 $中继，表明在$ 2 ^ {N} = 4 $个可能状态中只有$ N + 1 = 3 $个具有严格的正概率，足以将容量表征为不断的差距。大量的实验结果表明，对于具有$ Nleq 8 $的一般$ N $中继网络，最优调度最多具有$ N + 1 $个状态，且概率严格为正。作为对菱形网络提出的猜想的扩展，可以推测该结果适用于任何半双工中继网络和任何数量的中继。最后，对具有$ N = 2 $个中继的网络进行了详细研究，以说明选择最佳中继并非最优的信道条件，并强调由于多个中继而导致的速率增益的本质。

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