Communication networks are often designed and analyzed assuming tight synchronization among nodes. However, in applications that require communication in the energy-efficient regime of low signal-to-noise ratios, establishing tight synchronization among nodes in the network can result in a significant energy overhead. Motivated by a recent result showing that near-optimal energy efficiency can be achieved over the AWGN channel without requiring tight synchronization, we consider the question of whether the potential gains of cooperative communication can be achieved in the absence of synchronization. We focus on the symmetric Gaussian diamond network and establish that cooperative-communication gains are indeed feasible even with unsynchronized nodes. More precisely, we show that the capacity per unit energy of the unsynchronized symmetric Gaussian diamond network is within a constant factor of the capacity per unit energy of the corresponding synchronized network. To this end, we propose a distributed relaying scheme that does not require tight synchronization but nevertheless achieves most of the energy gains of coherent combining.
Since its introduction in @cite_14 , there have been numerous works analyzing the capacity of the synchronized Gaussian diamond network. The achievable rates of two well-known relaying schemes, decode-forward and amplify-forward, were analyzed for the two-relay diamond network in @cite_14 . To counter the poor performance of amplify-forward at low SNR, the bursty amplify-forward scheme was proposed in @cite_1 . This scheme was shown to be approximately optimal for the symmetric Gaussian diamond network with arbitrary number @math of relays in @cite_15 , both in the sense of a uniform additive gap of @math bits and a uniform multiplicative gap of a factor @math .
@cite_15 @cite_14 @cite_1
2548811864 1505858209 2107762903 2069554030
We consider the Gaussian “diamond” or parallel relay network, in which a source node transmits a message to a destination node with the help of N relays. Even for the symmetric setting, in which the channel gains to the relays are identical and the channel gains from the relays are identical, the capacity of this channel is unknown in general. The best known capacity approximation is up to an additive gap of order N bits and up to a multiplicative gap of order N2, with both gaps independent of the channel gains. In this paper, we approximate the capacity of the symmetric Gaussian N-relay diamond network up to an additive gap of 1.8 bits and up to a multiplicative gap of a factor 14. Both gaps are independent of the channel gains and, unlike the best previously known result, are also independent of the number of relays N in the network. Achievability is based on bursty amplify-and-forward, showing that this simple scheme is uniformly approximately optimal, both in the low-rate as well as in the high-rate regimes. The upper bound on capacity is based on a careful evaluation of the cut-set bound. We also present approximation results for the asymmetric Gaussian N-relay diamond network. In particular, we show that bursty amplify-and-forward combined with optimal relay selection achieves a rate within a factor O(log4(N)) of capacity with preconstant in the order notation independent of the channel gains. In this paper, we consider a class of single-source multicast relay networks. We assume that all outgoing channels of a node in the network to its neighbors are orthogonal while the incoming signals from its neighbors can interfere with each other. We first focus on Gaussian relay networks with interference and find an achievable rate using a lattice coding scheme. We show that the achievable rate of our scheme is within a constant bit gap from the information theoretic cut-set bound, where the constant depends only on the network topology, but not on the transmit power, noise variance, and channel gains. This is similar to a recent result by Avestimehr, Diggavi, and Tse, who showed an approximate capacity characterization for general Gaussian relay networks. However, our achievability uses a structured code instead of a random one. Using the idea used in the Gaussian case, we also consider a linear finite-field symmetric network with interference and characterize its capacity using a linear coding scheme. We study the capacity of the Gaussian two-pair fullduplex directional (or two-way) relay network with a single-relay supporting the communication of the pairs. This network is a generalization of the well known bidirectional relay channel, where we have only one pair of users. We propose a novel transmission technique which is based on a specific superposition of lattice codes and random Gaussian codes at the source nodes. The relay attempts to decode the Gaussian codewords and the superposition of the lattice codewords of each pair. Then it forwards this information to all users. We analyze the achievable rate of this scheme and show that for all channel gains it achieves to within 2 bits sec Hz per user of the cut-set upper bound on the capacity region of the two-pair bidirectional relay network. Consider several source nodes communicating across a wireless network to a destination node with the help of several layers of relay nodes. Recent work by Avestimehr has approximated the capacity of this network up to an additive gap. The communication scheme achieving this capacity approximation is based on compress-and-forward, resulting in noise accumulation as the messages traverse the network. As a consequence, the approximation gap increases linearly with the network depth. This paper develops a computation alignment strategy that can approach the capacity of a class of layered, time-varying wireless relay networks up to an approximation gap that is independent of the network depth. This strategy is based on the compute-and-forward framework, which enables relays to decode deterministic functions of the transmitted messages. Alone, compute-and-forward is insufficient to approach the capacity as it incurs a penalty for approximating the wireless channel with complex-valued coefficients by a channel with integer coefficients. Here, this penalty is circumvented by carefully matching channel realizations across time slots to create integer-valued effective channels that are well suited to compute-and-forward. Unlike prior constant gap results, the approximation gap obtained in this paper also depends closely on the fading statistics, which are assumed to be i.i.d. Rayleigh.