Abstract-We consider a wireless network composed of three nodes and limited by the half-duplex and total power constraints. This formulation encompasses many of the special cases studied in the literature and allows for capturing the common features shared by them. Here, we focus on three special cases, namely, 1) relay channel, 2) multicast channel, and 3) three-way channel. These special cases are judicially chosen to reflect varying degrees of complexity while highlighting the common ground shared by the different variants of the three-node wireless network. For the relay channel, we propose a new cooperation scheme that exploits the wireless feedback gain. This scheme combines the benefits of the decode-and-forward (DF) and compress-and-forward (CF) strategies and avoids the noiseless feedback assumption adopted in earlier works. Our analysis of the achievable rate of this scheme reveals the diminishing feedback gain in both the low and high signal-to-noise ratio (SNR) regimes. Inspired by the proposed feedback strategy, we identify a greedy cooperation framework applicable to both the multicast and three-way channels. Our performance analysis reveals the asymptotic optimality of the proposed greedy approach and the central role of list source-channel decoding in exploiting the receiver side information in the wireless network setting. Index Terms-List source-channel decoding, multicast channel, noisy feedback, relay channel, three-way channel. W E are in the midst of a new wireless revolution, brought on by the adoption of wireless networks for consumer, military, scientific, and wireless applications. For example, the consumer potential is clearly evident in the exploding popularity of wireless local-area networks (LANs) and Bluetooth-protocol devices. The military potential is also clear: wireless networks can be rapidly deployed, and the failure of individual nodes does not imply the failure of the network. Scientific data-collection applications using wireless sensor networks are also gaining in numbers. These applications have sparked a renewed interest in network information theory. Despite the recent progress (see [1]-[9] and references therein), developing a unified theory for network information flow remains an elusive task. In our work, we consider, perhaps, the most simplified scenario of wireless networks. Our network is composed of only three nodes and limited by the half-duplex and total power constraints. Despite this simplicity, this model encompasses many of the special cases that have been extensively studied in the literature. These special channels 1 are induced by the traffic generated at the nodes and the requirements imposed on the network. 2 More importantly, this model exposes the common features shared by these special cases and allows for constructing universal cooperation strategies that yield significant performance gains. In particular, we focus here on three special cases, namely 1) relay channel, 2) multicast channel, and 3) three-way channel. These channels are defined rigorously in Section I. We adopt a greedy framework for designing cooperation strategies and characterize the achievable rates of the proposed schemes. Our analysis reveals the structural similarities of the proposed strategies, in the three special cases, and establishes the asymptotic optimality of such strategies in several cases. More specifically, our contributions can be summarized as follows. 1) We propose a novel cooperation strategy for the relay channel with feedback. Our scheme combines the benefits of both the decode-and-forward (DF) and compressand-forward (CF) strategies and avoids the noiseless feedback assumption adopted in earlier works. Our analysis of the achievable rate of the proposed strategy reveals the diminishing gain of feedback in the asymptotic scenarios of low and large signal-to-noise ratio (SNR). 2) Inspired by the feedback strategy for the relay channel, we construct a new cooperation strategy for the multicast scenario. Motivated by a greedy approach, we show that the weak receiver is led to help the strong receiver first. 3 Based on the same greedy motivation, the strong user starts to assist the weak receiver after successfully decoding the transmitted codeword. We compute the corresponding achievable rate and use it to establish the significant gains offered by this strategy, as compared with the noncooperative scenario. 3) Motivated by the sensor networks application, we identify the three-way channel model as a special case of our 1 With a slight abuse of notation, we interchange "channel" and "network" in different places of the sequel for maximal consistency with the literature. 2 For example, the relay channel corresponds to the special case where the traffic is generated at one node and is required to be transmitted to only one of the remaining two nodes. 3 The notions of weak and strong receivers will be defined rigorously in the sequel.
In the relay case, REF uses an iterative scheme where the receiver first uses EAF to send information to the relay and then the relay decodes and uses DAF at the next time interval to help the receiver.
The three-node wireless network: achievable rates and Cooperation strategies
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Mathematics Computer Science