The @math -user additive white Gaussian noise multiway relay channel is investigated, where @math users exchange information at the same rate through a single relay. A new achievable rate region, based on the functional-decode-forward coding strategy, is derived. For the case where there are three or more users, and all nodes transmit at the same power, the capacity is obtained. For the case where the relay power scales with the number of users, it is shown that both compress-forward and functional-decode-forward achieve rates within a constant number of bits of the capacity at all SNR levels; in addition, functional-decode-forward outperforms compress-forward and complete-decode-forward at high SNR levels.
@cite_8: A main distinguishing feature of a wireless network compared with a wired network is its broadcast nature, in which the signal transmitted by a node may reach several other nodes, and a node may receive signals from several other nodes simultaneously. Rather than a blessing, this feature is treated more as an interference-inducing nuisance in most wireless networks today (e.g., IEEE 802.11). The goal of this paper is to show how the concept of network coding can be applied at the physical layer to turn the broadcast property into a capacityboosting advantage in wireless ad hoc networks. Specifically, we propose a physical-layer network coding (PNC) scheme to coordinate transmissions among nodes. In contrast to “straightforward” network coding which performs coding arithmetic on digital bit streams after they have been received, PNC makes use of the additive nature of simultaneously arriving electromagnetic (EM) waves for equivalent coding operation. PNC can yield higher capacity than straightforward network coding when applied to wireless networks. We believe this is a first paper that ventures into EM-wavebased network coding at the physical layer and demonstrates its potential for boosting network capacity. PNC opens up a whole new research area because of its implications and new design requirements for the physical, MAC, and network layers of ad hoc wireless stations. The resolution of the many outstanding but interesting issues in PNC may lead to a revolutionary new paradigm for wireless ad hoc networking.
@cite_1: 
@cite_15: Traditionally, interference is considered harmful. Wireless networks strive to avoid scheduling multiple transmissions at the same time in order to prevent interference. This paper adopts the opposite approach; it encourages strategically picked senders to interfere. Instead of forwarding packets, routers forward the interfering signals. The destination leverages network-level information to cancel the interference and recover the signal destined to it. The result is analog network coding because it mixes signals not bits. So, what if wireless routers forward signals instead of packets? Theoretically, such an approach doubles the capacity of the canonical 2-way relay network. Surprisingly, it is also practical. We implement our design using software radios and show that it achieves significantly higher throughput than both traditional wireless routing and prior work on wireless network coding.
@cite_13: We introduce a new class of problems called network information flow which is inspired by computer network applications. Consider a point-to-point communication network on which a number of information sources are to be multicast to certain sets of destinations. We assume that the information sources are mutually independent. The problem is to characterize the admissible coding rate region. This model subsumes all previously studied models along the same line. We study the problem with one information source, and we have obtained a simple characterization of the admissible coding rate region. Our result can be regarded as the max-flow min-cut theorem for network information flow. Contrary to one's intuition, our work reveals that it is in general not optimal to regard the information to be multicast as a "fluid" which can simply be routed or replicated. Rather, by employing coding at the nodes, which we refer to as network coding, bandwidth can in general be saved. This finding may have significant impact on future design of switching systems.
@cite_17: Abstract—We show that mutual exchange of independentinformation between two nodes in a wireless network can be efﬁ-ciently performed by exploiting network coding and the physical-layer broadcast property offered by the wireless medium. Theproposed approach improves upon conventional solutions thatseparate the processing of the two unicast sessions, correspondingto information transfer along one direction and the oppositedirection. We propose a distributed scheme that obviates theneed for synchronization and is robust to random packet lossand delay, and so on. The scheme is simple and incurs minoroverhead. I. I NTRODUCTION In this paper, we investigate the mutual exchange of inde-pendent information between two nodes in a wireless network.Let us name the two nodes in consideration a and b, respec-tively. Consider a packet-based communication network withall packets of equal size. The basic problem is very simple: awants to transmit a sequence of packets X 1 (n) to b andb wants to transmit a sequence of packets X
Besides the aforementioned classical relaying strategies for relay networks, @cite_17 and @cite_1 used the idea of network coding @cite_13 for the TWRC and proposed that the relay performs a modulo-two summation of the users' messages, and broadcasts the summation. After getting the sum of the messages, each user can then obtain the other user's message by subtracting its own message from the sum. The network-coding-like operation can also be achieved at the modulation level, if amplify-forward is carried out using binary phase-shift keying (BPSK) @cite_8 or minimum-shift keying (MSK) modulation @cite_15 .