You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
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.

Cited Abstract(s):
[1]: A relay channel consists of an input x_ l , a relay output y_ 1 , a channel output y , and a relay sender x_ 2 (whose transmission is allowed to depend on the past symbols y_ 1 . The dependence of the received symbols upon the inputs is given by p(y,y_ 1 |x_ 1 ,x_ 2 ) . The channel is assumed to be memoryless. In this paper the following capacity theorems are proved. 1)If y is a degraded form of y_ 1 , then C : = : !_ p(x_ 1 ,x_ 2 ) , I(X_ 1 ,X_ 2 ;Y), I(X_ 1 ; Y_ 1 |X_ 2 ) . 2)If y_ 1 is a degraded form of y , then C : = : !_ p(x_ 1 ) x_ 2 I(X_ 1 ;Y|x_ 2 ) . 3)If p(y,y_ 1 |x_ 1 ,x_ 2 ) is an arbitrary relay channel with feedback from (y,y_ 1 ) to both x_ 1 x_ 2 , then C : = : p(x_ 1 ,x_ 2 ) , I(X_ 1 ,X_ 2 ;Y),I ,(X_ 1 ;Y,Y_ 1 |X_ 2 ) . 4)For a general relay channel, C : : p(x_ 1 ,x_ 2 ) , I ,(X_ 1 , X_ 2 ;Y),I(X_ 1 ;Y,Y_ 1 |X_ 2 ) . Superposition block Markov encoding is used to show achievability of C , and converses are established. The capacities of the Gaussian relay channel and certain discrete relay channels are evaluated. Finally, an achievable lower bound to the capacity of the general relay channel is established.

[2]: We study the two-way communication problem for the relay channel. Hereby, two terminals communicate simultaneously in both directions with the help of one relay. We consider the restricted two-way problem, i.e., the encoders at both terminals do not cooperate. We provide achievable rate regions for different cooperation strategies, such as decode-and-forward based on block Markov superposition coding and compress-and-forward based on Wyner-Ziv source coding. We also evaluate the regions for the special case of additive white Gaussian noise channels. We show that a combined strategy of block Markov superposition coding and Wyner-Ziv coding achieves the cut-set upper bound on the sum-rate of the two-way relay channel when the relay is in the proximity of one of the terminals.

[3]: We study two-hop communication protocols where one or two relay terminals assist in the communication between two transceiver terminals. All terminals operate in half-duplex mode, i.e., may not receive and transmit simultaneously at the same time and frequency. This leads to a loss in spectral efficiency due to the pre-log factor 1 2 in corresponding expressions for the achievable rate (capacity). We propose and analyze two relaying protocols that avoid the pre-log factor 1 2 but still work with halfduplex relays. Firstly, we consider a relaying protocol where two half-duplex relays, either amplify-and-forward (AF) or decodeand-forward (DF), alternately forward messages from a source terminal to a destination terminal (two-path relaying). It is shown that the protocol can recover a significant portion of the halfduplex loss. Secondly, we propose a relaying protocol where a bidirectional connection between two transceiver terminals is established via one half-duplex AF or DF relay (two-way relaying). It is shown that the sum rate of the two-way half-duplex AF relay channel achieves the rate of the one-way full-duplex AF relay channel, whereas the sum rate of the two-way half-duplex DF relay channel achieves the rate of the one-way full-duplex DF relay channel only in certain cases.

[4]: Coding strategies that exploit node cooperation are developed for relay networks. Two basic schemes are studied: the relays decode-and-forward the source message to the destination, or they compress-and-forward their channel outputs to the destination. The decode-and-forward scheme is a variant of multihopping, but in addition to having the relays successively decode the message, the transmitters cooperate and each receiver uses several or all of its past channel output blocks to decode. For the compress-and-forward scheme, the relays take advantage of the statistical dependence between their channel outputs and the destination's channel output. The strategies are applied to wireless channels, and it is shown that decode-and-forward achieves the ergodic capacity with phase fading if phase information is available only locally, and if the relays are near the source node. The ergodic capacity coincides with the rate of a distributed antenna array with full cooperation even though the transmitting antennas are not colocated. The capacity results generalize broadly, including to multiantenna transmission with Rayleigh fading, single-bounce fading, certain quasi-static fading problems, cases where partial channel knowledge is available at the transmitters, and cases where local user cooperation is permitted. The results further extend to multisource and multidestination networks such as multiaccess and broadcast relay channels.
The MWRC is an extension of the two-way relay channel (TWRC), i.e., @math . Since there is an embedded relay channel from user 1 to user 2 via the relay, and vice versa, coding strategies proposed for relay networks [1] [4] , i.e., complete-decode-forward, This coding strategy is commonly known as decode-forward. We modify the name to distinguish this coding strategy and the functional-decode-forward coding strategy to be discussed next. compress-forward, and amplify-forward, have been modified for the TWRC [3] [2] .