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_18: The multi-user communication channel, in which multiple users exchange information with the help of a single relay terminal, called the multi-way relay channel, is considered. In this model, multiple interfering clusters of users communicate simultaneously, where the users within the same cluster wish to exchange messages among themselves. It is assumed that the users cannot receive each other's signals directly, and hence the relay terminal is the enabler of communication. A relevant metric to study in this scenario is the symmetric rate achievable by all users, which we identify for amplify-and-forward (AF), decode-and-forward (DF) and compress-and-forward (CF) protocols. We also present an upper bound for comparison. The two extreme cases, namely full data exchange, in which every user wants to receive messages of all other users, and pairwise data exchange, consisting of multiple two-way relay channels, are investigated and presented in detail.
@cite_3: We consider a communication system where two transmitters wish to exchange information through a central relay. The transmitter and relay nodes exchange data over synchronized, average power constrained additive white Gaussian noise channels with a real input with signal-to-noise ratio (SNR) of snr. An upper bound on the capacity is 1 2 log(1 + snr) bits per transmitter per use of the multiple access phase and broadcast phase of the bidirectional relay channel. We show that, using lattice codes and lattice decoding, we can obtain a rate of 1 2 log(1 2 + snr) bits per transmitter, which is essentially optimal at high SNR. The main idea is to decode the sum of the codewords modulo a lattice at the relay followed by a broadcast phase which performs Slepian-Wolf coding. We also show that if the two transmitters use identical lattices with minimum angle decoding, we can achieve the same rate of 1 2 log(1 2 + snr). The proposed scheme can be thought of as a joint physical-layer network-layer code which outperforms other recently proposed analog network coding schemes.
@cite_7: We derive the capacity of the binary multi-way relay channel, in which multiple users exchange messages at a common rate through a relay. The capacity is achieved using a novel functional-decode-forward coding strategy. In the functional-decode-forward coding strategy, the relay decodes functions of the users' messages without needing to decode individual messages. The functions to be decoded by the relay are defined such that when the relay broadcasts the functions back to the users, every user is able to decode the messages of all other users.
Complete-decode-forward, compress-forward, and amplify-forward for the TWRC were subsequently extended to the MWRC by G "und " @cite_18 . We extended functional-decode-forward to the binary MWRC @cite_7 . The idea was to split the uplink into @math blocks, and when the user pairs @math transmit in the blocks respectively. In each block, the relay decodes a function (in this case, the modulo-two sum) of the two corresponding messages, and broadcasts the function back to the users. If each user can decode the @math functions from the relay, it can then decode the messages of all the other users. In this paper, we extend this strategy to the AWGN MWRC. We propose a rotated scheme such that for each message to be sent, the uplink is again split into @math blocks, but different pairs of users are chosen from @math for each message in a round-robin fashion. This modification enables each user to transmit at a higher power when active while keeping the average transmitted power to @math . For each block, the two active users transmit using lattice codes as they do in the AWGN TWRC @cite_3 .