text: The multiway relay channel is a multicast network where L users exchange data through a relay. In this paper, the capacity region of a class of multiway relay channels is derived, where the channel inputs and outputs take values over finite fields. The cut-set upper bound to the capacity region is derived and is shown to be achievable by our proposed functional-decode-forward coding strategy. More specifically, for the general case where the users can transmit at possibly different rates, functional-decode-forward, combined with rate splitting and joint source-channel decoding, is proved to achieve the capacity region; while for the case where all users transmit at a common rate, rate splitting and joint source-channel decoding are not required to achieve the capacity. That the capacity-achieving coding strategies do not utilize the users' received signals in the users' encoding functions implies that feedback does not increase the capacity region of this class of multiway relay channels.
  @cite_37: The multiuser communication channel, in which multiple users exchange information with the help of a relay terminal, termed the multiway relay channel (mRC), is introduced. In this model, multiple interfering clusters of users communicate simultaneously, such that the users within the same cluster wish to exchange messages among themselves, i.e., each user multicasts its message to all the other users in its own cluster. It is assumed that the users cannot receive each other's signals directly. Hence, the relay terminal in this model is the enabler of communication. In particular, restricted encoders are considered, such that the encoding function of each user depends only on its own message and the received signal is used only for decoding the messages of the other users in the cluster. Achievable rate regions and an outer bound are characterized for the Gaussian mRC, and their comparison is presented in terms of the exchange rate, the symmetric rate point in the capacity region in a symmetric Gaussian mRC scenario. It is shown that the compress-and-forward (CF) protocol achieves exchange rates within a constant bit offset of the optimal exchange rate, independent of the power constraints of the terminals in the network. A finite bit gap between the exchange rates achieved by the CF and the amplify-and-forward protocols is also shown. The two special cases of the mRC, the full data exchange model, in which every user wants to receive messages of all other users, and the pairwise data exchange model which consists of multiple two-way relay channels, are investigated in detail. In particular for the pairwise data exchange model, in addition to the proposed random coding-based achievable schemes, a nested lattice coding-based scheme is also presented and is shown to achieve exchange rates within a constant bit gap of the exchange capacity.
  @cite_36: In two-way relaying, two sources exchange information via a relay. In the generalized two-way relay, private information is also sent by each source to the relay, which may be used for overhead data, such as for channel state information. We consider the generalized two-way relay in a multi-carrier system over the wireless channel. Our problem is to maximize the rate that the sources exchange information, subject to some minimum rates of private information. We employ a coding scheme based on time-sharing and superposition of lattice codes and multiple access codes for each subcarrier, and show that the problem of optimizing the time-sharing variables is solved as a linear program. To simplify implementation, we propose a heuristic scheme where the time-sharing variables are quasi-extremal , i.e., all time-sharing variables, except for at most one, are assigned the largest or smallest possible values. Interestingly, the proposed scheme is provably optimal under certain channel scenarios. Numerical results show that the proposed scheme performs close to the optimal scheme in most practical channel scenarios.
  @cite_9: In the conventional two-way relay channel, two sources exchange information with help from a relay. We introduce a generalized two-way relay channel where each source additionally sends private information to the relay. For this channel, we consider a protocol that consists of a multiple-access (MA) phase and a broadcast (BC) phase and obtain achievable rate regions for both phases. The MA phase is related to computation over the multiple-access channel (MAC).We show that our scheme achieves rates that always lie within half bit of the capacity region for computation over MAC, and is capacity achieving in the BC phase. This near optimality in the MA phase can be achieved by time sharing a capacity-achieving code for the MAC and a superposition code that uses a lattice code as its component code.
  @cite_32: The multi-pair bi-directional relay network under consideration consists of one base-station, multiple (say m) terminal nodes and one relay, all of which are half-duplex, in which, contrary to prior work, each node has a direct link with every other node. Each of the m terminal nodes exchanges messages with the base-station in a bi-directional fashion, leading to 2m total messages to be communicated with the (possible) help of the relay. Our contributions are: 1) the introduction of three new temporal protocols which fully exploit the two-way nature of the data, over-heard side-information through network coding, random binning, and compress-and-forward terminal node cooperation, 2) derivations of achievable rate regions and 3) cut-set based outer bounds for the multi-pair network, and 4) a numerical evaluation of the derived regions in Gaussian noise which illustrate the performance of the proposed protocols.
  @cite_31: In the two-way relay channel, two sources exchange information with help from a relay. We study a more general relay network with additional pairs of sources that perform pair-wise information exchange. We obtain achievable rate regions for amplify-and-forward and decode-and-forward (DF) relaying schemes based on both Gaussian codes and lattice codes, assuming a two-phase protocol. The lattice-code-based DF scheme is near optimal, in that the achievable rate region lies within one bit of the capacity region for two pairs of information exchange.
  @cite_20: In this paper we study the capacity region of the multi-pair bidirectional (or two-way) wireless relay network, in which a relay node facilitates the communication between multiple pairs of users. This network is a generalization of the well known bidirectional relay channel, where we have only one pair of users. We examine this problem in the context of the deterministic channel interaction model, which eliminates the channel noise and allows us to focus on the interaction between signals. We characterize the capacity region of this network when the relay is operating at either full-duplex mode or half-duplex mode (with non adaptive listen-transmit scheduling). In both cases we show that the cut-set upper bound is tight and, quite interestingly, the capacity region is achieved by a simple equation-forwarding strategy.
summary: The MWRC we consider herein, where each user is to decode the messages from all other users, can be seen as a generalization of the TWRC. Different extensions of the TWRC include: The multi-pair TWRC where multiple source-destination pairs exchange messages via one relay @cite_20 @cite_31 . Here, each destination only decodes the message from one source. The multi-pair TWRC where multiple users exchange messages with a base station via a relay @cite_32 . Here, each user sends its message to the base station, and the base station sends different messages to each user. The TWRC with additional private messages from the users to the relay @cite_9 @cite_36 . The MWRC where the users are separated into different groups and all users in each group exchange messages among themselves @cite_37 .