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.
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 .
@cite_37 @cite_36 @cite_9 @cite_32 @cite_31 @cite_20
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We propose and design a practical modulation-coded (MC) physical-layer network coding (PNC) scheme to approach the capacity limits of Gaussian and fading two-way relay channels (TWRCs). In the proposed scheme, an irregular repeataccumulate (IRA) MC over @math with the same random coset is employed at two users, which directly maps the message sequences into coded PAM or QAM symbol sequences. The relay chooses appropriate network coding coefficients and computes the associated finite-field linear combinations of the two users' message sequences using an iterative belief propagation algorithm. For a symmetric Gaussian TWRC, we show that, by introducing the same random coset vector at the two users and a time-varying accumulator in the IRA code, the MC-PNC scheme exhibits symmetry and permutation-invariant properties for the soft information distribution of the network-coded message sequence (NCMS). We explore these properties in analyzing the convergence behavior of the scheme and optimizing the MC to approach the capacity limit of a TWRC. For a block fading TWRC, we present a new MC linear PNC scheme and an algorithm used at the relay for computing the NCMS. We demonstrate that our developed schemes achieve near-capacity performance in both Gaussian and Rayleigh fading TWRCs. For example, our designed codes over GF(7) and GF(3) with a code rate of 3 4 are within 1 and 1.2 dB of the TWRC capacity, respectively. Our method can be regarded as a practical embodiment of the notion of compute-and-forward with a good nested lattice code, and it can be applied to a wide range of network configurations. 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. We develop communication strategies for the rate-constrained interactive decoding of a message broadcast to a group of interested users. This situation diers from the relay channel in that all users are interested in the transmitted message, and from the broadcast channel because no user can decode on its own. We focus on two-user scenarios, and describe a baseline strategy that uses ideas of coding with decoder side information. One user acts initially as a relay for the other. That other user then decodes the message and sends back random parity bits, enabling the first user to decode. We show how to improve on this schemes performance through a conversation consisting of multiple rounds of discussion. While there are now more messages, each message is shorter, lowering the overall rate of the conversation. Such multi-round conversations can be more ecient because earlier messages serve as side information known at both encoder and decoder. We illustrate these ideas for binary erasure channels. We show that multi-round conversations can decode using less overall rate than is possible with the single-round scheme. 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. 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 This paper investigates the impact of inter-user non-orthogonality and asynchronous communication on the information-outage probability performance of multi-user decode-and-forward (DF) cooperative diversity in a code-division multiple-access (CDMA) uplink. Each user in the proposed system transmits its own data towards the base station and also serves as a relay for other users. We assume full-duplex communication so that each user can transmit and receive simultaneously at the same frequency. Each user attempts to decode the messages of a plurality of other users and forwards the superposition of multiple re-encoded and re-spread messages. Our cooperative scheme employs a sub-optimum decorrelating receiver to suppress the multi-user interference at both the base station and the relay-side. We evaluate the information-outage probability performance of the proposed scheme in an underloaded, fully-loaded and overloaded CDMA uplink. We consider combining schemes at the base station where the source information is code combined with the relayed information, while the information from multiple relays is either code combined or diversity combined. Under the system parameters contemplated in this paper, diversity combining of the relayed information is nearly as good as code combining because of the associated probabilities of decoding at the relays. We then examine the effect of using practical modulation formats on the information-outage probability performance of the proposed DF multi-user sharing scheme under diversity combining. We see that the performance loss due to modulation constraints and the use of diversity combining instead of code combining is relatively small.