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 repeat–accumulate (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 scheme’s 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 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. 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. 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. We generalize the concept of multiuser peer-to-peer (MUP2P) relay networks, where K source-destination pairs communicate through L relays, to that of a multi-group multicasting (MGM) relay network. In the MGM scenario, each source may broadcast its message to a group of multiple users rather than to a single user only. Common distributed beamformer designs for MUP2P relay networks aim to minimize the total transmitted relay power subject to receiver quality-of-service (QoS) constraints. In state-of-the-art techniques, the resulting nonconvex problem is approximated by a convex one which is efficiently solvable using interior point methods. These techniques are shown to be straightforwardly extendable to more general MGM relay networks. However, as the number of receivers increases (which may be typical for the proposed MGM networks where each multicast group may contain many users), these approximations become more and more inaccurate leading to severe performance degradation and problem infeasibility. To avoid this drawback, we propose an iterative method where in each iteration, a convex approximation of the original problem is solved and then adapted to the solution obtained in this iteration. We show that the approximate solution can be successively improved using such iterations. Simulation results show that in scenarios with large numbers of destination users, the proposed method substantially outperforms the state-of-the-art methods developed for MUP2P relay networks. This paper presents the first real-time physical-layer network coding (PNC) prototype for the two-way relay wireless channel (TWRC). Theoretically, PNC could boost the throughput of TWRC by a factor of 2 compared with traditional scheduling (TS) in the high signal-to-noise (SNR) regime. Although there have been many theoretical studies on PNC performance, there have been few experimental and implementation efforts. We built the first prototype of PNC about a year ago. It was, however, an offline system in which an offline PNC decoder was used at the relay. For a real-time PNC system, there are many additional challenges, including the needs for tighter coordination of the transmissions by the two end nodes, fast real-time PNC decoding at the relay, and a PNC-compatible retransmission scheme (i.e., an ARQ protocol) to ensure reliability of packet delivery. In this paper, we describe a real-time PNC prototype, referred to as RPNC, that provides practical solutions to these challenges. Indoor environment experimental results show that RPNC boosts the throughput of TWRC by a factor of 2 compared with TS, as predicted theoretically. RPNC prototype provides an interface to the application layer, with which we demonstrate the exchange of two image data files between the two end nodes. 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 use of multi-user detection (MUD) in a cooperative CDMA network is investigated for the uplink in synchronous CDMA systems. Suppose that, at any instant in time, part of the users serve as sources while the others serve as relays. The proposed MUD scheme decorrelates the sources' messages at the destination with the help of precoding at the relays. Three cooperation methods are considered: (1) transmit beamforming, (2) selective relaying and (3) distributed space- time coding. The optimal weighting factors of each method are determined by taking the quality of the source-to-relay and or the relay-to-destination links into account. We show that significant improvements in terms of the spatial diversity and multiple-access interference (MAI) mitigation can be attained when precoding is employed at the relays to aid the decorrelation at the destination. The advantages are even more pronounced when selective relaying is combined with the other two schemes. An amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay network composed of a source, a relay, and a destination is considered, where transmit beamforming is employed both at the source and at the relay. The relay is a user who is willing to help the communication from the source to the destination. In our paper, however, the relay is untrusted in the sense that it may make a passive security attack; that is, it may decode messages of the source. We consider two ways to transmit confidential information of the source to the destination: noncooperative secure beamforming and cooperative secure beamforming. In the noncooperative scheme, the relay is simply treated as an eavesdropper, and does not participate in communication. In the cooperative scheme, the relay is asked to relay signals from the source to the destination. In this paper, the source and relay beamforming is jointly designed to maximize the secrecy rate in the cooperative scheme. The conditions under which the cooperative scheme achieves a higher secrecy rate than the noncooperative scheme are derived in the low and high signal-to-noise ratio (SNR) regimes of the source-relay and relay-destination links. The performance of the secure beamforming schemes is compared through extensive numerical simulations. We consider one-sided interference channel with two independent source-destination pairs, and a cognitive relay with only a link to the destination that observes interference. We first assume the relay non-causally obtains the signal messages (message cognitive) whereas the sources do not cooperate, and provide a general achievable rate region for the Gaussian case. We further analyze a more realistic set-up where instead of source messages, the relay knows the transmitted signals of both sources and is unaware of the codebooks. We investigate the achievable region under this signal cognitive assumption and further obtain a converse, thereby the capacity region under strong relay-interference conditions. Our results suggest that while relaying is usually utilized as an effective technique for boosting received signal quality, in the presence of interference, an equally important task of the relay is to manage the interference. In this paper, a point-to-point orthogonal-frequency- division multiplexing (OFDM) system with a decode-and- forward (DF) relay is considered. The transmission consists of two hops. The source transmits in the first hop, and the relay transmits in the second hop. Each hop occupies one time slot. The relay is half-duplex, and capable of decoding the message on a particular subcarrier in one time slot, and re-encoding and forwarding it on a different subcarrier in the next time slot. Thus, each message is transmitted on a pair of subcarriers in two hops. It is assumed that the destination is capable of combining the signals from the source and the relay pertaining to the same message. The goal is to maximize the weighted sum rate of the system by jointly optimizing subcarrier pairing and power allocation on each subcarrier in each hop. The weighting of the rates is to take into account the fact that different subcarriers may carry signals for different services. Both total and individual power constraints for the source and the relay are investigated. For the situations where the relay does not transmit on some subcarriers because doing so does not improve the weighted sum rate, we further allow the source to transmit new messages on these idle subcarriers. To the best of our knowledge, such a joint optimization inclusive of the destination combining has not been discussed in the literature. The problem is first formulated as a mixed integer programming problem. It is then transformed to a convex optimization problem by continuous relaxation, and solved in the dual domain. Based on the optimization results, algorithms to achieve feasible solutions are also proposed. Simulation results show that the proposed algorithms almost achieve the optimal weighted sum rate and outperform the existing methods in various channel conditions. We want to enable a pair of communicating users to exchange secret messages while hiding the fact that secret communication is taking place. We propose a linguistic steganography approach, where each human message is hidden in another human-like message. A hard open question is how to keep the steganographic message small -- existing related tools tend to blow up its size, thereby revealing the use of steganography. We encrypt by compressing each message, mapping it to a plausible sequence of words (using a language model), and letting the human user edit the outcome to produce a human-like message; we decrypt with a Viterbi-like state decoder. Our approach aims in producing text that a human can edit and fix with minimal effort. As a first step, we build a prototype of our system that helps users encrypt English messages (into English messages), and we report on first experiments on Mechanical Turk. Interference is usually viewed as an obstacle to communication in wireless networks. This paper proposes a new strategy, compute-and-forward, that exploits interference to obtain significantly higher rates between users in a network. The key idea is that relays should decode linear functions of transmitted messages according to their observed channel coefficients rather than ignoring the interference as noise. After decoding these linear equations, the relays simply send them towards the destinations, which given enough equations, can recover their desired messages. The underlying codes are based on nested lattices whose algebraic structure ensures that integer combinations of codewords can be decoded reliably. Encoders map messages from a finite field to a lattice and decoders recover equations of lattice points which are then mapped back to equations over the finite field. This scheme is applicable even if the transmitters lack channel state information. Three dependent users are physically separated but communicate with each other via a satellite. Each user generates data which it stores locally. In addition, each user sends a message to the satellite. The satellite processes the messages received from the users and broadcasts one common message to all three users. Each user must be capable of reconstructing the data of the other two users based upon the broadcast message and its own stored data. Our problem is to determine the minimum amount of information which must be transmitted to and from the satellite. The solution to this problem is obtained for the case where subsequent data triples that are produced by the users are independent and identically distributed. The three symbols within each triple are assumed to be dependent. Crucial for the solution is an achievability proof that involves cascaded Slepian-Wolf (1973) source coding. We study the application of convolutional codes to two-way relay networks (TWRNs) with physical-layer network coding (PNC). When a relay node decodes coded signals transmitted by two source nodes simultaneously, we show that the Viterbi algorithm (VA) can be used by approximating the maximum likelihood (ML) decoding for XORed messages as two-user decoding. In this setup, for given memory length constraint, the two source nodes can choose the same convolutional code that has the largest free distance in order to maximize the performance. Motivated from the fact that the relay node only needs to decode XORed messages, a low complexity decoding scheme is proposed using a reduced-state trellis. We show that the reduced-state decoding can achieve the same diversity gain as the full-state decoding for fading channels. A noisy network coding scheme for communicating messages between multiple sources and destinations over a general noisy network is presented. For multi-message multicast networks, the scheme naturally generalizes network coding over noiseless networks by Ahlswede, Cai, Li, and Yeung, and compress-forward coding for the relay channel by Cover and El Gamal to discrete memoryless and Gaussian networks. The scheme also extends the results on coding for wireless relay networks and deterministic networks by Avestimehr, Diggavi, and Tse, and coding for wireless erasure networks by Dana, Gowaikar, Palanki, Hassibi, and Effros. The scheme involves lossy compression by the relay as in the compress-forward coding scheme for the relay channel. However, unlike previous compress-forward schemes in which independent messages are sent over multiple blocks, the same message is sent multiple times using independent codebooks as in the network coding scheme for cyclic networks. Furthermore, the relays do not use Wyner-Ziv binning as in previous compress-forward schemes, and each decoder performs simultaneous decoding of the received signals from all the blocks without uniquely decoding the compression indices. A consequence of this new scheme is that achievability is proved simply and more generally without resorting to time expansion to extend results for acyclic networks to networks with cycles. The noisy network coding scheme is then extended to general multi-message networks by combining it with decoding techniques for the interference channel. For the Gaussian multicast network, noisy network coding improves the previously established gap to the cutset bound. We also demonstrate through two popular Gaussian network examples that noisy network coding can outperform conventional compress-forward, amplify-forward, and hash-forward coding schemes. An Interference Channel with Generalized Feedback (IFC-GF) models a wireless network where the sources can sense the channel activity. The signal overheard from the channel provides information about the activity of the other sources and thus furnishes the basis for cooperation. This two-part paper studies achievable strategies (Part I) and outer bounds (Part II) for the general discrete memoryless IFC-GF with two source-destination pairs. In Part I, the generalized feedback is used to gain knowledge about the message sent by the other source and then exploited in two ways: a) to relay the messages that can be decoded at both destinations, thus realizing the gains of beam-forming of a distributed multiantenna system, and b) to hide the messages that can not be decoded at the nonintended destination, thus leveraging the interference “precancellation” property of dirty-paper coding. We show that our achievable region generalizes several known achievable regions for the IFC-GF and that it reduces to known achievable regions for the channels subsumed by the IFC-GF model. For the Gaussian channel, it is shown that source cooperation enlarges the achievable rate region of the corresponding IFC without generalized feedback cooperation.