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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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. We consider a multiuser two-way relay network where multiple pairs of users communicate with their preassigned partners, using a common intermediate relay node, in a two-phase communication scenario employing code division multiple access (CDMA). By taking advantage of the bidirectional communication structure, we first propose that each pair of partners share a common spreading signature and design a jointly demodulate-and-XOR forward (JD-XOR-F) relaying scheme, where all users transmit to the relay simultaneously followed by the relay broadcasting an estimate of the XORed symbol for each user pair. We derive the decision rules and the corresponding bit error rates (BERs) at the relay and at the users' receivers. We then investigate the joint power control and receiver optimization problem for each phase for this multiuser two-way relay network with JD-XOR-F relaying. We solve each optimization problem by constructing the iterative power control and receiver updates that converge to the corresponding unique optimum. Simulation results are presented to demonstrate the performance of the proposed multiuser two-way JD-XOR-F relaying scheme in conjunction with the joint power control and receiver optimization algorithms. Specifically, we observe significant power savings and user capacity improvement with the proposed communication scheme as compared to the designs with a "one-way" communication perspective. 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. 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 consider a multiuser two-way relay network where multiple pairs of users communicate with their pre-assigned partners, using a common intermediate relay node, in a two-phase communication scenario. In this system, a pair of partners transmit to the relay sharing a common spreading signature in the first phase, and the relay broadcasts an estimate of the XORed symbol for each user pair in the second phase employing the relaying scheme termed jointly demodulate-and-XOR forward (JD-XOR-F) in [1]. We investigate the joint power control and receiver optimization problem for this multiuser two-way relay system with JD-XOR-F relaying. We show that the total power optimization problem decouples into two subproblems, one for each phase. We construct the distributed power control and receiver updates in each phase which converge to the corresponding unique optimum. Simulation results are presented to demonstrate the significant power savings of the multiuser two-way relay system with the proposed iterative power control and receiver optimization algorithms, as compared to the designs with a iquestone-wayiquest communication perspective. 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. 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-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. 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. This paper investigates the iterative decoding for spectrally efficient two-way relay (TWR) communications in which two end nodes exchange information through a relay (R). With the use of physical-layer network coding (PNC), information exchange throughput can be significantly improved as only two orthogonal time slots (TS) are required to realize both the multiple access (MAC) and the broadcast (BC) transmissions. During the MAC stage, transmitted symbols from the end nodes are superimposed at R which decodes the exclusive-or (XOR) information of the two end nodes. However, with a high order modulation, symbol superposition will cause demapping ambiguity. This paper proposes a TWR communication system that employs the bit-interleaved coded modulation (BICM). The iterative decoding, namely, the BICM-ID, is introduced to dissolve the demapping ambiguity. With iterative decoding, the transmitted symbol pair probabilities can be better estimated so that the demapper can provide better coded bit information for the decoder. The proposed work generalizes the iterative demapping-decoding approach for TWR channels. Our simulation results demonstrate significant iterative decoding gains can be achieved with a tendency of approaching the XOR-decoding bound. We consider a dense fading multi-user network with multiple active multi-antenna source-destination pair terminals communicating simultaneously through a large common set of K multi-antenna relay terminals in the full spatial multiplexing mode. We use Shannon-theoretic tools to analyze the tradeoff between energy efficiency and spectral efficiency (known as the power-bandwidth tradeoff) in meaningful asymptotic regimes of signal-to-noise ratio (SNR) and network size. We design linear distributed multi-antenna relay beamforming (LDMRB) schemes that exploit the spatial signature of multi-user interference and characterize their power-bandwidth tradeoff under a system-wide power constraint on source and relay transmissions. The impact of multiple users, multiple relays and multiple antennas on the key performance measures of the high and low SNR regimes is investigated in order to shed new light on the possible reduction in power and bandwidth requirements through the usage of such practical relay cooperation techniques. Our results indicate that point-to-point coded multi-user networks supported by distributed relay beamforming techniques yield enhanced energy efficiency and spectral efficiency, and with appropriate signaling and sufficient antenna degrees of freedom, can achieve asymptotically optimal power-bandwidth tradeoff with the best possible (i.e., as in the cutset bound) energy scaling of K-1 and the best possible spectral efficiency slope at any SNR for large number of relay terminals. Furthermore, our results help to identify the role of interference cancellation capability at the relay terminals on realizing the optimal power- bandwidth tradeoff; and show how relaying schemes that do not attempt to mitigate multi-user interference, despite their optimal capacity scaling performance, could yield a poor power- bandwidth tradeoff. In this paper, collocated and distributed space-time block codes (DSTBCs) which admit multi-group maximum likelihood (ML) decoding are studied. First the collocated case is considered and the problem of constructing space-time block codes (STBCs) which optimally tradeoff rate and ML decoding complexity is posed. Recently, sufficient conditions for multi-group ML decodability have been provided in the literature and codes meeting these sufficient conditions were called Clifford Unitary Weight (CUW) STBCs. An algebraic framework based on extended Clifford algebras is proposed to study CUW STBCs and using this framework, the optimal tradeoff between rate and ML decoding complexity of CUW STBCs is obtained for few specific cases. Code constructions meeting this tradeoff optimally are also provided. The paper then focuses on multi-group ML decodable DSTBCs for application in synchronous wireless relay networks and three constructions of four-group ML decodable DSTBCs are provided. Finally, the OFDM based Alamouti space-time coded scheme proposed by Li-Xia for a 2 relay asynchronous relay network is extended to a more general transmission scheme that can achieve full asynchronous cooperative diversity for arbitrary number of relays. It is then shown how differential encoding at the source can be combined with the proposed transmission scheme to arrive at a new transmission scheme that can achieve full cooperative diversity in asynchronous wireless relay networks with no channel information and also no timing error knowledge at the destination node. Four-group decodable DSTBCs applicable in the proposed OFDM based transmission scheme are also given. 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. 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. 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. In this paper, we investigate the transmission completion time minimization problem in an additive white Gaussian noise (AWGN) broadcast channel, where the transmitter is able to harvest energy from the nature, using a rechargeable battery. The harvested energy is modeled to arrive at the transmitter during the course of transmissions. The transmitter has a fixed number of packets to be delivered to each receiver. The objective is to minimize the time by which all of the packets are delivered to their respective destinations. To this end, we optimize the transmit powers and transmission rates in a deterministic setting. We first analyze the structural properties of the optimal transmission policy in a two-user broadcast channel via the dual problem of maximizing the departure region by a fixed time T. We prove that the optimal total transmit power sequence has the same structure as the optimal single-user transmit power sequence in . In addition, the total power is split optimally based on a cut-off power level; if the total transmit power is lower than this cut-off level, all transmit power is allocated to the stronger user; otherwise, all transmit power above this level is allocated to the weaker user. We then extend our analysis to an M-user broadcast channel. We show that the optimal total power sequence has the same structure as the two-user case and optimally splitting the total power among M users involves M-1 cut-off power levels. Using this structure, we propose an algorithm that finds the globally optimal policy. Our algorithm is based on reducing the broadcast channel problem to a single-user problem as much as possible. Finally, we illustrate the optimal policy and compare its performance with several suboptimal policies under different settings. 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 general Gaussian multiple-access wiretap channel (GGMAC-WT) and the Gaussian two-way wiretap channel (GTW-WT) are considered. In the GGMAC-WT, multiple users communicate with an intended receiver in the presence of an eavesdropper who receives their signals through another GMAC. In the GTW-WT, two users communicate with each other over a common Gaussian channel, with an eavesdropper listening through a GMAC. A secrecy measure that is suitable for this multiterminal environment is defined, and achievable secrecy rate regions are found for both channels. For both cases, the power allocations maximizing the achievable secrecy sum rate are determined. It is seen that the optimum policy may prevent some terminals from transmission in order to preserve the secrecy of the system. Inspired by this construct, a new scheme cooperative jamming is proposed, where users who are prevented from transmitting according to the secrecy sum rate maximizing power allocation policy ldquojamrdquo the eavesdropper, thereby helping the remaining users. This scheme is shown to increase the achievable secrecy sum rate. Overall, our results show that in multiple-access scenarios, users can help each other to collectively achieve positive secrecy rates. In other words, cooperation among users can be invaluable for achieving secrecy for the system. 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. This paper studies the simultaneous wireless information and power transfer (SWIPT) in a multiuser wireless system, in which distributed transmitters send independent messages to their respective receivers, and at the same time cooperatively transmit wireless power to the receivers via energy beamforming. Accordingly, from the wireless information transmission (WIT) perspective, the system of interest can be modeled as the classic interference channel, while it also can be regarded as a distributed multiple-input multiple-output (MIMO) system for collaborative wireless energy transmission (WET). To enable both information decoding (ID) and energy harvesting (EH) in SWIPT, we adopt the low-complexity time switching operation at each receiver to switch between the ID and EH modes over scheduled time. For the hybrid system, we aim to characterize the achievable rate-energy (R–E) trade-offs by various transmitter-side collaboration schemes. Specifically, to facilitate the collaborative energy beamforming, we propose a new signal splitting scheme at the transmitters, where each transmit signal is generally split into an information signal and an energy signal for WIT and WET, respectively. With this new scheme, first, we study the two-user SWIPT system over the fading channel and derive the optimal mode switching rule at the receivers as well as the corresponding transmit signal optimization to achieve various R-E trade-offs. We also compare the R-E performance of our proposed scheme with transmit energy beamforming and signal splitting against two existing schemes with partial or no cooperation of the transmitters. Next, the general case of SWIPT systems with more than two users is studied, for which we propose a practical transmit collaboration scheme by extending the result for the two-user case: we group users into different pairs and apply the cooperation schemes obtained in the two-user case to each paired group. Furthermore, we present a benchmarking scheme based on joint cooperation of all the transmitters inspired by the principle of interference alignment , against which the performance of the proposed scheme is compared.