Abstract—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), decodeand-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. I.

Abstract—When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted interference. This property of the wireless medium is typically viewed as a hindrance to reliable communication over a network. However, using a recently developed coding strategy, interference can in fact be harnessed for network coding. In a wired network, (linear) network coding refers to each intermediate node taking its received packets, computing a linear combination over a finite field, and forwarding the outcome towards the destinations. Then, given an appropriate set of linear combinations, a destination can solve for its desired packets. For certain topologies, this strategy can attain significantly higher throughputs over routing-based strategies. Reliable physical layer network coding takes this idea one step further: using judiciously chosen linear error-correcting codes, intermediate nodes in a wireless network can directly recover linear combinations of the packets from the observed noisy superpositions of transmitted signals. Starting with some simple examples, this survey explores the core ideas behind this new technique and the possibilities it offers for communication over interference-limited wireless networks. Index Terms—Digital communication, wireless networks, in-terference, network coding, channel coding, linear code, modula-tion, physical layer, fading, multiuser channels, multiple access, broadcast. I.

Abstract—A general class of wireless relay networks with a single source-destination pair is considered. Intermediate nodes in the network employ an amplify-and-forward scheme to relay their input signals. In this case the overall input-output channel from the source via the relays to the destination effectively behaves as an intersymbol interference channel with colored noise. Unlike previous work we formulate the problem of the maximum achievable rate in this setting as an optimization problem with no assumption on the network size, topology, and signal-to-noise ratio. Previous work considered only scenarios wherein relays use all their power to amplify their received signals. We demonstrate that this may not always maximize the achievable rate in amplify-and-forward relay networks. The proposed formulation allows us to not only recover known results on the performance of the amplify-and-forward schemes for some simple relay networks but also characterize the performance of such schemes in more complex relay networks which cannot be addressed in a straightforward manner with existing approaches. Using cut-set arguments, we derive simple upper bounds on the capacity of general wireless relay networks. Through various examples, we show that a large class of amplify-and-forward relay networks can achieve rates within a constant factor of these upper bounds asymptotically in network parameters. I.

In this paper, a new two-way relaying scheme based on compute-and-forward (CMF) framework and relay selection strategies is proposed, which provides a higher throughput than the conventional two-way relaying schemes. Two cases of relays with or without feedback transmission capability are considered. An upper bound on the computation rate of each relay is derived, and based on that, a lower bound on the outage probability of the system is presented assuming block Rayleigh fad-ing channels. Numerical results show that while the average sum rate of the system without feedback, named as Max Compute-and-Forward (M-CMF), reaches the de-rived upper bound only in low SNRs, that of the system with feedback, named as Aligned Compute-and-Forward (A-CMF) reaches the bound in all SNRs. However, both schemes approach the derived lower bound on the outage probability in all SNRs. For the A-CMF, another power assignment based on applying the constraint on the total powers of both users rather than on the power of each separately, is intro-duced. The result shows that the A-CMF performs better under the new constraint. Moreover, the numerical results show that the outage performance, average sum rate, and symbol error rate of the proposed schemes are significantly better than those of two-step and three-step decode-and-forward (DF) and amplify-and-forward (AF) strategies for the examples considered. Index Terms- compute and forward, max compute-and-forward, aligned compute-and-forward, feedback, two-way relaying, relay selection, outage probability, average sum rate, symbol error rate. I

Abstract—We design novel partial decode-forward (PDF) schemes for the Gaussian two-way relay channel with direct link. Different from pure decode-forward, each user divides its message into two parts and the relay decodes only one part of each. The relay then generates its codeword as a function of the two decoded parts and forwards to the two users. We propose PDF schemes for both the full- and half-duplex modes. In full duplex, the scheme is based on block Markov encoding and forward joint decoding over 2 consecutive blocks. In half duplex, the transmission is divided into 4 phases, in which one user transmits during the first phase, the other during the second phase, both users transmit during the third phase and the relay transmits during the last phase. The relay decodes a part of the messages from both users at the end of phase 3 and each user decodes only at the end of phase 4. Analysis and simulation show that if for one user, the direct link is stronger than the user-to-relay link, while for the other, the direct link is weaker, then PDF can achieve a rate region strictly larger than the timeshared region of pure decode-forward and direct transmission for both full- and half-duplex modes. I.

Abstract—In this paper we propose a novel power adaptive network coding (PANC) for a non-orthogonal multiple-access relay channel (MARC), where two sources transmit their in-formation simultaneously to the destination with the help of a relay. In contrast to the conventional XOR-based network coding (CXNC), the relay in PANC generates network coded symbols by considering the coefficients of the source-to-relay channels, and forwards each symbol with a pre-optimized power level. Specifically, by defining a symbol pair as two symbols from the two sources, we first derive the expression of symbol pair error rate (SPER) for the system. Noting that deriving the exact SPER are complex due to the irregularity of the decision regions caused by random channel coefficients, we propose a coordinate transform (CT) method on the received constellation to simplify the derivations of the SPER. Next, we obtain the optimal power level by decomposing it as a multiplication of a power scaling factor and a power adaptation factor. We prove that with the power scaling factor at the relay, our PANC scheme can achieve a full diversity gain, i.e., an order of two diversity gain, while the CXNC can achieve only an order of one diversity gain. In addition, we optimize the power adaptation factor at the relay to minimize the SPER at the destination by considering of the relationship between SPER and minimum Euclidean distance of the received constellation, resulting in an improved coding gain. Simulation results show that (1) the SPER derived based on our CT method can well approximate the exact SPER with a much lower complexity; (2) the PANC scheme with power adaptation optimizations and power scaling factor design can achieve a full diversity, and obtain a much higher coding gain than other network coding schemes. Index Terms—Network coding, power optimization, multiple access relay channel, error probability. I.

Abstract: Physical-layer Network Coding (PNC) can significantly improve the throughput of two-way relay channels. An interesting variant of PNC is Analog Network Coding (ANC). Almost all ANC schemes proposed to date, however, operate in a symbol by symbol manner (memoryless) and cannot exploit the redundant information in channel-coded packets to enhance performance. This paper proposes a non-memoryless ANC scheme. In particular, we design a soft-input soft-output decoder for the relay node to process the superimposed packets from the two end nodes to yield an estimated MMSE packet for forwarding back to the end nodes. Our decoder takes into account the correlation among different symbols in the packets due to channel coding, and provides significantly improved MSE performance. Our analysis shows that the SNR improvement at the relay node is lower bounded by 1/R (R is the code rate) with the simplest LDPC code (repeat code). The SNR improvement is also verified by numerical simulation with LDPC code. Our results indicate that LDPC codes of different degrees are preferred in different SNR regions. Generally speaking, smaller degrees are preferred for lower SNRs. I.

In this paper, we propose a new transmission scheme, named as Integer Forcing-and-Forward (IFF), for communications among multi-pair multiple-antenna users in which each pair exchanges their messages with the help of a single multi antennas relay in the multiple-access and broadcast phases. The proposed scheme utilizes compute-and-forward (CMF) strategy and Integer Forcing Linear Receiver (IFLR) at relay, which uses equations, i.e., linear integer-combinations of messages, to harness the intra-pair interference. Accordingly, we propose the design of mean squared error (MSE) based transceiver, including precoder and projection matrices for the relay and users, assuming that the perfect channel state information (CSI) is available. In this regards, in the multiple-access phase, we introduce two new MSE criteria for the related precoding and filter designs, i.e., the sum of the equations ’ MSE (Sum-Equation MSE) and the maximum of the equations ’ MSE (Max-Equation MSE), to exploit the equations in the relay. Moreover, in the broadcast phase, we use the two traditional MSE criteria, i.e. the sum of the users ’ mean squred errors (Sum MSE) and the maximum of the users ’ mean squared errors (Max MSE), to design the related precoding and filters for recovering relay’s equations in the users. Then, we consider a more practical scenario with imperfect CSI. For this case, IFLR receiver is modified, and another transceiver design is proposed, which take into account the effect of channels estimation error. We evaluate the performance of our proposed strategy and compare the results with the conventional amplify-and-forward (AF) and decode-and-forward (DF) strategies for the same scenario. The results

Abstract—The problem of maximum rate achievable with analog network coding for a unicast communication over a layered relay network with directed links is considered. A relay node performing analog network coding scales and forwards the signals received at its input. Recently this problem has been considered under certain assumptions on per node scaling factor and received SNR. Previously, we established a result that allows us to characterize the optimal performance of analog network coding in network scenarios beyond those that can be analyzed using the approaches based on such assumptions. The key contribution of this work is a scheme to greedily compute a lower bound to the optimal rate achievable with analog network coding in general layered networks. This scheme allows for exact computation of the optimal achievable rates in a wider class of layered networks than those that can be addressed using existing approaches. For the specific case of the Gaussian N-relay diamond network, to the best of our knowledge, the proposed scheme provides the first exact characterization of the optimal rate achievable with analog network coding. For general layered networks, our scheme allows us to compute optimal rates within a “small ” gap from the cut-set upper bound asymptotically in the source power. I.

We quantize the angular momentum of the electromagnetic field in a linear medium. We consider the interaction of an atom with an evanescent wave. We discuss the transfer of angular momentum in such a wave in relation to some recent experiments. 1.