The problem of joint shaping and precoding is studied in this paper. We introduce statistical dependencies among consecutive symbols to shape the constellation while minimizing the total transmit power when the signal goes through the precoding filter. We propose a stationary Markovian model for optimizing the transition probability of transmit symbols to avoid high-energy sequences when convolved with the precoding filter. A new algorithm based on arithmetic coding is proposed to generate a shaped sequence of symbols with the given Markov model transition probabilities.

We propose a novel digital-to-analog converter (DAC) weighting architecture that statistically minimizes the distortion caused by random current mismatches. Unlike binary, thermometer-coded, and segmented DACs, the current weights of the proposed architecture are not an integer power of 2 or any other integer number. We present a heuristic algorithm for a static mapping of DAC input codewords into corresponding DAC switches. High-level Matlab simulations are performed to illustrate the static performance improvement over the segmented structure.

In this paper, we develop the machinery of real interference alignment. This machinery is extremely powerful in achieving the sum degrees of freedom (DoF) of single antenna systems. The scheme of real interference alignment is based on designing single-layer and multilayer constellations used for modulating information messages at the transmitters. We show that constellations can be aligned in a similar fashion as that of vectors in multiple antenna systems and space can be broken up into fractional dimensions. The performance analysis of the signaling scheme makes use of a recent result in the field of Diophantine approximation, which states that the convergence part of the Khintchine-Groshev theorem holds for points on nondegenerate manifolds. Using real interference alignment, we obtain the sum DoF of two model channels, namely the Gaussian interference channel (IC) and the X channel. It is proved that the sum DoF of the K-user IC is (K/2) for almost all channel parameters. We also prove that the sum DoF of the X-channel with K transmitters and M receivers is (K M/K + M - 1) for almost all channel parameters.

This paper investigates the benefits of amplify-and-forward (AF) relaying in the setup of multiantenna wireless networks. For this purpose, random sequential (RS) relaying is studied. It is shown that random unitary matrix multiplication at the relay nodes empowers the RS scheme to achieve a better diversity-multiplexing tradeoff (DMT) as compared to the traditional AF relaying. First, the RS scheme is proved to achieve the optimum DMT for a multiantenna full-duplex single-relay two-hop network. Applying this result, a new achievable DMT is derived for the case of multiantenna half-duplex parallel relay network. Interestingly, it turns out that the DMT of the RS scheme is optimum for the case of multiantenna two parallel noninterfering half-duplex relays. Furthermore, random unitary matrix multiplication is shown to also improve the DMT of the nonorthogonal AF relaying scheme for the case of a multiantenna single relay channel. Finally, the general case of multiantenna full-duplex relay networks is studied. First, a new lower-bound is derived on its DMT using the RS scheme. Furthermore, maximum multiplexing gain of the network is also shown to be achievable by traditional amplify-forward relaying. The gain value is equal to the minimum vertex cut-set of the underlying graph of the network, which can be computed in polynomial time in terms of the number of network nodes.

This paper studies the setup of a parallel MIMO relay network in which K relays, each equipped with N antennas, assist in transmitting data between a source and a destination, each equipped with M antennas (M ≤ N), in the half-duplex mode. It is assumed that there is no direct source-destination link and the communication is performed in two hops. An amplify-and-forward relaying scheme called Incremental Cooperative Beamforming Scheme (ICBS) is introduced and shown to achieve the capacity of the network in the asymptotic case of K → ∞ with a gap scaling of at most [(log(K))/({4}√{K})]. This result is shown to hold as long as the power of each relay is significantly larger than [(log3(K) log(log(K)))/(K)]. In addition, in the case that the source power is equal to the relays' power and both tend to infinity, the proposed scheme is shown to achieve the full multiplexing gain regardless of the number of relays. Simulation results confirm the validity of analytical arguments.

This paper addresses a fundamental trade-off between rate and the diversity gain of an end-to-end connection in an erasure network. The erasure network is modeled by a directed graph whose links are orthogonal erasure channels. Furthermore, the erasure network is assumed to be non-ergodic, meaning that the erasure status of the links are assumed to be fixed during each block of transmission and change independently from block to block. The erasure status of the links is assumed to be known only by the destination node. First, we study the homogeneous erasure networks in which the links have the same erasure probability and capacity. We derive the optimum trade-off between diversity gain and the end-to-end rate and prove that a variant of the conventional routing strategy combined with an appropriate forward error correction at the end-nodes achieves the optimum diversity-rate trade-off. Next, we consider the general erasure networks in which different links may have different values of erasure probability and capacity. We prove that there exist general erasure networks for which any conventional routing strategy fails to achieve the optimum diversity-rate trade-off. However, for any general erasure graph, we show that there exists a linear network coding strategy which achieves the optimum diversity-rate trade-off. Unlike the previous works which suggest the potential benefit of linear network coding in the error-free multicast scenario (in terms of the achievable rate), our result introduces the benefit of linear network coding in the erasure single-source single-destination scenario (in terms of the diversity gain). Finally, we study the diversity-rate trade-off through simulations. The erasure graphs are constructed according to the Barabasi-Albert random model which is known to capture the scale-free property of the practical packet switched networks like the Internet. The error probability is depicted for different network strategies and different rate values. The depicted results confirm the trade-off between the rate and the diversity gain for each network strategy. Moreover, the diversity gain is plotted versus the rate for different conventional routing and the linear network coding strategies. It is observed that linear network coding outperforms all conventional routing strategies in terms of the diversity gain.

This paper studies the general multi-antenna multiple-relay network. Every two nodes of the network are either connected together through a Rayleigh fading channel or disconnected. We study the ergodic capacity of the network in the high SNR regime. We prove that the traditional amplify-forward relaying achieves the maximum multiplexing gain of the network. Furthermore, we show that the maximum multiplexing gain of the network is equal to the minimum vertex cut-set of the underlying graph of the network, which can be computed in polynomial time in terms of the number of network nodes. Finally, the argument is extended to the multicast and multi-access scenarios.

This study investigates the problem of communication for a network composed of two half-duplex parallel relays with additive white Gaussian noise (AWGN). There is no direct link between the source and the destination. However, the relays can communicate with each other through the channel between them. Two protocols, i.e.,simultaneousandsuccessiverelaying, associated with two possible relay schedulings are proposed. The simultaneous relaying protocol is based on theBroadcast-Multiaccess with Common Message (BCM)scheme considered in. For the successive relaying protocol: (i) anon-cooperativescheme based on theDirty Paper Coding (DPC)and (ii) acooperativescheme based on theBlock Markov Encoding (BME)are considered. The composite scheme of employing BME inat mostone relay and DPC inat leastanother one is also proposed. It is proved that this scheme achieves at least the same rate when compared to thecooperativeandnon-cooperativeschemes for the Gaussian case. ASimultaneous-Successive Relaying based on Dirty Paper Coding scheme (SSRD)is also proposed. The optimum scheduling of the relays, and hence the capacity of the half-duplex Gaussian parallel relay channel in the low and high signal-to-noise ratio (SNR) scenarios, is derived. In the low SNR scenario, it is revealed that under certain conditions for the channel coefficients the ratio of the achievable rate of the simultaneous relaying based on BCM to the cut-set bound tends to be 1. On the other hand, as SNR goes to infinity it is proved that successive relaying, based on the DPC, asymptotically achieves the capacity of the network.

Path diversity works by setting up multiple parallel connections between the endpoints using the topological path redundancy of the network. In this paper, forward error correction (FEC) is applied across multiple independent paths to enhance the end-to-end reliability. We prove that the probability of irrecoverable loss (PE) decays exponentially with the number of paths. Furthermore, the rate allocation (RA) problem across independent paths is studied. Our objective is to find the optimal RA, i.e., the allocation that minimizesPE. The RA problem is solved for a large number of paths. Moreover, it is shown that in such asymptotically optimal RA, each path is assigned a positive rate iff its quality is above a certain threshold. Finally, using memoization technique, a heuristic suboptimal algorithm with polynomial runtime is proposed for RA over a finite number of paths. This algorithm converges to the asymptotically optimal RA when the number of paths is large. For a practical number of paths, the simulation results demonstrate the close-to-optimal performance of the proposed algorithm .

In this paper, the degrees of freedom (DOF) of the symmetric 3-user Gaussian interference channel is considered. It is shown that by using un-coded signaling, the achievable DOF is a discontinuous function of the channel parameter. More importantly, for the set of irrational channel gains, which has measure 1 in real numbers, it is proved that the total system's DOF, i.e., 3/2, is achievable. This result is obtained using Hurwitz's theorem in number theory.

Schein and Gallager introduced the Gaussian parallel relay channel in 2000. They proposed the amplify-and-forward (AF) and the decode-and-forward (DF) strategies for this channel. For a long time, the best known achievable rate for this channel was based on the AF and DF with time sharing (AF-DF). A rematch-and-forward (RF) scheme for the scenario in which different amounts of bandwidth can be assigned to the first and second hops were proposed. In this paper, we propose acombinedamplify-and-decodeforward(CADF) scheme for the Gaussian parallel relay channel. We prove that the CADF scheme always gives a better achievable rate compared to the RF scheme, when there is a bandwidth mismatch between the first hop and the second hop. Furthermore, for the equal bandwidth case (Schein's setup), we show that the time sharing between the CADF and the DF schemes (CADF-DF) leads to a better achievable rate compared to the time sharing between the RF and the DF schemes (RF-DF) as well as the AF-DF.

This paper studies the setup of a multiple-relay network in which$K$half-duplex multiple-antenna relays assist in the transmission between either one or several multiple-antenna transmitter(s) and a multiple-antenna receiver. Each two nodes are assumed to be either connected through a quasi-static Rayleigh-fading channel, or disconnected. We propose a new scheme, which we callrandom sequential(RS), based on the amplify-and-forward relaying. We prove that for general multiple-antenna multiple-relay networks, the proposed scheme achieves the maximum diversity gain. Furthermore, we derive diversity–multiplexing tradeoff (DMT) of the proposed RS scheme for general single-antenna multiple-relay networks. It is shown that for single-antenna two-hop multiple-access multiple-relay$(K > 1)$networks (without direct link between the transmitter(s) and the receiver), the proposed RS scheme achieves the optimum DMT. However, for the case of multiple-access single-relay setup, we show that the RS scheme reduces to the naive amplify-and-forward (AF) relaying and is not optimum in terms of DMT, while the dynamic decode-and-forward (DF) scheme is shown to be optimum for this scenario.

An erasure channel with a fixed alphabet size q, where q Gt 1, is studied. It is proved that over any erasure channel (with or without memory),maximumdistanceseparable(MDS) codes achieve the minimum probability of error (assuming maximum likelihood decoding). Assuming a memoryless erasure channel, the error exponent of MDS codes are compared with that of random codes. It is shown that the envelopes of these two exponents are identical for rates above the critical rate. Noting the optimality of MDS codes, it is concluded that random coding is exponentially optimal as long as the block size N satisfies N < q + 1.

Path diversity works by setting up multiple parallel connections between the end points using the topological path redundancy of the network. In this paper, forward error correction (FEC) is applied across multiple independent paths to enhance the end-to-end reliability. Internet paths are modeled as erasure Gilbert-Elliot channels. First, it is shown that over any erasure channel, maximum distance separable (MDS) codes achieve the minimum probability of irrecoverable loss among all block codes of the same size. Then, we prove the probability of irrecoverable loss decays exponentially for the asymptotically large number of paths. Moreover, it is shown that in the optimal rate allocation, each path is assigned a positive rate iff its quality is above a certain threshold. The quality of a path is defined as the percentage of the time it spends in the bad state. Finally, using dynamic programming, a heuristic suboptimal algorithm with polynomial runtime is proposed for rate allocation over the available paths. This algorithm converges to the asymptotically optimal rate allocation when the number of paths is large. The simulation results show that the proposed algorithm approximates the optimal rate allocation very closely, and provides significant performance improvement compared to the alternative schemes of rate allocation.