Approaching Gaussian Relay Network Capacity in the High SNR Regime: End-to-End Lattice Codes

We present a natural and low-complexity technique for achieving the capacity of the Gaussian relay network in the high SNR regime. Specifically, we propose the use of end-to-end structured lattice codes with the amplify-and-forward strategy, where the source uses a nested lattice code to encode the messages and the destination decodes the messages by lattice decoding. All intermediate relays simply amplify and forward the received signals over the network to the destination. We show that the end-to-end lattice-coded amplify-and-forward scheme approaches the capacity of the layered Gaussian relay network in the high SNR regime. Next, we extend our scheme to non-layered Gaussian relay networks under the amplify-and-forward scheme, which can be viewed as a Gaussian intersymbol interference (ISI) channel. Compared with other schemes, our approach is significantly simpler and requires only the end-to-end design of the lattice precoding and decoding. It does not require any knowledge of the network topology or the individual channel gains

Multiple Unicast Capacity of 2-Source 2-Sink Networks

We study the sum capacity of multiple unicasts in wired and wireless multihop networks. With 2 source nodes and 2 sink nodes, there are a total of 4 independent unicast sessions (messages), one from each source to each sink node (this setting is also known as an X network). For wired networks with arbitrary connectivity, the sum capacity is achieved simply by routing. For wireless networks, we explore the degrees of freedom (DoF) of multihop X networks with a layered structure, allowing arbitrary number of hops, and arbitrary connectivity within each hop. For the case when there are no more than two relay nodes in each layer, the DoF can only take values 1, 4/3, 3/2 or 2, based on the connectivity of the network, for almost all values of channel coefficients. When there are arbitrary number of relays in each layer, the DoF can also take the value 5/3 . Achievability schemes incorporate linear forwarding, interference alignment and aligned interference neutralization principles. Information theoretic converse arguments specialized for the connectivity of the network are constructed based on the intuition from linear dimension counting arguments.Comment: 6 pages, 7 figures, submitted to IEEE Globecom 201

On the Non-Orthogonal Layered Broadcast Codes in Cooperative Wireless Networks

A multi-fold increase in spectral efficiency and throughput are envisioned in the fifth generation of cellular networks to meet the requirements of International Telecommunication Union (ITU) IMT-2020 on massive connectivity and tremendous data traffic. This is achieved by evolution in three aspects of current networks. The first aspect is shrinking the cell sizes and deploying dense picocells and femtocells to boost the spectral reuse. The second is to allocate more spectrum resources including millimeter-wave bands. The third is deploying highly efficient communications and multiple access techniques. Non-orthogonal multiple access (NOMA) is a promising communication technique that complements the current commercial spectrum access approach to boost the spectral efficiency, where different data streams/users’ data share the same time, frequency and code resource blocks (sub-bands) via superimposition with each other. The receivers decode their own messages by deploying the successive interference cancellation (SIC) decoding rule. It is known that the NOMA coding is superior to conventional orthogonal multiple access (OMA) coding, where the resources are split among the users in either time or frequency domain. The NOMA based coding has been incorporated into other coding techniques including multi-input multi-output (MIMO), orthogonal frequency division multiplexing (OFDM), cognitive radio and cooperative techniques. In cooperative NOMA codes, either dedicated relay stations or stronger users with better channel conditions, act as relay to leverage the spatial diversity and to boost the performance of the other users. The advantage of spatial diversity gain in relay-based NOMA codes, is deployed to extend the coverage area of the network, to mitigate the fading effect of multipath channel and to increase the system throughput, hence improving the system efficiency. In this dissertation we consider the multimedia content delivery and machine type communications over 5G networks, where scalable content and low complexity encoders is of interest. We propose cross-layer design for transmission of successive refinement (SR) source code interplayed with non-orthogonal layered broadcast code for deployment in several cooperative network architectures. Firstly, we consider a multi-relay coding scheme where a source node is assisted by a half-duplex multi-relay non-orthogonal amplify-forward (NAF) network to communicate with a destination node. Assuming the channel state information (CSI) is not available at the source node, the achievable layered diversity multiplexing tradeoff (DMT) curve is derived. Then, by taking distortion exponent (DE) as the figure of merit, several achievable lower bounds are proved, and the optimal expected distortion performance under high signal to noise ratio (SNR) approximation is explicitly obtained. It is shown that the proposed coding can achieve the multi-input single-output (MISO) upper bound under certain regions of bandwidth ratios, by which the optimal performance in these regions can be explicitly characterized. Further the non-orthogonal layered coding scheme is extended to a multi-hop MIMO decode-forward (DF) relay network where a set of DE lower bounds is derived. Secondly, we propose a layered cooperative multi-user scheme based on non-orthogonal amplify-forward (NAF) relaying and non-orthogonal multiple access (NOMA) codes, aiming to achieve multi-user uplink transmissions with low complexity and low signaling overhead, particularly applicable to the machine type communications (MTC) and internet of things (IoT) systems. By assuming no CSI available at the transmitting nodes, the proposed layered codes make the transmission rate of each user adaptive to the channel realization. We derive the close-form analytical results on outage probability and the DMT curve of the proposed layered NAF codes in the asymptotic regime of high SNR, and optimize the end-to-end performance in terms of the exponential decay rate of expected distortion. Thirdly, we consider a single relay network and study the non-orthogonal layered scheme in the general SNR regime. A layered relaying scheme based on compress-forward (CF) is introduced, where optimization of end to end performance in terms of expected distortion is conducted to jointly determine network parameters. We further derive the explicit analytical optimal solution with two layers in the absence of channel knowledge. Finally, we consider the problem of multicast of multi-resolution layered messages over downlink of a cellular system with the assumption of CSI is not available at the base station (BS). Without loss generality, spatially random users are divided into two groups, where the near group users with better channel conditions decode for both layers, while the users in the second group decode for base layer only. Once the BS launches a multicast message, the first group users who successfully decoded the message, deploy a distributed cooperating scheme to assist the transmission to the other users. The cooperative scheme is naive but we will prove it can effectively enhance the network capacity. Closed form outage probability is explicitly derived for the two groups of users. Further it is shown that diversity order equal to the number of users in the near group is achievable, hence the coding gain of the proposed distributed scheme fully compensate the lack of CSI at the BS in terms of diversity order

Analog network coding in general SNR regime: Performance of a greedy scheme

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 the 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 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. Further, for general layered networks, our scheme allows us to compute optimal rates within a constant gap from the cut-set upper bound asymptotically in the source power.Comment: 11 pages, 5 figures. Fixed an issue with the notation in the statement and proof of Lemma 1. arXiv admin note: substantial text overlap with arXiv:1204.2150 and arXiv:1202.037

Resource allocation for layered broadcast over relay-assisted channels

The topic of this thesis is on the application of “multilayer transmission” using the broadcast approach on a “relay-assisted” channel. Unlike single layer transmission, where all transmitted information bits have the same protection level by the channel coding scheme, multilayer transmission schemes combine successive refinement layered source coding with ordered protection levels of the source layers. Consequently, the receiver will be able to decode “some” information when the channel is faded and “all” information when the channel is good. The multilayer transmission schemes have gained a lot of interest in the information theory and the communication theory literature, where most researchers are interested in the “broadcast approach” since it is the optimal transmission strategy. In this thesis, we consider a fading relay channel where the source uses layered source coding with successive refinement. The source layers are transmitted using superposition coding at the source with optimal resource allocation. The destination applies successive interference cancellation after optimally combining the direct and relayed signals. The resource allocation for the layers is subject to optimization in order to maximize the expected user satisfaction that is usually defined by a differentiable concave increasing utility function of the total decoded rate at the destination. As special cases, we consider two utility functions; namely, the expected total decoded rate at the receiver and the expected rate distortion of a Gaussian source. We also assume that only the channel statistics are known at the receiver. The relay is half-duplex and applies different relaying strategies, and we have investigated the Amplify-and-Forward, and Decode-and-Forward strategies in particular. First, we consider the case of Decode-and-Forward relays where we consider two layers only with predetermined rates for simplicity, and we solve the problem of optimal power allocation among the two layers at the source and the relay using random search methods. After that, we solve the optimal power allocation problem for any number of layers with fixed rates over an Amplify-and-Forward relays. An approximation for the end-to-end channel quality is presented in terms of the statistics of the three links of the channel model. Furthermore, we obtain that for some conditions, it is optimal to send only one layer. Finally, we solve the joint optimal power and rate allocation problem for any number of layers over an Amplify-and-Forward relays. We also consider the theoretical case of infinite number of layers representing an upper bound for the performance. Moreover, we show that with a small number of layers, we can approach the performance upper bound. We provide many numerical examples for the three cases above to show the prospected gains of using the relays on the expected utility for different channel conditions