The Balanced Unicast and Multicast Capacity Regions of Large Wireless Networks

We consider the question of determining the scaling of the $n^2$-dimensional balanced unicast and the $n 2^n$-dimensional balanced multicast capacity regions of a wireless network with $n$ nodes placed uniformly at random in a square region of area $n$ and communicating over Gaussian fading channels. We identify this scaling of both the balanced unicast and multicast capacity regions in terms of $\Theta(n)$, out of $2^n$ total possible, cuts. These cuts only depend on the geometry of the locations of the source nodes and their destination nodes and the traffic demands between them, and thus can be readily evaluated. Our results are constructive and provide optimal (in the scaling sense) communication schemes.Comment: 37 pages, 7 figures, to appear in IEEE Transactions on Information Theor

Scaling Laws for Heterogeneous Wireless Networks

Thesis Supervisor: Devavrat Shah Title: Associate Professor Thesis Supervisor: Gregory W. Wornell Title: ProfessorThis thesis studies the problem of determining achievable rates in heterogeneous wireless networks. We analyze the impact of location, traffic, and service heterogeneity. Consider a wireless network with n nodes located in a square area of size n communicating with each other over Gaussian fading channels. Location heterogeneity is modeled by allowing the nodes in the wireless network to be deployed in an arbitrary manner on the square area instead of the usual random uniform node placement. For traffic heterogeneity, we analyze the n × n dimensional unicast capacity region. For service heterogeneity, we consider the impact of multicasting and caching. This gives rise to the n × 2n dimensional multicast capacity region and the 2n × n dimensional caching capacity region. In each of these cases, we obtain an explicit informationtheoretic characterization of the scaling of achievable rates by providing a converse and a matching (in the scaling sense) communication architecture.National Science Foundation. DARPA, and Hewlett-Packard under the MIT/HP Alliance

Identified the Cluster Based Stretch and Shrink Method Based On Load Balancing Algorithm for Ad Hoc Network Topology Stability

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Reduced complexity multicast beamforming and group assignment schemes for multi-antenna coded caching

Abstract. In spite of recent advancements in wireless communication technologies and data delivery networks, it is unlikely that the speeds supported by these networks will be able to keep up with the exponentially increasing demand caused by the widespread adoption of high-speed and large-data applications. One appealing idea proposed to address this issue is coded caching, which is an innovative data delivery technique that makes use of the network’s aggregate cache rather than the individual memory available to each user. This proposed idea of coded caching helps boost the data rates by distributing cache material throughout the network and delivering independent content to many users at a time. Despite the original theoretical promises for large caching gains, in reality, coded caching suffers from severe bottlenecks that dramatically limit these gains. Some of these bottlenecks are requiring complex successive interference cancellation (SIC) at the receiver, exponential increase in subpacketization, applicability to a limited range of input parameters, and performance losses in low- and mid- signal to noise ratio (SNR) regimes. In this study, we present a novel coded caching scheme based on user grouping for cache-aided multi-input single-output (MISO) networks. One special property of this new scheme is its applicability to every set of input values for the user count ($K$), transmitter-side antenna count ($L$), and the global coded caching gain ($t$). Moreover, for a fixed $t$, this scheme can achieve theoretical sum-DoF optimality with no limitations. This strategy yields superior performance in terms of subpacketization when input parameters satisfy $\frac{t+L}{t+1} \in \mathbb{N}$. This performance boost is enabled by the underlying user grouping structure during data delivery. However, when input parameters do not comply with $\frac{t+L}{t+1}$ $\in \mathbb{N}$, in order to guarantee symmetry of the scheme and optimal DoF, multicast and unicast messages need to be constructed using a tree diagram, resulting in excess subpacketization and transmission count. Nevertheless, the simple receiver structure without the SIC requirement not only simplifies the implementation complexity but also enables us to use state-of-the-art methods to readily design optimized transmit beamformers maximizing the achievable symmetric rate. Finally, we use numerical analysis to compare our new proposed scheme with well-known coded caching schemes in the literature

Performance Modelling and Optimisation of Multi-hop Networks

A major challenge in the design of large-scale networks is to predict and optimise the total time and energy consumption required to deliver a packet from a source node to a destination node. Examples of such complex networks include wireless ad hoc and sensor networks which need to deal with the effects of node mobility, routing inaccuracies, higher packet loss rates, limited or time-varying effective bandwidth, energy constraints, and the computational limitations of the nodes. They also include more reliable communication environments, such as wired networks, that are susceptible to random failures, security threats and malicious behaviours which compromise their quality of service (QoS) guarantees. In such networks, packets traverse a number of hops that cannot be determined in advance and encounter non-homogeneous network conditions that have been largely ignored in the literature. This thesis examines analytical properties of packet travel in large networks and investigates the implications of some packet coding techniques on both QoS and resource utilisation. Specifically, we use a mixed jump and diffusion model to represent packet traversal through large networks. The model accounts for network non-homogeneity regarding routing and the loss rate that a packet experiences as it passes successive segments of a source to destination route. A mixed analytical-numerical method is developed to compute the average packet travel time and the energy it consumes. The model is able to capture the effects of increased loss rate in areas remote from the source and destination, variable rate of advancement towards destination over the route, as well as of defending against malicious packets within a certain distance from the destination. We then consider sending multiple coded packets that follow independent paths to the destination node so as to mitigate the effects of losses and routing inaccuracies. We study a homogeneous medium and obtain the time-dependent properties of the packet’s travel process, allowing us to compare the merits and limitations of coding, both in terms of delivery times and energy efficiency. Finally, we propose models that can assist in the analysis and optimisation of the performance of inter-flow network coding (NC). We analyse two queueing models for a router that carries out NC, in addition to its standard packet routing function. The approach is extended to the study of multiple hops, which leads to an optimisation problem that characterises the optimal time that packets should be held back in a router, waiting for coding opportunities to arise, so that the total packet end-to-end delay is minimised