Network-Coded Macrocell Offloading in Femtocaching-Assisted Cellular Networks

In this article, we consider a buffer-aided two-way relay network in which a wireless-powered relay acts as an intermediate node for exchanging the data between two sources. The relay applies a time-switching (TS) policy to switch between data decoding (DD) and energy harvesting (EH) modes. Due to the presence of data queues at the relay, the relay is capable of employing opportunistic network coding (ONC) for transmission of the packets. Based on some realistic assumptions, we derive the stability region of such a network through designing TS and ONC policies. It is proved that the stability region is characterized by the TS policy and zero-wait ONC policy. Moreover, we derive the throughput-optimal and power-optimal policies and show that these policies provide the maximum coding opportunities. Also, we derive the average delay of an applied TS-ONC policy at the relay through modeling the data queues and energy buffer of the relay by two inter-related quasi-birth-death processes. We show that although waiting in ONC does not contribute to throughput-optimal and power-optimal policies, it can reduce the average delay. Finally, through simulation, we confirm our analytical results.

SummaryWe investigate the problem of joint downlink wireless backhaul bandwidth (WBB) and power allocation in heterogeneous cellular networks (HCNs). A WBB partitioning scheme is considered, which allocates the whole bandwidth between the macrocell and small cells for data transmission and backhauling. We formulate an optimization problem to maximize the weighted sum logarithmic utility function by jointly optimizing WBB portion and fronthaul power allocation of each base station with consideration of the backhaul capacity limitation on each small cell. In order to solve this joint optimization problem, we propose a hierarchical two‐level approach and decompose the original problem into two independent subproblems: the WBB allocation at the macrocell base station (MBS) and the power allocation at both the MBS and small cell base stations (SBSs). Accordingly, the optimal WBB portion and power allocation solutions are obtained, respectively. Furthermore, we develop a distributed algorithm to implement the joint WBB and power allocation. Numerical results verify the effectiveness of the proposed approach and analyze the impact of the weighted coefficient and backhaul capacity limitation on the network performance. In addition, significant performance gains can be achieved by the proposed approach over the benchmark.

Recently, it has been proven that retransmission based on Network Coding (NC) can greatly improve the performance of wireless networks with broadcast erasure channels. However, network coding also introduces additional delay at the both sending and receiving sides, resulting in the decline of the Quality of user Experience (QoE). In this paper, we consider the users' waiting time and the decoding delay as the performance metrics and then propose MixCode, a NC-based loss recovery method, to improve the delay performance in heterogeneous wireless networks. MixCode incorporates Opportunistic Network Coding (ONC) with Random Linear Network Coding (RLNC), where a NC packet can be decoded by simply XORing operation at some destinations, but by Gaussian elimination at other destinations. Simulation results show that our proposed algorithm can efficiently reduce both the waiting time and the decoding delay in comparison with the existing NC-based schemes.

Femtocell base station (FBS) is one solution to improve performance of indoor and outdoor user equipments (UEs) with low cost and low complexity. To gain the benefit of deployment of FBS, we consider a frequency assignment method to mitigate cross-tier interference between macrocell and femtocell. Previous studies proposed the channel assignment schemes where macrocell base stations (MBSs) and FBSs orthogonally use subbands. However, they have low efficiency in terms of frequency reuse and high complexity due to exchanging information of FBSs via network. Therefore, we consider the FBS with soft frequency reuse (SFR) scheme to improve the efficiency of frequency reuse. For performance improvement of macrocell UEs (MUEs), we propose a method to cluster FBSs with same SFR pattern. Since the proposed clustering scheme utilizes self-organization network (SON) technique without any information exchange of FBSs, it can improve the performance of MUEs with low complexity. By simulations, we confirm that FBSs with proposed clustering method mitigate cross-tier interference in downlink and increase the throughputs of MUEs.

Joint sub-carrier allocation and 3D beamforming design in OMA-NOMA based mmWave heterogeneous networks under channel uncertainties

A recent approach--COPE, presented by Katti et al. (Proc. ACM SIGCOMM 2006, pp. 243-254)--for improving the throughput of unicast traffic in wireless multihop networks exploits the broadcast nature of the wireless medium through opportunistic network coding. In this paper, we analyze throughput improvements obtained by COPE-type network coding in wireless networks from a theoretical perspective. We make two key contributions. First, we obtain a theoretical formulation for computing the throughput of network coding on any wireless network topology and any pattern of concurrent unicast traffic sessions. Second, we advocate that routing be made aware of network coding opportunities rather than, as in COPE, being oblivious to it. More importantly, our model considers the tradeoff between routing flows close to each other for utilizing coding opportunities and away from each other for avoiding wireless interference. Our theoretical formulation provides a method for computing source-destination routes and utilizing the best coding opportunities from available ones so as to maximize the throughput. We handle scheduling of broadcast transmissions subject to wireless transmit/receive diversity and link interference in our optimization framework. Using our formulations, we compare the performance of traditional unicast routing and network coding with coding-oblivious and coding-aware routing on a variety of mesh network topologies, including some derived from contemporary mesh network testbeds. Our evaluations show that a route selection strategy that is aware of network coding opportunities leads to higher end-to-end throughput when compared to coding-oblivious routing strategies.

In recent years, network coding has emerged as an innovative method that helps wireless network approaches its maximum capacity, by combining multiple unicasts in one broadcast. However, the majority of research conducted in this area is yet to fully utilize the broadcasting nature of wireless networks, and still assumes fixed route between the source and destination that every packet should travel through. This assumption not only limits coding opportunities, but can also cause buffer overflow in some specific intermediate nodes. Although some studies considered scattering of the flows dynamically in the network, they still face some limitations. This paper explains pros and cons of some prominent research in network coding and proposes FlexONC (Flexible and Opportunistic Network Coding) as a solution to such issues. The performance results show that FlexONC outperforms previous methods especially in worse quality networks, by better utilizing redundant packets spread in the network.

COPE, presented by Katti et al. (Proc. ACM SIGCOMM 2006, pp.243-254), exploits the broadcast nature of the wireless medium through opportunistic network coding. In this paper, we introduce the basic knowledge and characteristic of COPE, and propose a multi-channel multi-interface wireless network coding algorithm based on guesswork (GUESS-MCMI-COPE). By reducing the space of reception reports and implementing multi-channel multi-interface, GUESS-MCMI-COPE can increase network throughput. We evaluate our design on NS2, and discuss the results. The results show that the performance of GUESS-MCMI-COPE is superior to that of COPE.

In this paper, we investigate the downlink transmissions in wireless backhaul (WB) networks when unmanned aerial vehicles (UAVs) are used as flying small cell base stations. We propose to employ the non-orthogonal multiple access (NOMA) on the WB transmissions and introduce a novel cooperative transmission scheme for the wireless access links. Then, we formulate an optimization problem which jointly determines the radio resource allocation at the macro cell base station (MBS) and UAVs along with the optimization of the decoding order of the NOMA process and the positions of the UAVs in space to maximize the sum achievable rate of all users. The formulated problem is a general mixed integer non-convex program, which is very difficult to solve optimally within a polynomial time. Therefore, we propose a framework based on the method of difference of convex program characterized by the Lipschitz continuity to transform and approximate the original problem into a series of convex approximate ones and develop a low-complexity algorithm to sequentially solve for each approximate problem until convergence. Numerical evaluation and analysis show that our achieved solution, under the proposed framework and developed algorithm, can outperform the other schemes which aim at either optimizing without using cooperative NOMA or do not optimize the UAVs' positions.

This paper investigates network coding with full diversity and a high rate for improving the reliability of wireless communications against the co-channel interference. We consider a cellular network composed of two user terminals that are intended to communicate with a common base station (BS), where a two-way relay node is used to assist the bidirectional communications between the users and BS. We propose an opportunistic network coding (ONC) scheme with the two-way relay, called two-way ONC, which operates depending on whether or not the relay node successfully decodes data packets of the user terminals and BS. Closed-form outage probability expressions of the uplink transmission (from users to BS) and downlink transmission (from BS to users) are derived for the proposed two-way ONC scheme in the presence of co-channel interference over Rayleigh fading channels. We also develop the diversity-multiplexing tradeoff (DMT) of the two-way ONC scheme and show that it obtains the full diversity and an increased multiplexing gain , as compared with conventional one-way relay methods. Additionally, numerical outage probability results demonstrate that the proposed two-way ONC scheme outperforms the conventional one-way relay approaches in terms of improving the communication’s reliability against co-channel interference.

In this paper, we are concerned with extending the graph representation of generalized instantly decodable network coding (GIDNC) to a more general opportunistic network coding (ONC) scenario, referred to as order-2 GIDNC (O2-GIDNC). In the O2-GIDNC schem

For the purpose of improving the throughput and reliability of the two way decode-and-forward (DF) relay networks, we propose an opportunistic network coding and signal combining (ONCSC) based automatic repeat request (ARQ) protocol. We assume that the relay node (RN) has a buffer which can store the signals received. Hence, RN can combine the signals received from different time slots and judge to transmit or receive in the next time slot according to the output of the maximal likelihood (ML) detector. Two signal combining methods at the RN, namely maximal sum signal-to-noise ratio combining (MSSNR) and maximal minimum signal-to-noise ratio combining (MM-SNR) are proposed in this paper. Simulation results show that the proposed two signal combining methods outperform traditional No-ARQ and No-combining ARQ systems on the packets error ratio (PER) and throughput performances in the moderate SNR. Also the optimal power allocation factor between the sources and RN is discussed in the simulations.

This paper proposes a new application of the stochastic game model to solve the problem of self- organization of the Hamiltonian cycle of a graph. To do this, at the vertices of the undirected graph are placed game agents, whose pure strategies are options for choosing one of the incident edges. A random selection of strategies by all agents forms a set of local paths that begin at each vertex of the graph. Current player payments are defined as loss functions that depend on the strategies of neighboring players that control adjacent vertices of the graph. These functions are formed from a penalty for the choice of opposing strategies by neighboring players and a penalty for strategies that have reduced the length of the local path. Random selection of players’ pure strategies is aimed at minimizing their average loss functions. The generation of sequences of pure strategies is performed by a discrete distribution built on the basis of dynamic vectors of mixed strategies. The elements of the vectors of mixed strategies are the probabilities of choosing the appropriate pure strategies that adaptively take into account the values of current losses. The formation of vectors of mixed strategies is determined by the Markov recurrent method, for the construction of which the gradient method of stochastic approximation is used. During the game, the method increases the value of the probabilities of choosing those pure strategies that lead to a decrease in the functions of average losses. For given methods of forming current payments, the result of the stochastic game is the formation of patterns of self-organization in the form of cyclically oriented strategies of game agents. The conditions of convergence of the recurrent method to collectively optimal solutions are ensured by observance of the fundamental conditions of stochastic approximation. The game task is extended to random graphs. To do this, the vertices are assigned the probabilities of recovery failures, which cause a change in the structure of the graph at each step of the game. Realizations of a random graph are adaptively taken into account when searching for Hamiltonian cycles. Increasing the probability of failure slows down the convergence of the stochastic game. Computer simulation of the stochastic game provided patterns of self-organization of agents’ strategies in the form of several local cycles or a global Hamiltonian cycle of the graph, depending on the ways of forming the current losses of players. The reliability of experimental studies is confirmed by the repetition of implementations of self-organization patterns for different sequences of random variables. The results of the study can be used in practice for game-solving NP-complex problems, transport and communication problems, for building authentication protocols in distributed information systems, for collective decision-making in conditions of uncertainty.

Preface. 1 Introduction. 1.1 Two examples of combinatorial optimization. 1.2 Why study combinatorial optimization using statistical physics? 1.3 Textbooks. Bibliography. 2 Algorithms. 2.1 Pidgin Algol. 2.2 Iteration and recursion. 2.3 Divide-and-conquer. 2.4 Dynamic programming. 2.5 Backtracking. Bibliography. 3 Introduction to graphs. 3.1 Basic concepts and graph problems. 3.2 Basic graph algorithms. 3.3 Random graphs. Bibliography. 4 Introduction to complexity theory. 4.1 Turing machines. 4.2 Church's thesis. 4.3 Languages. 4.4 The halting problem. 4.5 Class P. 4.6 Class NP. 4.7 Definition of NP-completeness. 4.8 NP-complete problems. 4.9 Worst-case vs. typical-case complexity. Bibliography. 5 Statistical mechanics of the Ising model. 5.1 Phase transitions. 5.2 Some general notes on statistical mechanics. 5.3 The Curie-Weiss model of a ferromagnet. 5.4 The Ising model on a random graph. Bibliography. 6 Algorithms and numerical results for vertex covers. 6.1 Definitions. 6.2 Heuristic algorithms. 6.3 Branch-and-bound algorithm. 6.4 Results: Covering random graphs. 6.5 The leaf-removal algorithm. 6.6 Monte Carlo simulations. 6.7 Backbone. 6.8 Clustering of minimum vertex covers. Bibliography. 7 Statistical mechanics of vertex covers on a random graph. 7.1 Introduction. 7.2 The first-moment bound. 7.3 The hard-core lattice gas. 7.4 Replica approach. Bibliography. 8 The dynamics of vertex-cover algorithms. 8.1 The typical-case solution time of a complete algorithm. 8.2 The dynamics of generalized leaf-removal algorithms. 8.3 Random restart algorithms. Bibliography. 9 Towards new, statistical-mechanics motivated algorithms. 9.1 The cavity graph. 9.2 Warning propagation. 9.3 Belief propagation. 9.4 Survey propagation. 9.5 Numerical experiments on random graphs. Bibliography. 10 The satisfiability problem. 10.1 SAT algorithms. 10.2 Phase transitions in random K-SAT. 10.3 Typical-case dynamics of RandomWalkSAT. 10.4 Message-passing algorithms for SAT. Bibliography. 11 Optimization problems in physics. 11.1 Monte Carlo optimization. 11.2 Hysteric optimization. 11.3 Genetic algorithms. 11.4 Shortest paths and polymers in random media. 11.5 Maximum flows and random-field systems. 11.6 Submodular functions and free energy of Potts model. 11.7 Matchings and spin glasses. Bibliography. Index.

......... Non-deterministic polynomial time (commonly termed ‘NP-complete’) problems are relevant to many computational tasks of practical interest—such as the ‘travelling salesman problem’—but are difficult to solve: the computing time grows exponentially with problem size in the worst case. It has recently been shown that these problems exhibit ‘phase boundaries’, across which dramatic changes occur in the computational difficulty and solution character—the problems become easier to solve away from the boundary. Here we report an analytic solution and experimental investigation of the phase transition in K-satisfiability, an archetypal NP-complete problem. Depending on the input parameters, the computing time may grow exponentially or polynomially with problem size; in the former case, we observe a discontinuous transition, whereas in the latter case a continuous (second-order) transition is found. The nature of these transitions may explain the differing computational costs, and suggests directions for improving the efficiency of search algorithms. Similar types of transition should occur in other combinatorial problems and in glassy or granular materials, thereby strengthening the link between computational models and properties of physical systems. Many computational tasks of practical interest are surprisingly difficult to solve even using the fastest available machines. Such problems, found for example in planning, scheduling, machine learning, hardware design, and computational biology, generally belong to the class of NP-complete problems 1‐3 . NP stands for ‘nondeterministic polynomial time’, which denotes an abstract computational model with a rather technical definition. Intuitively speaking, this class of computational tasks consists of problems for which a potential solution can be checked efficiently for correctness, yet finding such a solution appears to require exponential time in the worst case. A good analogy can be drawn from mathematics: proving open conjectures in mathematics is extremely difficult, but verifying any given proof (or solution) is generally relatively straightforward. The class of NP-complete problems lies at the foundations of the theory of computational complexity in modern computer science. Literally thousands of computational problems have been shown to be NP-complete. The completeness property of NPcomplete problems means that if an efficient algorithm for solving just one of these problems could be found, one would immediately have an efficient algorithm for all NP-complete problems. However,