Computer Science

In this book chapter, we study a problem of distributed content caching in an ultra-dense edge caching network (UDCN), in which a large number of small base stations (SBSs) prefetch popular files to cope with the ever-growing user demand in 5G and beyond. In a UDCN, even a small misprediction of user demand may render a large amount of prefetched data obsolete. Furtherproacmore, the interference variance is high due to the short inter-SBS distances, making it difficult to quantify data downloading rates. Lastly, since the caching decision of each SBS interacts with those of all other SBSs, the problem complexity of exponentially increases with the number of SBSs, which is unfit for UDCNs. To resolve such challenging issues while reflecting time-varying and location-dependent user demand, we leverage mean-field game (MFG) theory through which each SBS interacts only with a single virtual SBS whose state is drawn from the state distribution of the entire SBS population, i.e., mean-field (MF) distribution. This MF approximation asymptotically guarantees achieving the epsilon Nash equilibrium as the number of SBSs approaches infinity. To describe such an MFG-theoretic caching framework, this chapter aims to provide a brief review of MFG, and demonstrate its effectiveness for UDCNs.

With the standardization of 5G, commercial millimeter wave (mmWave) communications has become a reality despite all the concerns about the unfavorable propagation characteristics of these frequencies. Even though the 5G systems are still being rolled out, it is argued that their gigabits per second rates may fall short in supporting many emerging applications, such as 3D gaming and extended reality. Such applications will require several hundreds of gigabits per second to several terabits per second data rates with low latency and high reliability, which are expected to be the design goals of the next generation 6G communications systems. Given the potential of terahertz (THz) communications systems to provide such data rates over short distances, they are widely regarded to be the next frontier for the wireless communications research. The primary goal of this chapter is to equip readers with sufficient background about the mmWave and THz bands so that they are able to both appreciate the necessity of using these bands for commercial communications in the current wireless landscape and to reason the key design considerations for the communications systems operating in these bands. Towards this goal, this chapter provides a unified treatment of these bands with particular emphasis on their propagation characteristics, channel models, design and implementation considerations, and potential applications to 6G wireless. A brief summary of the current standardization activities related to the use of these bands for commercial communications applications is also provided.

Age of Incorrect Information (AoII) is a newly introduced performance metric that is adaptable to a variety of communication goals. It has advantages over both the traditional performance metrics and the recently introduced metric - Age of Information (AoI). However, the fundamental nature of AoII has been elusive so far. In this work, we consider the AoII in a system where a transmitter sends updates about a multi-state Markovian source to a remote receiver through an unreliable channel. The communication goal is to minimize AoII subject to a power constraint. We cast the problem into a Constrained Markov Decision Process (CMDP) and prove that the optimal policy is a mixture of two deterministic threshold policies. Afterward, by leveraging the notion of Relative Value Iteration (RVI) and the structural properties of threshold policy, we propose an efficient algorithm to find the threshold policies as well as the mixing coefficient. Lastly, numerical results are laid out to highlight the effects of system parameters on the performance of AoII-optimal policy.

The age of Incorrect Information (AoII) has been introduced recently to address the shortcomings of the standard Age of information metric (AoI) in real-time monitoring applications. In this paper, we consider the problem of monitoring the states of remote sources that evolve according to a Markovian Process. A central scheduler selects at each time slot which sources should send their updates in such a way to minimize the Mean Age of Incorrect Information (MAoII). The difficulty of the problem lies in the fact that the scheduler cannot know the states of the sources before receiving the updates and it has then to optimally balance the exploitation-exploration trade-off. We show that the problem can be modeled as a partially Observable Markov Decision Process Problem framework. We develop a new scheduling scheme based on Whittle's index policy. The scheduling decision is made by updating a belief value of the states of the sources, which is to the best of our knowledge has not been considered before in the Age of Information area. To that extent, we proceed by using the Lagrangian Relaxation Approach, and prove that the dual problem has an optimal threshold policy. Building on that, we shown that the problem is indexable and compute the expressions of the Whittle's indices. Finally, we provide some numerical results to highlight the performance of our derived policy compared to the classical AoI metric.

This paper focuses on error-correcting codes that can handle a predefined set of specific error patterns. The need for such codes arises in many settings of practical interest, including wireless communication and flash memory systems. In many such settings, a smaller field size is achievable than that offered by MDS and other standard codes. We establish a connection between the minimum alphabet size for this generalized setting and the combinatorial properties of a hypergraph that represents the prespecified collection of error patterns. We also show a connection between error and erasure correcting codes in this specialized setting. This allows us to establish bounds on the minimum alphabet size and show an advantage of non-linear codes over linear codes in a generalized setting. We also consider a variation of the problem which allows a small probability of decoding error and relate it to an approximate version of hypergraph coloring.

We derive an upper bound on the reliability function of mismatched decoding for zero-rate codes. The bound is based on a result by Komlós that shows the existence of a subcode with certain symmetry properties. The bound is shown to coincide with the expurgated exponent at rate zero for a broad family of channel-decoding metric pairs.

Estimation of missing mass with the popular Good-Turing (GT) estimator is well-understood in the case where samples are independent and identically distributed (iid). In this article, we consider the same problem when the samples come from a stationary Markov chain with a rank-2 transition matrix, which is one of the simplest extensions of the iid case. We develop an upper bound on the absolute bias of the GT estimator in terms of the spectral gap of the chain and a tail bound on the occupancy of states. Borrowing tail bounds from known concentration results for Markov chains, we evaluate the bound using other parameters of the chain. The analysis, supported by simulations, suggests that, for rank-2 irreducible chains, the GT estimator has bias and mean-squared error falling with number of samples at a rate that depends loosely on the connectivity of the states in the chain.

We develop mobility-aware routing and caching strategies to solve the network cost minimization problem for dense small-cell networks. The challenge mainly stems from the insufficient backhaul capacity of small-cell networks and the limited storing capacity of small-cell base stations (SBSs). The optimization problem is NP-hard since both the mobility patterns of the mobilized users (MUs), as well as the MUs' preference for contents, are unknown. To tackle this problem, we start by dividing the entire geographical area into small sections, each of which containing one SBS and several MUs. Based on the concept of one-stop-shop (OSS), we propose a federated routing and popularity learning (FRPL) approach in which the SBSs cooperatively learn the routing and preference of their respective MUs, and make caching decision. Notably, FRPL enables the completion of the multi-tasks in one shot, thereby reducing the average processing time per global aggregation. Theoretical and numerical analyses show the effectiveness of our proposed approach.

We consider a multi-source status update system in which status updates are transmitted as packets containing the measured value of the monitored process and a time stamp representing the time when the sample was generated. The packets of each source are generated according to the Poisson process and the packets are served according to an exponentially distributed service time. We assume that the received status update packets needs further processing before being used (hence, computation-intensive). This is mathematically modeled by introducing an additional server at the sink node. The sink server serves the packets according to an exponentially distributed service time. We introduce two packet management policies, namely, i) a preemptive policy and ii) a blocking policy and derive the moment generating function (MGF) of the AoI of each source under both policies. In the preemptive policy, a new arriving packet preempts any possible packet that is currently under service regardless of the packet's source index. In the blocking policy, when a server is busy at the arrival instant of a packet the arriving packet is blocked and cleared. We assume that the same preemptive/blocking policy is employed in both transmitter and sink servers. Numerical results are provided to assess the results.

A new spectrum sensing detector is proposed and analytically studied, when it operates under generalized noise channels. Particularly, the McLeish distribution is used to model the underlying noise, which is suitable for both non-Gaussian (impulsive) as well as classical Gaussian noise modeling. The introduced detector adopts a moment-based approach, whereas it is not required to know the transmit signal and channel fading statistics (i.e., blind detection). Important performance metrics are presented in closed forms, such as the false-alarm probability, detection probability and decision threshold. Analytical and simulation results are cross-compared validating the accuracy of the proposed approach. Finally, it is demonstrated that the proposed approach outperforms the conventional energy detector in the practical case of noise uncertainty, yet introducing a comparable computational complexity.