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The metaverse gradually evolves into a virtual world containing a series of interconnected sub-metaverses. Diverse digital resources, including identities, contents, services, and supporting data, are key components of the sub-metaverse. Therefore, a Domain Name System (DNS)-like system is necessary for efficient management and resolution. However, the legacy DNS was designed with security vulnerabilities and trust risks due to centralized issues. Blockchain is used to mitigate these concerns due to its decentralized features. Additionally, it supports identity management as a default feature, making it a natural fit for the metaverse. While there are several DNS alternatives based on the blockchain, they either manage only a single type of identifiers or isolate identities from other sorts of identifiers, making it difficult for sub-metaverses to coexist and connect with each other. This article proposes a Multi-Identifier management and resolution System (MIS) in the metaverse, supporting the registration, resolution, and inter-translation functions. The basic MIS is portrayed as a four-tier architecture on a consortium blockchain due to its manageability, enhanced security, and efficiency properties. On-chain data is lightweight and compressed to save on storage while accelerating reading and writing operations. The resource data is encrypted based on the attributes of the sub-metaverse in the storage tier for privacy protection and access control. For users with decentralization priorities, a modification named EMIS is built on top of Ethereum. Finally, MIS is implemented on two testbeds and is available online as the open-source system. The first testbed consists of 4 physical servers located in the UK and Malaysia while the second is made up of 200 virtual machines (VMs) spread over 26 countries across all 5 continents on Google Cloud. Experiments indicate that MIS provides efficient reading and writing performance than the legacy DNS and other public blockchain-based workarounds including EMIS and Ethereum Name Service (ENS). [ABSTRACT FROM AUTHOR]

A multistage interconnection network (MIN) consisting of 2 x 2 nodes constructs a nonblocking switch if the network is rearrangeable. When a [2.sup.n] x [2.sup.n] bit-permuting network is rearrangeable with the minimum depth of 2n - 1, the initial (resp. final) n stages of the network form a banyan-type network and hence the network is equivalent to the tandem connection between two banyan-type networks. Let [gamma] denote the guide permutation of a [2.sup.n] x [2.sup.n] banyan-type network and [tau] the trace permutation of another. These are permutations on numbers from 1 to n. This paper proves that, when the permutation [gamma][[tau].sup.-1] is the transposition between the number n and some number k < n, the tandem connection between the two networks is rearrangeable. This sufficient condition for rearrangeability covers a wide class of tandem connections. For example, the first network in tandem can be the omega network appended with the banyan exchange of any rank while the second is the reversed omega network. Index Terms--multistage interconnection network, banyan-type network, bit-permuting network, rearrangeability, tandem connection, trace, guide, permutation, transposition.

The two-stage interconnection network is conceivably the most compact design for interconnecting small switches into a large switch. Switches so constructed typically can be controlled in the self-routing manner, because the route from an input to an output is unique. Different orderings of network input/output result in different versions of the two-stage interconnection network, two of which are known to preserve various classes of conditionally nonblocking switches. This paper adds Latin-square switches, rotators, reflectors, twisters, and untwisters to this set of classes with applications in load balancing, crosstalk-free optical switching, full connectivity among multiple users, etc. Knowledge of switch preservation under a certain style of multistage interconnection not only allows recursive construction of indefinitely large switches, but also provides insight, generality, and algorithmic flexibility in the construction. Index Terms--Banyan-type networks, conditionally non-blocking switches, in-band control, multistage interconnection networks (MINs), optical switches, switch preservation under two-stage interconnection, two-stage interconnection networks.

Cloud computing provides blockchain a flexible and cost-effective service by on-demand resource sharing, which also introduces additional security risks. Adaptive Cyber Defense (ACD) provides a solution that continuously changes the attack surface according to the cloud environments. The dynamic characteristics of ACDs give defenders a tactical advantage against threats. However, when assessing the effectiveness of ACDs, the structure of traditional security evaluation methods becomes unstable, especially when combining multiple ACD techniques. Therefore, there is still a lack of standard methods to quantitatively evaluate the effectiveness of ACDs. In this paper, we conducted a thorough evaluation with a hierarchical model named SPM. The proposed model is made up of three layers integrating Stochastic Reward net (SRN), Poisson process, and Martingale theory incorporated in the Markov chain. SPM provides two main advantages: (1) it allows explicit quantification of the security with a straightforward computation; (2) it helps obtain the effectiveness metrics of interest. Moreover, the hierarchical architecture of SPM allows each layer to be used independently to evaluate the effectiveness of each adopted ACD method. The simulation results show that SPM is efficient in evaluating various ACDs and the synergy effect of their combination, which thus helps improve the system configuration accordingly. [ABSTRACT FROM AUTHOR]

The 2-stage interconnection network is the most compact design in recursive construction of switches. Its 2X and X2 versions preserve several types of conditionally nonblocking switches and thereby enable recursive construction. This paper introduces hybrid preservation of new types of conditionally nonblocking switches. One application is in the construction of distributors. Index Terms--Multistage interconnection network, 2-stage interconnection network, conditionally nonblocking switch, switch preservation, hybrid preservation.

The authors would like to thank Chung Ping Kwong and David Tse for the useful discussions, and Siu-Wai Ho for converting part of the manuscript from Word to LATEX. They [...]

In Part I of this tutorial, we have discussed the single-source network coding problem in an algebraic setting. Each communication channel in the network is assumed to have unit capacity. [...]

In Part I, we have shown that for single-source network coding, linear codes are sufficient for achieving asymptotic optimality. It is not clear whether this continues to hold for multi-source [...]

2.1 Achievable information rate region In Part I, the capacity of direct transmission from a node to its neighbor is determined by the multiplicity of the channels between them. This [...]

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In this appendix, we define global linearity and local linearity of a network code based on the first principle. We shall show that global linearity implies local linearity. This justifies [...]

Abstract Store-and-forward had been the predominant technique for transmitting information through a network until its optimality was refuted by network coding theory. Network coding offers a new paradigm for network [...]

A central focus of switching theory is on non‐blocking properties of switches and their scalability. Several types of conditionally non‐blocking switches have been known to be preserved by the two‐stage interconnection network. The preservation of each type is by a separate theory. This study presents a coherent theory that yields an infinite family of preserved types, incorporating all known ones. Recursive two‐stage interconnection networks, including all banyan‐type networks, construct conditionally non‐blocking switches that are most compact in connecting every input to every output and rich in applications. [ABSTRACT FROM AUTHOR]

In order to guarantee data reliability, erasure codes have been used in distributed storage systems. Nevertheless, this mechanism suffers from the repair problem that excess data are needed to repair a single failure, causing both high bandwidth consuming for the network and heavy computing load on the replacement node. To reduce repair traffic, researchers pointed out the tradeoff between storage and repair traffic and proposed regenerating codes by combining network coding. However, the combination only focuses on the storage terminal and the construction of the codes is quite complicated. Therefore, this paper further combines network coding with network structure and proposes a repair tree model based on general erasure codes to simplify the repair procedure. By decomposing repair computing and distributing it among the tree nodes, our model can mitigate the computing tension. The performance of repair tree is analyzed and evaluated by preliminary emulation. The result shows it can make about three times faster computing than conventional measure and the repair throughput is doubled if there are network bottlenecks. For proper topology, it can significantly reduce the repair traffic. We present algorithms to generate trees across the network topology. At last, we present the idea of extending repair tree to repair multiple failures. [ABSTRACT FROM AUTHOR]

For a (single-source) multicast network, the size of a base field is the most known and studied algebraic identity that is involved in characterizing its linear solvability over the base field. In this paper, we design a new class \mathcal N of multicast networks and obtain an explicit formula for the linear solvability of these networks, which involves the associated coset numbers of a multiplicative subgroup in a base field. The concise formula turns out to be the first that matches the topological structure of a multicast network and algebraic identities of a field other than size. It further facilitates us to unveil infinitely many new multicast networks linearly solvable over GF( q ) but not over GF( q' ) with q < q' , based on a subgroup order criterion. In particular: 1) for every k\geq 2 ) but not over GF( 2^{2k+1} ) and 2) for arbitrary distinct primes p and p' , there are infinitely many k and k' ) but not over GF( p'^k' ) with p^k < p'^k' . [ABSTRACT FROM PUBLISHER]

Scheduling algorithms are crucial for most existing switches to improve the throughput. However, the delay of the switching fabric cannot be guaranteed with such scheduling algorithms. This paper aims to design a novel load-balanced wire-speed multicast switching fabric along with the attractive merits of network coding. We adopt a two-phase self-routing switching fabric constructed by Boolean-multicast concentrators (SRBMCs), where the first SRBMC distributes the incoming cells to its outputs uniformly and the second allows the distributed cells to be self-routed and multicast to their destinations concurrently. To further improve the switching performance, linear network coding is smoothly combined with SRBMC to reduce the packet loss rate. Theoretical analysis and numerical simulation demonstrate that the proposed switching fabric cannot only achieve wire-speed multicast switching but also be recursively constructed into an indefinite large-scale one with such merits as no internal buffers, low complexity, and guarantee in switching delay. Finally, we implement the proposed fabric on Field-Programmable Gate Array and verify its performance in multicast switching. [ABSTRACT FROM AUTHOR]

A fibre memory is a serial connection of fibre-switch blocks, each combining fibre delay lines with one optical switch. With enhanced flexibility in processing fluid optical data, fibre memories allow ramified applications in the existing literature. This study concentrates on the implementations of timeslot interchangers (TSIs) by fibre memories based on a special type of low-complexity switches, called rotators, under periodic switching control. The proposed TSI structure achieves an economic tradeoff between control and component complexities in the construction of large-scale optical TSIs. [ABSTRACT FROM AUTHOR]

We study the profit maximization problem of a cognitive virtual network operator in a dynamic network environment. We consider a downlink OFDM communication system with various network dynamics, including dynamic user demands, uncertain sensing spectrum resources, dynamic spectrum prices, and time-varying channel conditions. In addition, heterogeneous users and imperfect sensing technology are incorporated to make the network model more realistic. By exploring the special structural of the problem, we develop a low-complexity online control policies that determine pricing and resource scheduling without knowing the statistics of dynamic network parameters. We show that the proposed algorithms can achieve arbitrarily close to the optimal profit with a proper tradeoff with the queuing delay. [ABSTRACT FROM PUBLISHER]

For a linear network code (LNC), various senses of optimality are defined by linear independence among certain coding vectors. A generic LNC is optimal in an extreme sense. Over an acyclic network, there has been a characterization of a generic LNC by the coincidence between the matroid of linearly independent sets of coding vectors of the LNC and the network matroid, which is defined by the existence of appropriate edge-disjoint paths. It turns out that this characterization is still valid when the network contains cycles, despite the fact that it is not straightforward to extend theoretic results on LNCs over acyclic networks to cyclic ones. Meanwhile, the variable-rate property of a generic LNC on an acyclic network also extends to cyclic networks. [ABSTRACT FROM PUBLISHER]

Cross-layer optimization is a key step in wireless network design that coordinates the resources allocated to different layers in order to achieve globally optimal network performance. Existing work on cross-layer optimization for wireless networks often adopts simplistic physical-layer models for wireless channels, such as treating interference as noise or interference avoidance. This crude modeling of physical layer often leads to inefficient utilization of resources. In this paper, we adopt a deterministic channel model proposed in refid="ref1"/, refid="ref2"/, a simple abstraction of the physical layer that effectively captures the effect of channel strength, broadcast and superposition in wireless channels. This model allows us to go beyond “treating interference as noise” and as a consequence are able to achieve higher throughput and utility. Within the network utility maximization (NUM) framework, we study the cross-layer optimization for wireless networks based on this deterministic channel model. First, we extend the well-studied conflict graph model to capture the flow interactions over the deterministic channels and characterize the feasible rate region. Then we study distributed algorithms for general wireless multi-hop networks with both link-centric formulation and node-centric formulation. The convergence of algorithms is proved by applying Lyapunov stability theorem and stochastic approximation method. Further, we show the convergence to the bounded neighborhood of optimal solutions with probability one under constant step sizes and constant update intervals. Our numerical evaluations validate the analytical results and show the advantage of deterministic channel model over simple physical layer models such as treating interference as noise. [ABSTRACT FROM AUTHOR]

The fundamental result of linear network coding asserts the existence of an optimal code on an acyclic single-source multicast network when the symbol field is sufficiently large. The restriction to acyclic networks turns out to stem from the customary structure of the symbol alphabet as a field. Adopting data units belonging to a discrete valuation ring (DVR), that is, a PID with a unique maximal ideal, much of the network coding theory extends to cyclic single-source multicast networks. Convolutional network coding is the instance of DVR-based network coding when the DVR consists of rational power series over the symbol field. Meanwhile, a field can be regarded as a degenerate DVR since it is a PID with the maximal ideal 0. Thus the conventional field-based network coding theory becomes a degenerate version of the DVR-based theory. This paper also delves into the issue of constructing optimal network codes on cyclic networks. Inspired by matroid duality theory, a novel method is devised to take advantage of all existing acyclic algorithms for network code construction. It associates every cyclic network with a quadratically large acyclic network so that essentially every optimal code on the acyclic network directly induces one on the cyclic network. [ABSTRACT FROM AUTHOR]

Abstract: A distributor is a time-multiplexed switch that sorts input signals to output ports in the round-robin fashion. We present an efficient construction of distributors for all in the form of parallel distributed-control networks, where the maximum size of a building block is the largest prime factor of . The construction achieves the lowest known complexity for distributors of all sizes within the practical range. Meanwhile, we also offer an algorithm for the adaptation of a larger distributor into a smaller distributor. The adaptation is useful when the size contains large prime factors. Rigorous algebraic formulation throughout the paper keeps the algorithmic construction transparent and affords many variations for the flexibility in implementation. [Copyright &y& Elsevier]

Consider a communication network in which certain source nodes multicast information to other nodes on the network in the multihop fashion where every node can pass on any of its received data to others. We are interested in how fast each node can receive the complete information, or equivalently, what the informarion rate arriving at each node is. Allowing a node to encode its received data before passing it on, the question involves optimization of the multicast mechanisms at the nodes. Among the simplest coding schemes is linear coding, which regards a block of data as a vector over a certain base field and allows a node to apply a linear transformation to a vector before passing it on. We formulate this multicast problem and prove that linear coding suffices to achieve the optimum, which is the max-flow from the source to each receiving node. [ABSTRACT FROM AUTHOR]

Presents a detailed analysis of the maximum aperiodic autocorrelation of the original polyphase sequences. Equivalence relationships among Chu sequences, P3/P4 codes and Golomb sequences; Maximum autocorrelation of original Frank sequences; Maximum autocorrelation of original Chu sequences; Minimax correlation of two polyphase Barker sequences of length three; Minimax correlation of two polyphase sequences of length three; Conclusions.

Peer-to-peer (P2P) systems have provided a scalable and cost effective way for file sharing and multimedia streaming in the past decade. The implementation of P2P systems usually involves two transmission schemes: routing (store-and-forward), and network coding. In this paper, we make a theoretical investigation of the rate that can be achieved by routing vs. network coding. We model P2P networks as node-capacitated networks with constraints on both node upload capacity and node download capacity. We compare routing and network coding for unicast, multicast and broadcast transmissions with both single-source scenario and multi-source scenario. Our results present not only a unification of existing results, but also extensions to new scenarios for node-capacitated networks. [ABSTRACT FROM PUBLISHER]