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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.

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 information 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. Index Terms--Coding, network routing, switching.

In the first part of this correspondence, a detailed analysis of the maximum aperiodic autocorrelation of the original Chu sequences (equivalently, P3/P4 pulse compression codes) is presented. The result implies the best known upper bound on the minimax aperiodic autocorrelation for polyphase sequences except when the length is very small or a perfect square. It is well known that determining the minimax aperiodic correlation for polyphase sequence sets is an intractable task. In the second part, the simplest nontrivial cases for Barker and general polyphase sequences are solved for the first time. Index Terms - Autocorrelation, Barker sequences, Chu sequences, crosscorrelation, Frank sequences, Golomb sequences, minimax aperiodic correlation, P3 and P4 pulse compression codes.

This article introduces a slotted protocol for multi-user access to a LAN over parallel OR-type channels. An OR-type channel is defined as a digital communication channel such that, when a bit signal is injected into the channel, the channel content at the bit position becomes logically ORed with the injected bit. The protocol applies a dynamic coding scheme to achieve 100% channel efficiency in the sense that, in each transmission session, all intended messages, or at least as many as the number of channels, are successfully broadcast. Message reception is through decoding from the OR composition of user injected bits. The coding scheme is a substitute for such approaches as slot reservation, permission token, and collision resolution that are used in most media access protocols.

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 [...]

We introduce a new class of problems called network information flow which is inspired by computer network applications. Consider a point-to-point communication network on which a number of information sources are to be mulitcast to certain sets of destinations. We assume that the information sources are mutually independent. The problem is to characterize the admissible coding rate region. This model subsumes all previously studied models along the same line. In this paper, we study the problem with one information source, and we have obtained a simple characterization of the admissible coding rate region. Our result can be regarded as the Max-flow Min-cut Theorem for network information flow. Contrary to one's intuition, our work reveals that it is in general not optimal to regard the information to be multicast as a "fluid" which can simply be routed or replicated. Rather, by employing coding at the nodes, which we refer to as network coding, bandwidth can in general be saved. This finding may have significant impact on future design of switching systems. Index Terms--Diversity coding, multicast, network coding, switching, multiterminal source coding.