arXiv subjects

Wing Shing Wong

Publications and source records attributed to Wing Shing Wong.

34 records · Page 2Linked to original sources

arXiv2018

The Undirected Optical Indices of Complete $m$-ary Trees

The routing and wavelength assignment problem arises from the investigation of optimal wavelength allocation in an optical network that employs Wavelength Division Multiplexing (WDM). Consider an optical network that is represented by a connected, simple graph $G$. An all-to-all routing $R$ in $G$ is a set of paths connecting all pairs of vertices of $G$. The undirected optical index of $G$ is the minimum integer $k$ to guarantee the existence of a mapping $ϕ:R\to\{1,2,\ldots,k\}$, such that $ϕ(P)\neqϕ(P')$ if $P$ and $P'$ have common edge(s), over all possible routings $R$. A natural lower bound of the undirected optical index of $G$ is the (undirected) edge-forwarding index, which is defined to be the minimum of the maximum edge-load over all possible all-to-all routings. In this paper, we first derive the exact value of the optical index of the complete $m$-ary trees, and then investigate the gap between undirected optical and edge-forwarding indices.

math.CO↗

arXiv2018

Forwarding and Optical Indices in an All-Optical BCube Network

BCube is a highly scalable and cost-effective networking topology, which has been widely applied to modular datacenters. Optical technologies based on Wavelength Division Multiplexing (WDM) are gaining popularity for Data Center Networks (DCNs) due to their technological strengths such as low communication latency, low power consumption, and high link bandwidth. Therefore, it is worth investigating optical techniques into the BCube architecture for future DCNs. For this purpose, we study the forwarding and optical indices in an all-optical BCube network. Consider an all-optical BCube network in which every host sets up a connection with every other host. The optical index is the minimum number of wavelengths required by the network to support such a host-to-host traffic, under the restriction that each connection is assigned a wavelength that remains constant in the network. A routing is a set of directed paths specified for all host pairs. By defining the maximum link load of a routing as the maximum number of paths passing through any link, the forwarding index is measured to be the minimum of maximum link load over all possible routings. The forwarding index turns out to be a natural lower bound of the optical index. In this paper, we first compute the forwarding index of an all-optical BCube network. Then, we derive an upper bound of the optical index by providing an oblivious routing and wavelength assignment (RWA) schemes, which attains the lower bound given by the forwarding index in some small cases. Finally, a tighter upper bound is obtained by means of the chromatic numbers in Graph Theory.

cs.DC↗

arXiv2017

Recursive Exponential Weighting for Online Non-convex Optimization

In this paper, we investigate the online non-convex optimization problem which generalizes the classic {online convex optimization problem by relaxing the convexity assumption on the cost function. For this type of problem, the classic exponential weighting online algorithm has recently been shown to attain a sub-linear regret of $O(\sqrt{T\log T})$. In this paper, we introduce a novel recursive structure to the online algorithm to define a recursive exponential weighting algorithm that attains a regret of $O(\sqrt{T})$, matching the well-known regret lower bound. To the best of our knowledge, this is the first online algorithm with provable $O(\sqrt{T})$ regret for the online non-convex optimization problem.

cs.LG↗

arXiv2017

New CRT sequence sets for a collision channel without feedback

Protocol sequences are binary and periodic sequences used for deterministic multiple access in a collision channel without feedback. In this paper, we focus on user-irrepressible (UI) protocol sequences that can guarantee a positive individual throughput per sequence period with probability one for a slot-synchronous channel, regardless of the delay offsets among the users. As the sequence period has a fundamental impact on the worst-case channel access delay, a common objective of designing UI sequences is to make the sequence period as short as possible. Consider a communication channel that is shared by $M$ active users, and assume that each protocol sequence has a constant Hamming weight $w$. To attain a better delay performance than previously known UI sequences, this paper presents a CRTm construction of UI sequences with $w=M+1$, which is a variation of the previously known CRT construction. For all non-prime $M\geq 8$, our construction produces the shortest known sequence period and the shortest known worst-case delay of UI sequences. Numerical results show that the new construction enjoys a better average delay performance than the optimal random access scheme and other constructions with the same sequence period, in a variety of traffic conditions. In addition, we derive an asymptotic lower bound on the minimum sequence period for $w=M+1$ if the sequence structure satisfies some technical conditions, called equi-difference, and prove the tightness of this lower bound by using the CRTm construction.

cs.IT↗

arXiv2016

Partially user-irrepressible sequence sets and conflict-avoiding codes

In this paper we give a partial shift version of user-irrepressible sequence sets and conflict-avoiding codes. By means of disjoint difference sets, we obtain an infinite number of such user-irrepressible sequence sets whose lengths are shorter than known results in general. Subsequently, the newly defined partially conflict-avoiding codes are discussed.

cs.IT↗

arXiv2016

Channel Hopping Sequences for Maximizing Rendezvous Diversity in Cognitive Radio Networks

In cognitive radio networks (CRNs), establishing a communication link between a pair of secondary users (SUs) requires them to rendezvous on a common channel which is not occupied by primary users (PUs). Under time-varying PU traffic, asynchronous sequence-based channel hopping (CH) with the maximal rendezvous diversity is a representative technique to guarantee an upper bounded time-torendezvous (TTR) for delay-sensitive services in CRNs, without requiring global clock synchronization. Maximum TTR (MTTR) and maximum conditional TTR (MCTTR) are two commonly considered metrics for evaluating such CH sequences, and minimizing these two metrics is the primary goal in the sequence design of various paper reported in the literature. In this paper, to investigate the fundamental limits of these two metrics, we first derive lower bounds on the MCTTR and MTTR, and then propose an asymmetric design which has the minimum MCTTR and an improvement on MTTR than other previously known algorithms. Moreover, when the number of licensed channels is odd, our proposed design achieves the minimum MTTR. We also present the TTR performance of the proposed design via simulation.

cs.IT↗

arXiv2015

The Global Packing Number for an Optical Network

The global packing number problem arises from the investigation of optimal wavelength allocation in an optical network that employs Wavelength Division Multiplexing (WDM). Consider an optical network that is represented by a connected, simple graph $G$. We assume all communication channels are bidirectional, so that all links and paths are undirected. It follows that there are ${|G|\choose 2}$ distinct node pairs associated with $G$, where $|G|$ is the number of nodes in $G$. A path system $\mathcal{P}$ of $G$ consists of ${|G|\choose 2}$ paths, one path to connect each of the node pairs. The global packing number of a path system $\mathcal{P}$, denoted by $Φ(G,\mathcal{P})$, is the minimum integer $k$ to guarantee the existence of a mapping $ω:\mathcal{P}\to\{1,2,\ldots,k\}$, such that $ω(P)\neqω(P')$ if $P$ and $P'$ have common edge(s). The global packing number of $G$, denoted by $Φ(G)$, is defined to be the minimum $Φ(G,\mathcal{P})$ among all possible path systems $\mathcal{P}$. If there is no wavelength conversion along any optical transmission path for any node pair in the network, the global packing number signifies the minimum number of wavelengths required to support simultaneous communication for all pairs in the network. In this paper, the focus is on ring networks, so that $G$ is a cycle. Explicit formulas for the global packing number of a cycle is derived. The investigation is further extended to chain networks. A path system, $\mathcal{P}$, that enjoys $Φ(G,\mathcal{P})=Φ(G)$ is called ideal. A characterization of ideal path systems is also presented. We also describe an efficient heuristic algorithm to assign wavelengths that can be applied to a general network with more complicated traffic load.

cs.DM↗

arXiv2015

Sparsest Error Detection via Sparsity Invariant Transformation based $\ell_1$ Minimization

This paper presents a new method, referred to here as the sparsity invariant transformation based $\ell_1$ minimization, to solve the $\ell_0$ minimization problem for an over-determined linear system corrupted by additive sparse errors with arbitrary intensity. Many previous works have shown that $\ell_1$ minimization can be applied to realize sparse error detection in many over-determined linear systems. However, performance of this approach is strongly dependent on the structure of the measurement matrix, which limits application possibility in practical problems. Here, we present a new approach based on transforming the $\ell_0$ minimization problem by a linear transformation that keeps sparsest solutions invariant. We call such a property a sparsity invariant property (SIP), and a linear transformation with SIP is referred to as a sparsity invariant transformation (SIT). We propose the SIT-based $\ell_1$ minimization method by using an SIT in conjunction with $\ell_1$ relaxation on the $\ell_0$ minimization problem. We prove that for any over-determined linear system, there always exists a specific class of SIT's that guarantees a solution to the SIT-based $\ell_1$ minimization is a sparsest-errors solution. Besides, a randomized algorithm based on Monte Carlo simulation is proposed to search for a feasible SIT.

stat.ME↗

arXiv2014

Optimal strongly conflict-avoiding codes of even length and weight three

Strongly conflict-avoiding codes (SCACs) are employed in a slot-asynchronous multiple-access collision channel without feedback to guarantee that each active user can send at least one packet successfully in the worst case within a fixed period of time. Assume all users are assigned distinct codewords, the number of codewords in an SCAC is equal to the number of potential users that can be supported. SCACs have different combinatorial structure compared with conflict-avoiding codes (CACs) due to additional collisions incurred by partially overlapped transmissions. In this paper, we establish upper bounds on the size of SCACs of even length and weight three. Furthermore, it is shown that some optimal CACs can be used to construct optimal SCACs of weight three.

cs.IT↗

arXiv2014

Protocol Sequences for Multiple-Packet Reception

Consider a time slotted communication channel shared by $K$ active users and a single receiver. It is assumed that the receiver has the ability of the multiple-packet reception (MPR) to correctly receive at most $γ$ ($1 \leq γ< K$) simultaneously transmitted packets. Each user accesses the channel following a specific periodical binary sequence, called the protocol sequence, and transmits a packet within a channel slot if and only if the sequence value is equal to one. The fluctuation in throughput is incurred by inevitable random relative shifts among the users due to the lack of feedback. A set of protocol sequences is said to be throughput-invariant (TI) if it can be employed to produce invariant throughput for any relative shifts, i.e., maximize the worst-case throughput. It was shown in the literature that the TI property without considering MPR (i.e., $γ=1$) can be achieved by using shift-invariant (SI) sequences, whose generalized Hamming cross-correlation is independent of relative shifts. This paper investigates TI sequences for MPR; results obtained include achievable throughput value, a lower bound on the sequence period, an optimal construction of TI sequences that achieves the lower bound on the sequence period, and intrinsic structure of TI sequences. In addition, we present a practical packet decoding mechanism for TI sequences that incorporates packet header, forward error-correcting code, and advanced physical layer blind signal separation techniques.

cs.IT↗

arXiv2013

Transmission Sequence Design and Allocation for Wide Area Ad Hoc Networks

In this paper we examine the problem of designing and allocating transmission sequences to users in a mobile ad hoc network that has no spatial boundary. A basic tenet of the transmission sequence approach for addressing media access control is that under normal operating conditions, there is no feedback triggered re-transmission. This obviously is a major departure from the Slotted-ALOHA or CSMA type approaches. While these solutions enjoy excellent throughput performance, a fundamental drawback is that they are based on feedback information. For systems without naturally defined central controller that can play the role of a base station, the task of providing feedback information could easily become unmanageable. This highlights the advantage of the feedback-free approach. A second advantage is the ability to handle unlimited spatial coverage. We propose in this paper a concept for media access control that is akin to frequency reuse. However, instead of reusing frequency, the new approach allows transmission sequences be reused. A study of the transmission sequence approach against other approaches is conducted by comparing the minimal frame lengths that can guarantee the existence of conflict-free transmissions.

cs.NI↗

arXiv2012

Cooperative Target Realization in Multi-Agent Systems Allowing Choice-Based Actions

In this paper, we study cooperative multi-agent systems in which the target objective and the controls exercised by the agents are dependent on the choices they made at initial system time. Such systems have been investigated in several recently published papers, mainly from the perspective of system analysis on issues such as control communication complexity, control energy cost and the feasibility of realization of target functions. This paper continues this line of research by developing optimal control design methodology for linear systems that are collaboratively manipulated by multiple agents based on their distributed choices. For target matrices that satisfy particular structural constraints, we derive control algorithms that can achieve the specified targets with minimum control cost. We compare state-feedback as well as open-loop control strategies for target realization and extend the optimality result to an arbitrary target matrix. The optimal control solutions are obtained by minimizing the average control cost subject to the set of specified target-state constraints by means of modern variation theory and the Lagrange multiplier method.

eess.SY↗

arXiv2012

Control Communication Complexity of Distributed Actions

Recent papers have treated {\em control communication complexity} in the context of information-based, multiple agent control systems including nonlinear systems of the type that have been studied in connection with quantum information processing. The present paper continues this line of investigation into a class of two-agent distributed control systems in which the agents cooperate in order to realize common goals that are determined via independent actions undertaken individually by the agents. A basic assumption is that the actions taken are unknown in advance to the other agent. These goals can be conveniently summarized in the form of a {\em target matrix}, whose entries are computed by the control system responding to the choices of inputs made by the two agents. We show how to realize such target matrices for a broad class of systems that possess an input-output mapping that is bilinear. One can classify control-communication strategies, known as {\em control protocols}, according to the amount of information sharing occurring between the two agents. Protocols that assume no information sharing on the inputs that each agent selects and protocols that allow sufficient information sharing for identifying the common goals are the two extreme cases. Control protocols will also be evaluated and compared in terms of cost functionals given by integrated quadratic functions of the control inputs. The minimal control cost of the two classes of control protocols are analyzed and compared. The difference in the control costs between the two classes reflects an inherent trade-off between communication complexity and control cost.

eess.SY↗

arXiv2010

Construction and Applications of CRT Sequences

Protocol sequences are used for channel access in the collision channel without feedback. Each user accesses the channel according to a deterministic zero-one pattern, called the protocol sequence. In order to minimize fluctuation of throughput due to delay offsets, we want to construct protocol sequences whose pairwise Hamming cross-correlation is as close to a constant as possible. In this paper, we present a construction of protocol sequences which is based on the bijective mapping between one-dimensional sequence and two-dimensional array by the Chinese Remainder Theorem (CRT). In the application to the collision channel without feedback, a worst-case lower bound on system throughput is derived.

cs.IT↗

arXiv2010

A General Upper Bound on the Size of Constant-Weight Conflict-Avoiding Codes

Conflict-avoiding codes are used in the multiple-access collision channel without feedback. The number of codewords in a conflict-avoiding code is the number of potential users that can be supported in the system. In this paper, a new upper bound on the size of conflict-avoiding codes is proved. This upper bound is general in the sense that it is applicable to all code lengths and all Hamming weights. Several existing constructions for conflict-avoiding codes, which are known to be optimal for Hamming weights equal to four and five, are shown to be optimal for all Hamming weights in general.

cs.IT↗

arXiv2010

Construction of Short Protocol Sequences with Worst-Case Throughput Guarantee

Protocol sequences are used in channel access for the multiple-access collision channel without feedback. A new construction of protocol sequences with a guarantee of worst-case system throughput is proposed. The construction is based on Chinese remainder theorem. The Hamming crosscorrelation is proved to be concentrated around the mean. The sequence period is much shorter than existing protocol sequences with the same throughput performance. The new construction reduces the complexity in implementation and also shortens the waiting time until a packet can be sent successfully.

cs.IT↗