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We investigate coding schemes that map source symbols into multisets of an alphabet set. Such a formulation of source coding is an alternative approach to the traditional framework and is inspired by an object tracking problem over proximity sensor networks. We define a \textit{multiset combinatorial Gray code} as a mulitset code with fixed multiset cardinality that possesses combinatorial Gray code characteristic. For source codes that are organized as a grid, namely an integer lattice, we propose a solution by first constructing a mapping from the grid to the alphabet set, the codes are then defined as the images of rectangular blocks in the grid of fixed dimensions. We refer to the mapping as a \textit{color mapping} and the code as a \textit{color multiset code}. We propose the idea of product multiset code that enables us to construct codes for high dimensional grids based on 1-dimensional (1D) grids. We provide a detailed analysis of color multiset codes on 1D grids, focusing on codes that require the minimal number of colors. To illustrate the application of such a coding scheme, we consider an object tracking problem on 2D grids and show its efficiency, which comes from exploiting transmission parallelism. Some numerical results are presented to conclude the paper., Comment: 30 pages, 4 figures

In this paper, we investigate the mean-square stabilization for discrete-time stochastic systems that endure both multiple input delays and multiplicative control-dependent noises. For such multi-delay stochastic systems, we for the first time put forward two stabilization criteria: Riccati type and Lyapunov type. On the one hand, we adopt a reduction method to reformulate the original multi-delay stochastic system to a delay-free auxiliary system and present their equivalent proposition for stabilization. Then, by introducing a delay-dependent algebraic Riccati equation (DDARE), we prove that the system under consideration is stabilizable if and only if the developed DDARE has a unique positive definite solution. On the other hand, we characterize the delay-dependent Lyapunov equation (DDLE)-based criterion, which can be verified by linear matrix inequality (LMI) feasibility test. Besides, under some restricted structure, we propose an existence theorem of delay margin and more importantly, derive an explicit formula for computing its exact value.

Group consensus implies reaching multiple groups where agents belonging to the same cluster reach state consensus. This paper focuses on linear multi-agent systems under nonnegative directed graphs. A new necessary and sufficient condition for ensuring group consensus is derived, which requires the spanning forest of the underlying directed graph and that of its quotient graph induced with respect to a clustering partition to contain equal minimum number of directed trees. This condition is further shown to be equivalent to containing cluster spanning trees, a commonly used topology for the underlying graph in the literature. Under a designed controller gain, lower bound of the overall coupling strength for achieving group consensus is specified. Moreover, the pattern of the multiple consensus states formed by all clusters is characterized when the overall coupling strength is large enough., Comment: to be published in IEEE Transactions on Automatic Control

Conflict-avoiding codes (CACs) were introduced by Levenshtein as a single-channel transmission scheme for a multiple-access collision channel without feedback. When the number of simultaneously active source nodes is less than or equal to the weight of a CAC, it is able to provide a hard guarantee that each active source node transmits at least one packet successfully within a fixed time duration, no matter what the relative time offsets between the source nodes are. In this paper, we extend CACs to multichannel CACs for providing such a hard guarantee over multiple orthogonal channels. Upper bounds on the number of codewords for multichannel CACs of weights three and four are derived, and constructions that are optimal with respect to these bounds are presented., Comment: 12 pages. Accepted for publication in IEEE Transaction on Information Theory

We consider a single-hop ad hoc network in which each node aims to broadcast packets to its neighboring nodes by using multiple slotted, TDD collision channels. There is no cooperation among the nodes. To ensure successful broadcast, we propose to pre-assign each node a periodic sequence to schedule transmissions and receptions at each time slot. These sequences are referred to as schedule sequences. Since each node starts its transmission schedule independently, there exist relative time offsets among the schedule sequences they use. Our objective is to design schedule sequences such that each node can transmit at least one packet to each of its neighbors successfully within a common period, no matter what the time offsets are. The sequence period should be designed as short as possible. In this paper, we analyze the lower bound on sequence period, and propose a sequence construction method by which the period can achieve the same order as the lower bound. We also consider the random scheme in which each node transmits or receives on a channel at each time slot with a pre-determined probability. The frame length and broadcast completion time under different schemes are compared by numerical studies.

Transparent topology is common in many mobile ad hoc networks (MANETs) such as vehicle ad hoc networks (VANETs), unmanned aerial vehicle (UAV) ad hoc networks, and wireless sensor networks due to their decentralization and mobility nature. There are many existing works on distributed scheduling scheme design for topology-transparent MANETs. Most of them focus on delay-unconstrained settings. However, with the proliferation of real-time applications over wireless communications, it becomes more and more important to support delay-constrained traffic in MANETs. In such applications, each packet has a given hard deadline: if it is not delivered before its deadline, its validity will expire and it will be removed from the system. This feature is fundamentally different from the traditional delay-unconstrained one. In this paper, we for the first time investigate distributed scheduling schemes for a topology-transparent MANET to support delay-constrained traffic. We analyze and compare probabilistic ALOHA scheme and deterministic sequence schemes, including the conventional time division multiple access (TDMA), the Galois field (GF) sequence scheme proposed in \cite{chlamtac1994making}, and the combination sequence scheme that we propose for a special type of sparse network topology.We use both theoretical analysis and empirical simulations to compare all these schemes and summarize the conditions under which different individual schemes perform best.

We consider time synchronization attack against multi-system scheduling in a remote state estimation scenario where a number of sensors monitor different linear dynamical processes and schedule their transmissions through a shared collision channel. We show that by randomly injecting relative time offsets on the sensors, the malicious attacker is able to make the expected estimation error covariance of the overall system diverge without any system knowledge. For the case that the attacker has full system information, we propose an efficient algorithm to calculate the optimal attack, which spoofs the least number of sensors and leads to unbounded average estimation error covariance. To mitigate the attack consequence, we further propose a countermeasure by constructing shift invariant transmission policies and characterize the lower and upper bounds for system estimation performance. Simulation examples are provided to illustrate the obtained results., Comment: 8 pages, 3 figures

In this paper, we mainly investigate an integrated system operating under a software defined network (SDN) protocol. SDN is a new networking paradigm in which network intelligence is centrally administered and data is communicated via channels that are physically separated from those conveying user data. Under the SDN architecture, it is feasible to set up multiple flows for transmitting control signals to an actuator with high priority for each individual application. While each flow may suffer random transmission delay, we focus on the stabilization problem under the joint design of the event-driven strategy in actuator and the control policy in decision-maker. By introducing a predefined application time, the integrated system can be reformulated as the form of stochastic system with input delay and multiplicative noise. For such system, we propose a set of necessary and sufficient stabilization conditions. Specifically, for the scalar system, we derive the allowable sampling period bound that can guarantee stabilization in terms of the probability distributions of the random transmission delays. A simple example is included to show the performance of our theoretic results.

In this paper, we study a wireless networked control system (WNCS) with $N \ge 2$ sub-systems sharing a common wireless channel. Each sub-system consists of a plant and a controller and the control message must be delivered from the controller to the plant through the shared wireless channel. The wireless channel is unreliable due to interference and fading. As a result, a packet can be successfully delivered in a slot with a certain probability. A network scheduling policy determines how to transmit those control messages generated by such $N$ sub-systems and directly influences the transmission delay of control messages. We first consider the case that all sub-systems have the same sampling period. We characterize the stability condition of such a WNCS under the joint design of the control policy and the network scheduling policy by means of $2^N$ linear inequalities. We further simplify the stability condition into only one linear inequality for two special cases: the perfect-channel case where the wireless channel can successfully deliver a control message with certainty in each slot, and the symmetric-structure case where all sub-systems have identical system parameters. We then consider the case that different sub-systems can have different sampling periods, where we characterize a sufficient condition for stability.

In this paper, we propose a learning approach to analyze dynamic systems with asymmetric information structure. Instead of adopting a game theoretic setting, we investigate an online quadratic optimization problem driven by system noises with unknown statistics. Due to information asymmetry, it is infeasible to use classic Kalman filter nor optimal control strategies for such systems. It is necessary and beneficial to develop a robust approach that learns the probability statistics as time goes forward. Motivated by online convex optimization (OCO) theory, we introduce the notion of regret, which is defined as the cumulative performance loss difference between the optimal offline known statistics cost and the optimal online unknown statistics cost. By utilizing dynamic programming and linear minimum mean square biased estimate (LMMSUE), we propose a new type of online state feedback control policies and characterize the behavior of regret in finite time regime. The regret is shown to be sub-linear and bounded by O(ln T). Moreover, we address an online optimization problem with output feedback control policies.

In this paper, we study the delay-constrained input-queued switch where each packet has a deadline and it will expire if it is not delivered before its deadline. Such new scenario is motivated by the proliferation of real-time applications in multimedia communication systems, tactile Internet, networked controlled systems, and cyber-physical systems. The delay-constrained input-queued switch is completely different from the well-understood delay-unconstrained one and thus poses new challenges. We focus on three fundamental problems centering around the performance metric of timely throughput: (i) how to characterize the capacity region? (ii) how to design a feasibility/throughput-optimal scheduling policy? and (iii) how to design a network-utility-maximization scheduling policy? We use three different approaches to solve these three fundamental problems. The first approach is based on Markov Decision Process (MDP) theory, which can solve all three problems. However, it suffers from the curse of dimensionality. The second approach breaks the curse of dimensionality by exploiting the combinatorial features of the problem. It gives a new capacity region characterization with only a polynomial number of linear constraints. The third approach is based on the framework of Lyapunov optimization, where we design a polynomial-time maximum-weight T-disjoint-matching scheduling policy which is proved to be feasibility/throughput-optimal. Our three approaches apply to the frame-synchronized traffic pattern but our MDP-based approach can be extended to more general traffic patterns.

For a connected graph $G$, an instance $I$ is a set of pairs of vertices and a corresponding routing $R$ is a set of paths specified for all vertex-pairs in $I$. Let $\mathfrak{R}_I$ be the collection of all routings with respect to $I$. The undirected optical index of $G$ with respect to $I$ refers to the minimum integer $k$ to guarantee the existence of a mapping $\phi:R\to\{1,2,\ldots,k\}$, such that $\phi(P)\neq\phi(P')$ if $P$ and $P'$ have common edge(s), over all routings $R\in\mathfrak{R}_I$. A natural lower bound of the undirected optical index is the edge-forwarding index, which is defined to be the minimum of the maximum edge-load over all possible routings. Let $w(G,I)$ and $\pi(G,I)$ denote the undirected optical index and edge-forwarding index with respect to $I$, respectively. In this paper, we derive the inequality $w(T,I_A)<\frac{3}{2}\pi(T,I_A)$ for any tree $T$, where $I_A:=\{\{x,y\}:\,x,y\in V(T)\}$ is the all-to-all instance., Comment: 17 pages, 3 figures

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., Comment: 8 pages, 4 figures, a conference paper

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.

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 $\phi:R\to\{1,2,\ldots,k\}$, such that $\phi(P)\neq\phi(P')$ 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., Comment: 12 pages, 3 figures

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., Comment: 21 pages, 1 figure, 4 tables

The collision channel without feedback (CCw/oFB) model introduced by Massey and Mathys, depicts a scenario in which M users share a thermal noise-free communication channel with random relative time offsets among their clocks. This paper considers an extension of this model, which allows the receiver to use successive interference cancellation (SIC) to iteratively cancel the interference caused by those collided packets that have been decoded by the receiver. As the main result of this paper, we derive the zero-error capacity region of this channel in the slot-synchronous case, and present a zero-error capacity achieving scheme by joint protocol sequences and channel coding design. It is shown that the negative impact on the zero-error capacity due to a lack of time synchronization can be removed by the help of SIC. Moreover, we characterize the protocol sequences that can be used to achieve zero-error capacity 1 [packets/slot] by proving new results on shift-invariant sequences and throughput-invariant sequences; these sequences have been known to achieve zero-error capacity for the basic CCw/oFB model without SIC. This characterization sheds light on the minimum sequence period required in order to attain zero-error capacity 1., Comment: We find some mistakes in basic definitions

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., Comment: 24 pages, 8 figures, 1 table. submitted to TWC

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 $\Phi(G,\mathcal{P})$, is the minimum integer $k$ to guarantee the existence of a mapping $\omega:\mathcal{P}\to\{1,2,\ldots,k\}$, such that $\omega(P)\neq\omega(P')$ if $P$ and $P'$ have common edge(s). The global packing number of $G$, denoted by $\Phi(G)$, is defined to be the minimum $\Phi(G,\mathcal{P})$ 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 $\Phi(G,\mathcal{P})=\Phi(G)$ 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., Comment: 23 pages, 3 figures

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., Comment: 20 pages, single column. 7 Figures. To be submitted and under review

This paper considers the cluster synchronization problem of generic linear dynamical systems whose system models are distinct in different clusters. These nonidentical linear models render control design and coupling conditions highly correlated if static couplings are used for all individual systems. In this paper, a dynamic coupling structure, which incorporates a global weighting factor and a vanishing auxiliary control variable, is proposed for each agent and is shown to be a feasible solution. Lower bounds on the global and local weighting factors are derived under the condition that every interaction subgraph associated with each cluster admits a directed spanning tree. The spanning tree requirement is further shown to be a necessary condition when the clusters connect acyclically with each other. Simulations for two applications, cluster heading alignment of nonidentical ships and cluster phase synchronization of nonidentical harmonic oscillators, illustrate essential parts of the derived theoretical results., Comment: accepted version by International Journal of Robust and Nonlinear Control

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., Comment: 13 pages, 4 figures, 3 tables. Published in Designs, Codes and Cryptography

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., Comment: 18 pages, 1 figure. Submitted to Designs, Codes and Cryptography. 1st revision

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 $\gamma$ ($1 \leq \gamma < K$) 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., $\gamma=1$) 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., Comment: 25 pages, 4 figures. A revision submitted to IEEE Trans. Inform. Theory

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.

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., Comment: 31 pages, 5 figures

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., Comment: 34 pages, 1 figure, To appear in the IEEE Trans. Automatic Control

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., Comment: 16 pages, 5 figures. Some typos in Section V are corrected

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., Comment: Conference paper submitted to 2010 IEEE Int. Symp. on Information Theory

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., Comment: 10 pages, 1 figure