An Experimental Study of Robustness to Asynchronism for Elementary Cellular Automata

Cellular Automata (CA) are a class of discrete dynamical systems that have been widely used to model complex systems in which the dynamics is specified at local cell-scale. Classically, CA are run on a regular lattice and with perfect synchronicity. However, these two assumptions have little chance to truthfully represent what happens at the microscopic scale for physical, biological or social systems. One may thus wonder whether CA do keep their behavior when submitted to small perturbations of synchronicity. This work focuses on the study of one-dimensional (1D) asynchronous CA with two states and nearest-neighbors. We define what we mean by ``the behavior of CA is robust to asynchronism'' using a statistical approach with macroscopic parameters. and we present an experimental protocol aimed at finding which are the robust 1D elementary CA. To conclude, we examine how the results exposed can be used as a guideline for the research of suitable models according to robustness criteria.Comment: Version : Feb 13th, 2004, submitted to Complex System

Asynchronous Communication: Exact Synchronization, Universality, and Dispersion

Recently, Tchamkerten and coworkers proposed a novel variation of the problem of joint synchronization and error correction. This paper considers a strengthened formulation that requires the decoder to estimate both the message and the location of the codeword exactly. Such a scheme allows for transmitting data bits in the synchronization phase of the communication, thereby improving bandwidth and energy efficiencies. It is shown that the capacity region remains unchanged under the exact synchronization requirement. Furthermore, asynchronous capacity can be achieved by universal (channel independent) codes. Comparisons with earlier results on another (delay compensated) definition of rate are made. The finite blocklength regime is investigated and it is demonstrated that even for moderate blocklengths, it is possible to construct capacity-achieving codes that tolerate exponential level of asynchronism and experience only a rather small loss in rate compared to the perfectly synchronized setting; in particular, the channel dispersion does not suffer any degradation due to asynchronism. For the binary symmetric channel, a translation (coset) of a good linear code is shown to achieve the capacity-synchronization tradeoff.National Science Foundation (U.S.) (Center for Science of Information Grant CCF-0939370

Asynchronous Communication: Capacity Bounds and Suboptimality of Training

Several aspects of the problem of asynchronous point-to-point communication without feedback are developed when the source is highly intermittent. In the system model of interest, the codeword is transmitted at a random time within a prescribed window whose length corresponds to the level of asynchronism between the transmitter and the receiver. The decoder operates sequentially and communication rate is defined as the ratio between the message size and the elapsed time between when transmission commences and when the decoder makes a decision. For such systems, general upper and lower bounds on capacity as a function of the level of asynchronism are established, and are shown to coincide in some nontrivial cases. From these bounds, several properties of this asynchronous capacity are derived. In addition, the performance of training-based schemes is investigated. It is shown that such schemes, which implement synchronization and information transmission on separate degrees of freedom in the encoding, cannot achieve the asynchronous capacity in general, and that the penalty is particularly significant in the high-rate regime.Comment: 27 pages, 8 figures, submitted to the IEEE Transactions on Information Theor

On Bounded Weight Codes

The maximum size of a binary code is studied as a function of its length N, minimum distance D, and minimum codeword weight W. This function B(N,D,W) is first characterized in terms of its exponential growth rate in the limit as N tends to infinity for fixed d=D/N and w=W/N. The exponential growth rate of B(N,D,W) is shown to be equal to the exponential growth rate of A(N,D) for w <= 1/2, and equal to the exponential growth rate of A(N,D,W) for 1/2< w <= 1. Second, analytic and numerical upper bounds on B(N,D,W) are derived using the semidefinite programming (SDP) method. These bounds yield a non-asymptotic improvement of the second Johnson bound and are tight for certain values of the parameters

Silent MST approximation for tiny memory

In network distributed computing, minimum spanning tree (MST) is one of the key problems, and silent self-stabilization one of the most demanding fault-tolerance properties. For this problem and this model, a polynomial-time algorithm with $O(\log^2\!n)$ memory is known for the state model. This is memory optimal for weights in the classic $[1,\text{poly}(n)]$ range (where $n$ is the size of the network). In this paper, we go below this $O(\log^2\!n)$ memory, using approximation and parametrized complexity. More specifically, our contributions are two-fold. We introduce a second parameter~$s$, which is the space needed to encode a weight, and we design a silent polynomial-time self-stabilizing algorithm, with space $O(\log n \cdot s)$. In turn, this allows us to get an approximation algorithm for the problem, with a trade-off between the approximation ratio of the solution and the space used. For polynomial weights, this trade-off goes smoothly from memory $O(\log n)$ for an $n$-approximation, to memory $O(\log^2\!n)$ for exact solutions, with for example memory $O(\log n\log\log n)$ for a 2-approximation

Façonnement de l'Interférence en vue d'une Optimisation Globale d'un Système Moderne de Communication

A communication is impulsive whenever the information-bearing signal is burst-like in time. Examples of the impulsive concept are: impulse-radio signals, that is, wireless signals occurring within short intervals of time; optical signals conveyed by photons; speech signals represented by sound pressure variations; pulse-position modulated electrical signals; a sequence of arrival/departure events in a queue; neural spike trains in the brain. Understanding impulsive communications requires to identify what is peculiar to this transmission paradigm, that is, different from traditional continuous communications.In order to address the problem of understanding impulsive vs. non-impulsive communications, the framework of investigation must include the following aspects: the different interference statistics directly following from the impulsive signal structure; the different interaction of the impulsive signal with the physical medium; the actual possibility for impulsive communications of coding information into the time structure, relaxing the implicit assumption made in continuous transmissions that time is a mere support. This thesis partially addresses a few of the above issues, and draws future lines of investigation. In particular, we studied: multiple access channels where each user adopts time-hopping spread-spectrum; systems using a specific prefilter at the transmitter side, namely the transmit matched filter (also known as time reversal), particularly suited for ultrawide bandwidhts; the distribution function of interference for impulsive systems in several different settings.Une communication est impulsive chaque fois que le signal portant des informations est intermittent dans le temps et que la transmission se produit à rafales. Des exemples du concept impulsife sont : les signaux radio impulsifs, c’est-à-dire des signaux très courts dans le temps; les signaux optiques utilisé dans les systèmes de télécommunications; certains signaux acoustiques et, en particulier, les impulsions produites par le système glottale; les signaux électriques modulés en position d’impulsions; une séquence d’événements dans une file d’attente; les trains de potentiels neuronaux dans le système neuronal. Ce paradigme de transmission est différent des communications continues traditionnelles et la compréhension des communications impulsives est donc essentielle. Afin d’affronter le problème des communications impulsives, le cadre de la recherche doit inclure les aspects suivants : la statistique d’interférence qui suit directement la structure des signaux impulsifs; l’interaction du signal impulsif avec le milieu physique; la possibilité pour les communications impulsives de coder l’information dans la structure temporelle. Cette thèse adresse une partie des questions précédentes et trace des lignes indicatives pour de futures recherches. En particulier, nous avons étudié: un système d'accès multiple où les utilisateurs adoptent des signaux avec étalement de spectre par saut temporel (time-hopping spread spectrum) pour communiquer vers un récepteur commun; un système avec un préfiltre à l'émetteur, et plus précisément un transmit matched filter, également connu comme time reversal dans la littérature de systèmes à bande ultra large; un modèle d'interférence pour des signaux impulsifs

ROBUST KULLBACK-LEIBLER DIVERGENCE AND ITS APPLICATIONS IN UNIVERSAL HYPOTHESIS TESTING AND DEVIATION DETECTION

The Kullback-Leibler (KL) divergence is one of the most fundamental metrics in information theory and statistics and provides various operational interpretations in the context of mathematical communication theory and statistical hypothesis testing. The KL divergence for discrete distributions has the desired continuity property which leads to some fundamental results in universal hypothesis testing. With continuous observations, however, the KL divergence is only lower semi-continuous; difficulties arise when tackling universal hypothesis testing with continuous observations due to the lack of continuity in KL divergence. This dissertation proposes a robust version of the KL divergence for continuous alphabets. Specifically, the KL divergence defined from a distribution to the Levy ball centered at the other distribution is found to be continuous. This robust version of the KL divergence allows one to generalize the result in universal hypothesis testing for discrete alphabets to that for continuous observations. The optimal decision rule is developed whose robust property is provably established for universal hypothesis testing. Another application of the robust KL divergence is in deviation detection: the problem of detecting deviation from a nominal distribution using a sequence of independent and identically distributed observations. An asymptotically -optimal detector is then developed for deviation detection where the Levy metric becomes a very natural distance measure for deviation from the nominal distribution. Lastly, the dissertation considers the following variation of a distributed detection problem: a sensor may overhear other sensors\u27 transmissions and thus may choose to refine its output in the hope of achieving a better detection performance. While this is shown to be possible for the fixed sample size test, asymptotically (in the number of samples) there is no performance gain, as measured by the KL divergence achievable at the fusion center, provided that the observations are conditionally independent. For conditionally dependent observations, however, asymptotic detection performance may indeed be improved when overhearing is utilized