We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Information Theory and Reliable Communication

This document provides updates to IEEE Std 802.16's MIB for the MAC, PHY and asso- ciated management procedures in order to accommodate recent extensions to the standard.

IEEE Standard for Local and Metropolitan Area Networks Part 16: Air Interface for Fixed Broadband Wireless Access Systems Draft Amendment: Management Information Base Extensions

tions. Bootstrap has found many applications in engineering field, including artificial neural networks, biomedical engineering, environmental engineering, image processing, and radar and sonar signal processing. Basic concepts of the bootstrap are summarized in each section as a step-by-step algorithm for ease of implementation. Most of the applications are taken from the signal processing literature. The principles of the bootstrap are introduced in Chapter 2. Both the nonparametric and parametric bootstrap procedures are explained. Babu and Singh (1984) have demonstrated that in general, these two procedures behave similarly for pivotal (Studentized) statistics. The fact that the bootstrap is not the solution for all of the problems has been known to statistics community for a long time; however, this fact is rarely touched on in the manuscripts meant for practitioners. It was first observed by Babu (1984) that the bootstrap does not work in the infinite variance case. Bootstrap Techniques for Signal Processing explains the limitations of bootstrap method with an example. I especially liked the presentation style. The basic results are stated without proofs; however, the application of each result is presented as a simple step-by-step process, easy for nonstatisticians to follow. The bootstrap procedures, such as moving block bootstrap for dependent data, along with applications to autoregressive models and for estimation of power spectral density, are also presented in Chapter 2. Signal detection in the presence of noise is generally formulated as a testing of hypothesis problem. Chapter 3 introduces principles of bootstrap hypothesis testing. The topics are introduced with interesting real life examples. Flow charts, typical in engineering literature, are used to aid explanations of the bootstrap hypothesis testing procedures. The bootstrap leads to second-order correction due to pivoting; this improvement in the results due to pivoting is also explained. In the second part of Chapter 3, signal processing is treated as a regression problem. The performance of the bootstrap for matched filters as well as constant false-alarm rate matched filters is also illustrated. Chapters 2 and 3 focus on estimation problems. Chapter 4 introduces bootstrap methods used in model selection. Due to the inherent structure of the subject matter, this chapter may be difficult for nonstatisticians to follow. Chapter 5 is the most impressive chapter in the book, especially from the standpoint of statisticians. It provides real data bootstrap applications to illustrate the theory covered in the earlier chapters. These include applications to optimal sensor placement for knock detection and land-mine detection. The authors also provide a MATLAB toolbox comprising frequently used routines. Overall, this is a very useful handbook for engineers, especially those working in signal processing.

Probability and Random Processes

Renyi divergence is related to Renyi entropy much like Kullback-Leibler divergence is related to Shannon's entropy, and comes up in many settings. It was introduced by Renyi as a measure of information that satisfies almost the same axioms as Kullback-Leibler divergence, and depends on a parameter that is called its order. In particular, the Renyi divergence of order 1 equals the Kullback-Leibler divergence. We review and extend the most important properties of Renyi divergence and Kullback-Leibler divergence, including convexity, continuity, limits of \(\sigma \) -algebras, and the relation of the special order 0 to the Gaussian dichotomy and contiguity. We also show how to generalize the Pythagorean inequality to orders different from 1, and we extend the known equivalence between channel capacity and minimax redundancy to continuous channel inputs (for all orders) and present several other minimax results.

Rényi Divergence and Kullback-Leibler Divergence

This paper considers the problem of guessing the realization of a finite alphabet source when some side information is provided. The only knowledge the guesser has about the source and the correlated side information is that the joint source is one among a family. A notion of redundancy is first defined and a new divergence quantity that measures this redundancy is identified. This divergence quantity shares the Pythagorean property with the Kullback-Leibler divergence. Good guessing strategies that minimize the supremum redundancy (over the family) are then identified. The min-sup value measures the richness of the uncertainty set. The min-sup redundancies for two examples - the families of discrete memoryless sources and finite-state arbitrarily varying sources - are then determined

Guessing Under Source Uncertainty

The problem of guessing a random string is revisited. A close relation between guessing and compression is first established. Then it is shown that if the sequence of distributions of the information spectrum satisfies the large deviation property with a certain rate function, then the limiting guessing exponent exists and is a scalar multiple of the Legendre-Fenchel dual of the rate function. Other sufficient conditions related to certain continuity properties of the information spectrum are briefly discussed. This approach highlights the importance of the information spectrum in determining the limiting guessing exponent. All known prior results are then re-derived as example applications of our unifying approach.

Guessing Revisited: A Large Deviations Approach

We study in this paper the question of determining locations of base stations (BSs) that may belong to the same or to competing service providers, taking into account the impact of these decisions on the behavior of intelligent mobile terminals who can connect to the base station that offers the best utility. We first study the SINR association-game: we determine the cells corresponding to each base stations, i.e. the locations at which mobile terminals prefer to connect to a given base station than to other. The signal to interference and noise ratio (SINR) is used as the quantity that determines the association. We make some surprising observations: (i) displacing a base station a little in one direction may result in a displacement of the boundary of the corresponding cell to the opposite direction; (ii) A cell corresponding to a BS may be the union of disconnected sub-cells. We then study the Stackelberg equilibrium in the combined BS location and mobile association problem: we determine where to locate the BSs so as to maximize the revenues obtained at the induced SINR mobile association game. We consider the cases of single frequency band and two frequency bands of operation. Finally, we also consider Stackelberg equilibria in two frequency systems with successive interference cancellation.

/pdf/spatial-sinr-games-combining-base-station-placement-and-1a96h2okp4.pdf

Spatial SINR Games Combining Base Station Placement and Mobile Association

To transmit information by timing arrivals to a single-server queue, we consider using the exponential server channel's maximum likelihood decoder. For any server with service times that are stationary and ergodic with mean 1//spl mu/ seconds, we show that the rate e/sup -1//spl mu/ nats per second (capacity of the exponential server timing channel) is achievable using this decoder. We show that a similar result holds for the timing channel with feedback. We also show that if the server jams communication by adding an arbitrary amount of time to the nominal service time, then the rate e/sup -1//spl mu//sub 1//spl mu//sub 2//(/spl mu//sub 1/+/spl mu//sub 2/) nats per second is achievable with random codes, where the nominal service times are stationary and ergodic with mean 1//spl mu//sub 1/ seconds, and the arithmetic mean of the delays added by the server does not exceed 1//spl mu//sub 2/ seconds. This is a model of an arbitrarily varying channel where the current delay and the current input can affect future outputs. We also show the counterpart of these results for single-server discrete-time queues.

Rajesh Sundaresan

Papers

Guessing Under Source Uncertainty

Guessing Revisited: A Large Deviations Approach

Guessing Revisited: A Large Deviations Approach

Spatial SINR Games Combining Base Station Placement and Mobile Association

Robust decoding for timing channels