2831656
Universal coding of nonstationary sources
We investigate the performance of the Lempel-Ziv (1978) incremental parsing scheme on nonstationary sources. We show that it achieves the best rate achievable by a finite-state block coder for the nonstationary source. We also show a similar result for a lossy coding scheme given by Yang and Kieffer (see ibid., vol.42, p.239-45, 1996) which uses a Lempel-Ziv scheme to perform lossy coding.
7846439
Universal lossless source coding with the Burrows Wheeler Transform
The Burrows Wheeler transform (1994) is a reversible sequence transformation used in a variety of practical lossless source-coding algorithms. In each, the BWT is followed by a lossless source code that attempts to exploit the natural ordering of the BWT coefficients. BWT-based compression schemes are widely touted as low-complexity algorithms giving lossless coding rates better than those of the Ziv-Lempel codes (commonly known as LZ'77 and LZ'78) and almost as good as those achieved by prediction by partial matching (PPM) algorithms. To date, the coding performance claims have been made primarily on the basis of experimental results. This work gives a theoretical evaluation of BWT-based coding. The main results of this theoretical evaluation include: (1) statistical characterizations of the BWT output on both finite strings and sequences of length n /spl rarr/ /spl infin/, (2) a variety of very simple new techniques for BWT-based lossless source coding, and (3) proofs of the universality and bounds on the rates of convergence of both new and existing BWT-based codes for finite-memory and stationary ergodic sources. The end result is a theoretical justification and validation of the experimentally derived conclusions: BWT-based lossless source codes achieve universal lossless coding performance that converges to the optimal coding performance more quickly than the rate of convergence observed in Ziv-Lempel style codes and, for some BWT-based codes, within a constant factor of the optimal rate of convergence for finite-memory sources.
2125855
A deterministic approach to throughput scaling in wireless networks
We address the problem of how throughput in a wireless network scales as the number of users grows. Following the model of Gupta and Kumar, we consider n identical nodes placed in a fixed area. Pairs of transmitters and receivers wish to communicate but are subject to interference from other nodes. Throughput is measured in bit-meters per second. We provide a very elementary deterministic approach that gives achievability results in terms of three key properties of the node locations. As a special case, we obtain /spl Omega/(/spl radic/n) throughput for a general class of network configurations in a fixed area. Results for random node locations in a fixed area can also be derived as special cases of the general result by verifying the growth rate of three parameters. For example, as a simple corollary of our result we obtain a stronger (almost sure) version of the /spl radic/n//spl radic/(logn) throughput for random node locations in a fixed area obtained by Gupta and Kumar. Results for some other interesting non-independent and identically distributed (i.i.d.) node distributions are also provided.
7606261
Rates of convergence of nearest neighbor estimation under arbitrary sampling
Rates of convergence for nearest neighbor estimation are established in a general framework in terms of metric covering numbers of the underlying space. The first result is to find explicit finite sample upper bounds for the classical independent and identically distributed (i.i.d.) random sampling problem in a separable metric space setting. The convergence rate is a function of the covering numbers of the support of the distribution. For example, for bounded subsets of R/sup r/, the convergence rate is O(1/n/sup 2/r/). The main result is to extend the problem to allow samples drawn from a completely arbitrary random process in a separable metric space and to examine the performance in terms of the individual sample sequences. The authors show that for every sequence of samples the asymptotic time-average of nearest neighbor risks equals twice the time-average of the conditional Bayes risks of the sequence. Finite sample upper bounds under arbitrary sampling are again obtained in terms of the covering numbers of the underlying space. In particular, for bounded subsets of R/sup r/ the convergence rate of the time-averaged risk is O(1/n/sup 2/r/). The authors then establish a consistency result for k/sub n/-nearest neighbor estimation under arbitrary sampling and prove a convergence rate matching established rates for i.i.d. sampling. Finally, they show how their arbitrary sampling results lead to some classical i.i.d. sampling results and in fact extend them to stationary sampling. The framework and results are quite general while the proof techniques are surprisingly elementary. >
1752947
Learning decision rules for pattern classification under a family of probability measures
In this paper, uniformly consistent estimation (learnability) of decision rules for pattern classification under a family of probability measures is investigated. In particular, it is shown that uniform boundedness of the metric entropy of the class of decision rules is both necessary and sufficient for learnability under each of two conditions: (i) the family of probability measures is totally bounded, with respect to the total variation metric, and (ii) the family of probability measures contains an interior point, when equipped with the same metric. In particular, this shows that insofar as uniform consistency is concerned, when the family of distributions contains a total variation neighborhood, nothing is gained by this knowledge about the distribution. Then two sufficient conditions for learnability are presented. Specifically, it is shown that learnability with respect to each of a finite collection of families of probability measures implies learnability with respect to their union; also, learnability with respect to each of a finite number of measures implies learnability with respect to the convex hull of the corresponding families of uniformly absolutely continuous probability measures.
9782780
A paradigm for class identification problems
The following problem arises in many applications involving classification, identification, and inference. There is a set of objects X, and a particular x /spl isin/ X is chosen (unknown to us). Based on information obtained about x in a sequential manner, one wishes to decide whether x belongs to one class of objects A/sub 0/ or a different class of objects A/sub 1/. The authors study a general paradigm applicable to a broad range of problems of this type, which they refer to as problems of class identification or discernibility. They consider various types of information sequences, and various success criteria including discernibility in the limit, discernibility with a stopping criterion, uniform discernibility, and discernibility in the Cesaro sense. They consider decision rules both with and without memory. Necessary and sufficient conditions for discernibility are provided for each case in terms of separability conditions on the sets A/sub 0/ and A/sub 1/. They then show that for any sets A/sub 0/ and A/sub 1/, various types of separability can be achieved by allowing failure on appropriate sets of small measure. Applications to problems in language identification, system identification, and discrete geometry are discussed. >
11497337
Secret instantiation in ad-hoc networks
Abstract In this paper, we focus our attention on the problem of assigning initial secrets to users in ad-hoc network (respectively, sensors in a sensor network) so that they can use those secrets to ensure authentication and privacy during their communication. The goal of this assignment is to ensure that any two users can communicate securely with each other even though each user maintains only a small number of secrets. With this motivation, we present a protocol that maintains O ( n ) secrets per user where n is the number of users in the system. We show that our secret distribution protocol suffices for privacy and authentication as well as secure multihop communication between two users. Furthermore, we show that the number of secrets maintained in this protocol is within a constant factor of the optimal. For the case where user capability prevents them from maintaining the necessary secrets, we propose two probabilistic protocols that maintain O(log n) secrets and where the probability of security compromise between two users is inversely proportional to the number of secrets they maintain. Thus, our protocols provide a continuum where the level of privacy and authentication depends upon user requirements and capabilities.
42521024
Designing Masking Fault-Tolerance via Nonmasking Fault-Tolerance
Masking fault-tolerance guarantees that programs continually satisfy their specification in the presence of faults. By way of contrast, nonmasking fault-tolerance does not guarantee as much: it merely guarantees that when faults stop occurring, program executions converge to states from where programs continually (re)satisfy their specification. We present in this paper a component based method for the design of masking fault-tolerant programs. In this method, components are added to a fault-intolerant program in a stepwise manner, first, to transform the fault-intolerant program into a nonmasking fault-tolerant one and, then, to enhance the fault-tolerance from nonmasking to masking. We illustrate the method by designing programs for agreement in the presence of Byzantine faults, data transfer in the presence of message loss, triple modular redundancy in the presence of input corruption, and mutual exclusion in the presence of process fail-stops. These examples also serve to demonstrate that the method accommodates a variety of fault-classes. It provides alternative designs for programs usually designed with extant design methods, and it offers the potential for improved masking fault-tolerant programs.
12683811
Proactive Reliable Bulk Data Dissemination in Sensor Networks
One of the problems in network reprogramming is to guarantee 100 percent delivery of a large amount of data (the entire binary image) in a lossy wireless channel. All the existing protocols on network reprogramming [1–6] use automatic repeat request (ARQ) scheme to recover from packet losses. We propose a new reliability scheme which is a hybrid approach of forward error correction (FEC) and ARQ. We perform a case study on MNP, a multihop network reprogramming protocol, and study the effect of adding two different FEC codes: simple XOR code and Reed-Solomon (RS) codes [7], to MNP. We evaluate the new reliability approach using TOSSIM. The simulation results show that adding simple XOR code to MNP can achieve up to 10% improvement on reprogramming speed and up to 18% reduction on active radio time (the major part of energy consumption). And we show that RS codes perform even better.
2311914
Exploiting Symbolic Techniques in Automated Synthesis of Distributed Programs with Large State Space
Automated formal analysis methods such as program verification and synthesis algorithms often suffer from time complexity of their decision procedures and also high space complexity known as the state explosion problem. Symbolic techniques, in which elements of a problem are represented by Boolean formulae, are desirable in the sense that they often remedy the state explosion problem and time complexity of decision procedures. Although symbolic techniques have successfully been used in program verification, their benefits have not yet been exploited in the context of program synthesis and transformation extensively. In this paper, we present a symbolic method for automatic synthesis of fault-tolerant distributed programs. Our experimental results on synthesis of classical fault-tolerant distributed problems such as Byzantine agreement and token ring show a significant performance improvement by several orders of magnitude in both time and space complexity. To the best of our knowledge, this is the first illustration where programs with large state space (beyond 2100) is handled during synthesis.
14320923
Scalable Clustering for Large High-Dimensional Data Based on Data Summarization
Clustering large data sets with high dimensionality is a challenging data-mining task. This paper presents a framework to perform such a task efficiently. It is based on the notion of data space reduction, which finds high density areas, or dense cells, in the given feature space. The dense cells store summarized information of the data. A designated partitioning or hierarchical clustering algorithm can be used as the second step to find clusters based on the data summaries. Using Kmeans as an example, this paper presents GARDEN-Kmeans, which performs data space reduction using Gamma Region DENsity partition, and utilizes Kmeans to cluster the summarized information. The experimental study shows that GARDEN-Kmeans executes several orders of magnitude faster than basic Kmeans and the recursive bisection Kmeans algorithm of CLUTO, while producing comparable clustering quality