46127177
Extended synchronizing codewords for binary prefix codes
Synchronizing codewords (SCs) have been previously studied as a means to stop error propagation in variable-length codes. However, SCs retain one disadvantage: the symbols after the SC may be put in the wrong positions since the number of decoded symbols before the SC can be different from the original number due to channel errors. Thus we propose the idea of extended synchronizing codewords (ESCs) which can overcome the drawback of SCs. After the decoder receives an ESC, the decoder correctly knows it is in synchronization, regardless of the preceding slippage. We derive some of the essential properties of ESCs and provide several upper bounds on the amount of overhead needed in designing a code with an ESC.
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.
6063474
PAC learning with generalized samples and an application to stochastic geometry
In this paper, we introduce an extension of the standard PAC learning model which allows the use of generalized samples. We view a generalized sample as a pair consisting of a functional on the concept class together with the value obtained by the functional operating on the unknown concept. It appears that this model can be applied to a number of problems in signal processing and geometric reconstruction to provide sample size bounds under a PAC criterion. We consider a specific application of the model to a problem of curve reconstruction, and discuss some connections with a result from stochastic geometry.
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.
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. >
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. >
15091862
A physical design tool for built-in self-repairable static RAMs
A novel physical design tool, BISRAMGEN, that generates layout geometries of parametrized built-in self-repairable SRAM modules, producing significant improvement in testability, reliability, production yield and manufacturing cost of ASICs and microprocessors with embedded RAMs, is presented.
14446337
Multitolerant Barrier Synchronization
Abstract We designed a multitolerant program for synchronizing the phases of concurrent processes. The tolerances of the program enable processes to: (i) execute all phases correctly in the presence of faults that corrupt the process state in a detectable manner, and (ii) execute only a minimum possible number of phases incorrectly before resuming correct computation in the presence of faults that corrupt the process state in an undetectable manner.
10924262
Automated synthesis of multitolerance
We concentrate on automated synthesis of multitolerant programs, i.e., programs that tolerate multiple classes of faults and provide a (possibly) different level of fault-tolerance to each class. We consider three levels of fault-tolerance: (1) failsafe, where in the presence of faults, the synthesized program guarantees safety, (2) nonmasking, where in the presence of faults, the synthesized program recovers to states from where its safety and liveness are satisfied, and (3) masking where in the presence of faults the synthesized program satisfies safety and recovers to states from where its safety and liveness are satisfied. We focus on the automated synthesis of finite-state multitolerant programs in high atomicity model where the program can read and write all its variables in an atomic step. We show that if one needs to add failsafe (respectively, nonmasking) fault-tolerance to one class of faults and masking fault-tolerance to another class of faults then such addition can be done in polynomial time in the state space of the fault-intolerant program. However, if one needs to add failsafe fault-tolerance to one class of faults and nonmasking fault-tolerance to another class of faults then the resulting problem is NP-complete. We find this result to be counterintuitive since adding failsafe and nonmasking fault-tolerance to the same class of faults (which is equivalent to adding masking fault-tolerance to that class of faults) can be done in polynomial time, whereas adding failsafe fault-tolerance to one class of faults and nonmasking fault-tolerance to a different class of faults is NP-complete.
6871855
The complexity of adding failsafe fault-tolerance
In this paper, we focus our attention on the problem of automating the addition of failsafe fault-tolerance where fault-tolerance is added to an existing (fault-intolerant) program. A failsafe fault-tolerant program satisfies its specification (including safety and liveness) in the absence of faults. And, in the presence of faults, it satisfies its safety specification. We present a somewhat unexpected result that, in general, the problem of adding failsafe fault-tolerance in distributed programs is NP-hard. Towards this end, we reduce the 3-SAT problem to the problem of adding failsafe fault-tolerance. We also identify a class of specifications, monotonic specifications and a class of programs, monotonic programs. Given a (positive) monotonic specification and a (negative) monotonic program, we show that failsafe fault-tolerance can be added in polynomial time. We note that the monotonicity restrictions are met for commonly encountered problems such as Byzantine agreement, distributed consensus, and atomic commitment. Finally, we argue that the restrictions on the specifications and programs are necessary to add failsafe fault-tolerance in polynomial time; we prove that if only one of these conditions is satisfied, the addition of failsafe fault-tolerance is still NP-hard.
1530693
Component Based Design of Multitolerant Systems
The concept of multitolerance abstracts problems in system dependability and provides a basis for improved design of dependable systems. In the abstraction, each source of undependability in the system is represented as a class of faults, and the corresponding ability of the system to deal with that undependability source is represented as a type of tolerance. Multitolerance thus refers to the ability of the system to tolerate multiple fault classes, each in a possibly different way. We present a component based method for designing multitolerance. Two types of components are employed by the method, namely detectors and correctors. A theory of detectors, correctors, and their interference free composition with intolerant programs is developed, which enables stepwise addition of components to provide tolerance to a new fault class while preserving the tolerances to the previously added fault classes. We illustrate the method by designing a fully distributed multitolerant program for a token ring.