16511980
On the Design of Soft-Decision Fusion Rule for Coding Approach in Wireless Sensor Networks
In this work, two soft-decision fusion rules, which are respectively named the maximum a priori (MAP) and the suboptimal minimum Euclidean distance (MED) fusion rules, are designed based on a given employed sensor code and associated local classification. Their performance comparison with the distributed classification fusion using soft-decision decoding (DCSD) proposed in an earlier work is also performed. Simulations show that when the number of faulty sensors is small, the MAP fusion rule remains the best at either low sensor observation signal-to-noise ratios (OSNRs) or low communication channel signal-to-noise ratios (CSNRs), and yet, the DCSD fusion rule gives the best performance at middle to high OSNRs and high CSNRs. However, when the number of faulty sensor nodes grows large, the least complex MED fusion rule outperforms the MAP fusion rule at high OSNRs and high CSNRs.
45162382
Efficient priority-first search maximum-likelihood soft-decision decoding of linear block codes
The authors present a novel and efficient maximum-likelihood soft-decision decoding algorithm for linear block codes. The approach used here converts the decoding problem into a search problem through a graph that is a trellis for an equivalent code of the transmitted code. A generalized Dijkstra's algorithm, which uses a priority-first search strategy, is employed to search through this graph. This search is guided by an evaluation function f defined to take advantage of the information provided by the received vector and the inherent properties of the transmitted code. This function f is used to reduce drastically the search space and to make the decoding efforts of this decoding algorithm adaptable to the noise level. For example, for most real channels of the 35 000 samples tried, simulation results for the (128,64) binary extended BCH code show that the proposed decoding algorithm is fifteen orders of magnitude more efficient in time and in space than that proposed by Wolf (1978). Simulation results for the (104, 52) binary extended quadratic residue code are also given. >
2350989
Privacy-Preserving Multivariate Statistical Analysis: Linear Regression and Classification
Multivariate statistical analysis is an important data analysis technique that has found applications in various areas. In this paper, we study some multivariate statistical analysis methods in Secure 2-party Computation (S2C) framework illustrated by the following scenario: two parties, each having a secret data set, want to conduct the statistical analysis on their joint data, but neither party is willing to disclose its private data to the other party or any third party. The current statistical analysis techniques cannot be used directly to support this kind of computation because they require all parties to send the necessary data to a central place. In this paper, We define two Secure 2-party multivariate statistical analysis problems: Secure 2-party Multivariate Linear Regression problem and Secure 2-party Multivariate Classification problem. We have developed a practical security model, based on which we have developed a number of building blocks for solving these two problems.
17603130
Asymptotic Minimum Covering Radius of Block Codes
In this paper, we restudy the covering radius of block codes from an information theoretic point of view by ignoring the combinatorial formulation of the problem. In the new setting, the formula of the statistically defined minimum covering radius, for which the probability mass of uncovered space by M spheres can be made arbitrarily small, is reduced to a minimization of a statistically defined spectrum formula among codeword-selecting distributions. The advantage of the new view is that no assumptions need to be made on the code alphabet (such as finite, countable, etc.) and the distance measure (such as additive, symmetric, bounded, etc.) in the problem transformation, and hence the spectrum formula can be applied in most general situations. We next address a sufficient condition under which uniform codeword-selecting distribution minimizes the spectrum formula. With the condition, the asymptotic minimum covering radius for block codes under J-ary quantized channels and constant weight codes under Hamming distance measure are determined to display the usage of the spectrum formula.
69690
New Encoding/Decoding Methods for Designing Fault-Tolerant Matrix Operations
Algorithm-based fault tolerance (ABFT) can provide a low-cost error protection for array processors and multiprocessor systems. Several ABFT techniques (weighted check-sum) have been proposed to design fault-tolerant matrix operations. In these schemes, encoding/decoding uses either multiplications or divisions so that overhead is high. In this paper, new encoding/decoding methods are proposed for designing fault-tolerant matrix operations. The unique feature of these new methods is that only additions and subtractions are used in encoding/decoding. In this paper, new algorithms are proposed to construct error detecting/correcting codes with the minimum Hamming distance 3 and 4. We will show that the overhead introduced due to the incorporation of fault tolerance is drastically reduced by using these new coding schemes.
10463694
Balanced-energy sleep scheduling scheme for high density cluster-based sensor networks
In order to conserve battery power in very dense sensor networks, some sensor nodes may be put into the sleep state while other sensor nodes remain active for the sensing and communication tasks. However, determining which of the sensor nodes should be put into the sleep state is non-trivial. As the goal of allowing nodes to sleep is to extend network lifetime, we propose and analyze a Balanced-energy Scheduling (BS) scheme in the context of cluster-based sensor networks. The BS scheme aims to evenly distribute the energy load of the sensing and communication tasks among all the nodes in the cluster, thereby extending the time until the cluster can no longer provide adequate sensing coverage. Two related sleep scheduling schemes, the Distance-based Scheduling (DS) scheme and the Randomized Scheduling (RS) scheme are also studied in terms of the coefficient of variation of their energy consumption. Analytical and simulation results are presented to evaluate the proposed BS scheme. It is shown that the BS scheme extends the cluster's overall network lifetime significantly while maintaining a similar sensing coverage compared with the DS and the RS schemes for sensor clusters.
8761097
Prime Decompositions of Regular Languages
We investigate factorizations of regular languages in terms of prime languages. A language is said to be strongly prime decomposable if any way of factorizing the language yields a prime decomposition in a finite number of steps. We give a characterization of the strongly prime decomposable regular languages and using the characterization we show that every regular language over a unary alphabet has a prime decomposition. We show that there exist co-context-free languages that do not have prime decompositions.
10385992
A New Linearizing Restriction in the Pattern Matching Problem
In the pattern matching problem, there can be a quadratic number of matching substrings in the size of a given text. The linearizing restriction finds, at most, a linear number of matching substrings. We first explore two well-known linearizing restriction rules, the longest-match rule and the shortest-match substring searchrule, and show that both rules give the same result when a pattern is an infix-free set even though they have different semantics. Then, we introduce a new linearizing restriction, the leftmost non-overlapping match rule that is suitable for find-and-replace operations in text searching, and propose an efficient algorithm when the pattern is a regular language according to the new match rule.
14544092
Intercode Regular Languages
Intercodes are a generalization of comma-free codes. Using the structural properties of finite-state automata recognizing an intercode we develop a polynomial-time algorithm for determining whether or not a given regular language L is an intercode. If the answer is yes, our algorithm yields also the smallest index k such that L is a k-intercode. 
 
Furthermore, we examine the prime intercode decomposition of intercode regular languages and design an algorithm for the intercode primality test of an intercode recognized by a finite-state automaton. We also propose an algorithm that computes the prime intercode decomposition of an intercode regular language in polynomial time. Finally, we demonstrate that the prime intercode decomposition need not be unique.
18478207
Prefix-Free Regular-Expression Matching
We explore the regular-expression matching problem with respect to prefix-freeness of the pattern. We show that the prefix-free regular expression gives only linear number of matching substrings in the size of a given text. Based on this observation, we propose an efficient algorithm for the prefix-free regular-expression matching problem. Furthermore, we suggest an algorithm to determine whether or not a given regular language is prefix-free.
1251651
Obtaining shorter regular expressions from finite-state automata
We consider the use of state elimination to construct shorter regular expressions from finite-state automata (FAs). Although state elimination is an intuitive method for computing regular expressions from FAs, the resulting regular expressions are often very long and complicated. We examine the minimization of FAs to obtain shorter expressions first. Then, we introduce vertical chopping based on bridge states and horizontal chopping based on the structural properties of given FAs. We prove that we should not eliminate bridge states until we eliminate all non-bridge states to obtain shorter regular expressions. In addition, we suggest heuristics for state elimination that leads to shorter regular expressions based on vertical chopping and horizontal chopping.