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.
8730288
On the existence of prime decompositions
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 it 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 non-regular unary languages that do not have prime decompositions. We also consider infinite factorizations of unary languages.
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.
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.
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.
661428
Scheduling Sleeping Nodes in 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. In this paper, we study the node sleep scheduling problem in the context of clustered sensor networks. We propose and analyze the Linear Distance-based Scheduling (LDS) technique for sleeping in each cluster. The LDS scheme selects a sensor node to sleep with higher probability when it is farther away from the cluster head. We analyze the energy consumption, the sensing coverage property, and the network lifetime of the proposed LDS scheme. The performance of the LDS scheme is compared with that of the conventional Randomized Scheduling (RS) scheme. It is shown that the LDS scheme yields more energy savings while maintaining a similar sensing coverage as the RS scheme for sensor clusters. Therefore, the LDS scheme results in a longer network lifetime than the RS scheme.
10524443
Distance-spectrum formulas on the largest minimum distance of block codes
A general formula for the asymptotic largest minimum distance (in block length) of deterministic block codes under generalized distance functions (not necessarily additive, symmetric, and bounded) is presented. As revealed in the formula, the largest minimum distance can be fully determined by the ultimate statistical characteristics of the normalized distance function evaluated under a properly chosen random-code generating distribution. Interestingly, the new formula has an analogous form to the general information-spectrum expressions of the channel capacity and the optimistic channel capacity, respectively derived by Verdu and Han (1994) and Chen and Alajaji (1998, 1999). As a result, a minor class of distance functions for which the largest minimum distance can be derived is characterized. A general Varshamov-Gilbert lower bound is next addressed. Some discussions on the tightness of the general Varshamov-Gilbert bound are also provided. Finally, lower bounds on the largest minimum distances for several specific block coding schemes are rederived in terms of the new formulas, followed by comparisons with the known results devoted to the same codes.
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. >
46047704
A New Decoding Algorithm for Complete Decoding of Linear Block Codes
In this paper we present and describe an improved version of the Zero-Neighbors algorithm, which we call the Zero-Coverings algorithm. We also present a method for finding a smallest subset of codewords ( Zero-Coverings) which need to be stored to perform the Zero-Coverings algorithm. For some short codes, the sizes of Zero-Coverings are obtained by computer searches; for long codes, an asymptotic bound on the sizes of such subsets is also given.
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.