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. >
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.
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.
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.
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.
27623648
Twinned principal curves
Principal Curves are extensions of Principal Component Analysis and are smooth curves, which pass through the middle of a data set. We extend the method so that, on pairs of data sets which have underlying non-linear correlations, we have pairs of curves which go through the 'centre' of data sets in such a way that the non-linear correlations between the data sets are captured. The core of the method is to iteratively average the current local projections of the data points which produces an increasingly sparsified set of nodes. The Twinned Principal Curves are generated in three ways: by joining up the nodes in order, by performing Local Canonical Correlation Analysis and by performing Local Exploratory Correlation Analysis (Koetsier et al., 2002). The latter two are shown to improve the forecasting capability of the method but at an increased computational load. We show that it is crucial to terminate the algorithm after a small number of iterations for the first method and investigate several criteria for doing so.
33469096
The generalization of generalized automata: expression automata
We explore expression automata with respect to determinism and minimization. We define determinism of expression automata using prefix-freeness. This approach is, to some extent, similar to that of Giammarresi and Montalbano's definition of deterministic generalized automata. We prove that deterministic expression automata languages are a proper subfamily of the regular languages. We close by defining the minimization of deterministic expression automata.
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.
14156578
Shorter Regular Expressions from Finite-State Automata
We consider the use of state elimination to construct shorter regular expressions from finite-state automata. Although state elimination is an intuitive method for computing regular expressions from finite-state automata, the resulting regular expressions are often very long and complicated. We examine the minimization of finite-state automata to obtain shorter expressions first. Then, we introduce vertical chopping based on bridge states and horizontal chopping based on the structural properties of given finite-state automata. 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 lead to shorter regular expressions based on vertical chopping and horizontal chopping. 
 
Note that we have omitted almost all proofs in this preliminary version.
38202538
Infix-free Regular Expressions and Languages
We study infix-free regular languages. We observe the structural properties of finite-state automata for infix-free languages and develop a polynomial-time algorithm to determine infix-freeness of ...