A direct method is proposed to get the solution of linear systems of equations with circulant-like coefficient matrices that find important application in engineering, the elements of solutions are functions of zero p...
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A direct method is proposed to get the solution of linear systems of equations with circulant-like coefficient matrices that find important application in engineering, the elements of solutions are functions of zero points of the characteristic polynomial g(z) and g'(z) of circulant matrix, three examples to get the inverse matrix, and the solutions of linear system are presented in the paper. (C) 2013 Elsevier Inc. All rights reserved.
Erasure codes are essential for providing efficient resilience against node failures in distributed storage. Typically, an [n, k] erasure code encodes k symbols into n symbols which are then stored in different nodes....
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Erasure codes are essential for providing efficient resilience against node failures in distributed storage. Typically, an [n, k] erasure code encodes k symbols into n symbols which are then stored in different nodes. Recent work by Kadekodi et al. shows that the failure rates of storage nodes vary significantly over time, and that changing the rate of the code (via a change in n and k) in response to such variations provides substantial storage space savings. However, the resource overhead of re-encoding the already encoded data is prohibitively high. We present a new theoretical framework formalizing code conversion-the process of converting data encoded with an [n(I), k(I)] code into data encoded with an [n(F), k(F)] code while maintaining desired decodability properties. We then introduce convertible codes, a new class of codes that allow for code conversions in a resource-efficient manner. This paper begins the study on convertible codes by focusing on linear MDS codes and the access cost of conversion. We derive a lower bound on the access cost of conversion and present an explicit optimal construction matching this bound for an important subclass of conversions. Additionally, we propose constructions with low field-size requirement for a broad subset of parameters. Our results show that it is possible to achieve code conversions with significantly less resources than the default approach of re-encoding for a wide range of parameters.
Optimal sensor placement (OSP) technique plays a key role in the structural health monitoring (SHM) of large-scale structures. Based on the criterion of the OSP for the modal test, an improved genetic algorithm, calle...
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Optimal sensor placement (OSP) technique plays a key role in the structural health monitoring (SHM) of large-scale structures. Based on the criterion of the OSP for the modal test, an improved genetic algorithm, called "generalized genetic algorithm (GGA)", is adopted to find the optimal placement of sensors. The dual-structure coding method instead of binary coding method is proposed to code the solution. Accordingly, the dual-structure coding-based selection scheme, crossover strategy and mutation mechanism are given in detail. The tallest building in the north of China is implemented to demonstrate the feasibility and effectiveness of the GGA. The sensor placements obtained by the GGA are compared with those by exiting genetic algorithm, which shows that the GGA can improve the convergence of the algorithm and get the better placement scheme.
Wavelet difference reduction (WDR) has recently been proposed as a method for efficient embedded image coding. In this paper, the WDR algorithm is analysed and four new techniques are proposed to either reduce its com...
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Wavelet difference reduction (WDR) has recently been proposed as a method for efficient embedded image coding. In this paper, the WDR algorithm is analysed and four new techniques are proposed to either reduce its complexity or improve its rate distortion (RD) performance. The first technique, dubbed modified WDR-A (MWDR-A), focuses on improving the efficiency of the arithmetic coding (AC) stage of the WDR. Based on experiments with the statistics of the output symbol sequence, it is shown that the symbols can either be arithmetic coded under different contexts or output without AC. In the second technique, MWDR-B, the AC stage is dropped from the coder. By employing MWDR-B, up to 20% of coding time can be saved without sacrificing the RD performance, when compared to WDR. The third technique focuses on the improvement of RD performance using context modelling. A low-complexity context model is proposed to exploit the statistical dependency among the wavelet coefficients. This technique is termed context-modelled WDR (CM-WDR), and acts without the AC stage to improve the RD performance by up to 1.5 dB over WDR on a set of test images, at various bit rates. The fourth technique combines CM-WDR with AC and achieves a 0.2 dB improvement over CM-WDR in terms of PSNR. The proposed techniques retain all the features of WDR, including low complexity, region-of-interest capability, and embeddedness.
We continue the study of list recovery properties of high-rate tensor codes, initiated by Hemenway, Ron-Zewi, and Wootters (FOCS'17). In that work it was shown that the tensor product of an efficient (poly-time) h...
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We continue the study of list recovery properties of high-rate tensor codes, initiated by Hemenway, Ron-Zewi, and Wootters (FOCS'17). In that work it was shown that the tensor product of an efficient (poly-time) high-rate globally list recoverable code is approximately locally list recoverable, as well as globally list recoverable in probabilistic near-linear time. This was used in turn to give the first capacity-achieving list decodable codes with (1) local list decoding algorithms, and with (2) probabilistic near-linear time global list decoding algorithms. This also yielded constant-rate codes approaching the Gilbert-Varshamov bound with probabilistic near-linear time global unique decoding algorithms. In the current work we obtain the following results: 1) The tensor product of an efficient (poly-time) high-rate globally list recoverable code is globally list recoverable in deterministic near-linear time. This yields in turn the first capacity-achieving list decodable codes with deterministic near-linear time global list decoding algorithms. It also gives constant-rate codes approaching the Gilbert-Varshamov bound with deterministic near-linear time global unique decoding algorithms. 2) If the base code is additionally locally correctable, then the tensor product is (genuinely) locally list recoverable. This yields in turn (non-explicit) constant-rate codes approaching the Gilbert-Varshamov bound that are locally correctable with query complexity and running time N-o(1). This improves over prior work by Gopi et. al. (SODA'17;IEEE Transactions on Information theory' 18) that only gave query complexity N-epsilon with rate that is exponentially small in 1/epsilon. 3) A nearly-tight combinatorial lower bound on output list size for list recovering high-rate tensor codes. This bound implies in turn a nearly-tight lower bound of N-Omega(1/log logN) on the product of query complexity and output list size for locally list recovering high-rate tensor codes.
A general algebraic method for decoding all types of binary cyclic codes is presented. It is shown that such a method can correct t = [(d - 1) / 2] errors, where d is the true minimum distance of the given cyclic code...
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A general algebraic method for decoding all types of binary cyclic codes is presented. It is shown that such a method can correct t = [(d - 1) / 2] errors, where d is the true minimum distance of the given cyclic code. The key idea behind this decoding technique is a systematic application of the algorithmic procedures of Grobner bases to obtain the error-locator polynomial L(z). The discussion begins from a set of syndrome polynomials F and the ideal I(F) generated by F. It is proved here that the process of transforming F to the normalized reduced Grobner basis of I(F) with respect to the ''purely lexicographical'' ordering automatically converges to L(z). Furthermore, it is shown that L(z) can be derived from any normalized Grobner basis of I(F) with respect to ally admissible total ordering. To illustrate this new decoding method, examples are given.
In this paper we investigate whether the distance between fuzzy code words, fuzzy subsets of n -tuples over a set F , is dependent upon the dimension of the space as well as the distance between the non-fuzzy code wor...
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In this paper we investigate whether the distance between fuzzy code words, fuzzy subsets of n -tuples over a set F , is dependent upon the dimension of the space as well as the distance between the non-fuzzy code words on which they are based. This is done for both asymmetric errors and unidirectional errors. The results are compared and contrasted with the work of von Kaenel [3] on fuzzy codes for symmetric errors.
We consider subspace codes, called multicomponent codes with zero prefix (MZP codes), whose subspace code distance is twice their dimension. We find values of parameters for which the codes are of the maximum cardinal...
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We consider subspace codes, called multicomponent codes with zero prefix (MZP codes), whose subspace code distance is twice their dimension. We find values of parameters for which the codes are of the maximum cardinality. We construct combined codes where the last component of the multicomponent code is the code from [1] found by exhaustive search for particular parameter values. As a result, we obtain a family of subspace codes with maximum cardinality for a number of parameters. We show that the family of maximum-cardinality codes can be extended by using dual codes.
We investigate binary orthogonal arrays by making use of the fact that all possible distance distributions of the arrays under investigation and of related arrays can be computed. We apply certain relations for reduci...
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We investigate binary orthogonal arrays by making use of the fact that all possible distance distributions of the arrays under investigation and of related arrays can be computed. We apply certain relations for reducing the number of feasible distance distributions. In some cases this leads to nonexistence results. In particular, we prove that there exist no binary orthogonal arrays with parameters (strength, length, cardinality) = (4, 10, 6 center dot 2(4)), (4, 11, 6 center dot 2(4)), (4, 12, 7 center dot 2(4)), (5, 11, 6 center dot 2(5)), (5, 12, 6 center dot 2(5)), and (5, 13, 7 center dot 2(5)).
This paper is a survey of matrix error correcting codes and presents existing theory for matrix code literature since 1950. A brief description of several contributions and books concerned with the theory relevant onl...
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This paper is a survey of matrix error correcting codes and presents existing theory for matrix code literature since 1950. A brief description of several contributions and books concerned with the theory relevant only to matrix codes is presented. Two and three dimensional arrays of digital information occur frequently in today's applications in digital communication systems, computer systems and automatia. The error control of such systems (like error detection and correction) is a fact that takes place for a variety of reasons. Matrix codes, which are a straight forward application of the one, two, or more dimensional arrays, have a great advantages over the other codes surveyed. These codes use a systematic specification with simple parity checking. For this reason we are giving a survey of the existing literature about matrix codes today with relevant comments. Most of the references used here are cited to illustrate these themes. [ABSTRACT FROM AUTHOR]
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