A systolic power-sum circuit designed to perform AB(+) + C computations in the finite field GF(2(m)) is presented, where A, B, and C are arbitrary elements of GF(2(m)). This new circuit is constructed by m(2) identica...
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A systolic power-sum circuit designed to perform AB(+) + C computations in the finite field GF(2(m)) is presented, where A, B, and C are arbitrary elements of GF(2(m)). This new circuit is constructed by m(2) identical cells, each of which consists of three 2-input AND logical gates, one 2-input XOR gate, one 3-input XOR gate, and ten latches. The AB(2) + C computation is required in decoding many error-correcting codes. This brief contribution shows that a decoder implemented using the new power-sum circuit will have less complex circuitry and shorter decoding delay than one implenmented using conventional product-sum multipliers.
Most color indexing techniques proposed in the literature are similar: images are represented by color histograms, and a metric on the color histogram space is used to determine the similarity of images. In this paper...
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ISBN:
(纸本)0819414808
Most color indexing techniques proposed in the literature are similar: images are represented by color histograms, and a metric on the color histogram space is used to determine the similarity of images. In this paper we determine the limits of these color indexing techniques. We propose two functions to measure the discrimination power of indexing techniques: the capacity (how many distinguishable histograms can be stored) and the maximal match number (the maximal number of retrieved images). We derive bounds for these functions. These bounds have two practical aspects. First, they help a user to decide whether color histograms effectively index database images from a given domain. Second, they facilitate the choice of a good threshold for the distance below which histograms are considered similar. Our arguments are based on an analysis of the metrical properties of the histogram space and results from coding theory. The results show that over a large range of reasonable parameters the capacity is very large. Thus, the set of parameters for which color indexing works well can be described as the set of parameters for which the maximal match number is below an application-dependent maximum.
In the band-limited signal space, the mutual relation between continuous time signal and discrete time signal is expressed by the sampling theorem of Whittaker-Someya-Shannon. This theorem consists of an orthonormal e...
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In the band-limited signal space, the mutual relation between continuous time signal and discrete time signal is expressed by the sampling theorem of Whittaker-Someya-Shannon. This theorem consists of an orthonormal expansion formula using sinc functions. In that formula, the expansion coefficients are identical to the sample values of signals. In general, the band-limited signal space is not always suited to model the signals in nature. The authors have proposed a new model for signal processing based on finite times continuously differentiable functions. This paper aims to complete the sampling theorem for the spline signal spaces, which corresponds to the sampling theorem of Whittaker-Someya-Shannon in the band-limited signal space. Since the obtained sampling theorem gives the simplest representation of signals, it is considered to be the most fundamental characterization of spline functions used for signal processing. The biorthonormal basis derived in this paper is considered to be a system of delta functions at sampling points with some continuous differentiability.
This paper presents a fresh approach to a general education mathematics course. The basic idea is to turn the customary mathematics class on its head by focusing on applications first, through a reading of articles fr...
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The problem of disk allocation addresses the issue of how to distribute a file on several disks in order to maximize concurrent disk accesses in response to a partial match query. In this paper a coding-theoretic anal...
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The problem of disk allocation addresses the issue of how to distribute a file on several disks in order to maximize concurrent disk accesses in response to a partial match query. In this paper a coding-theoretic analysis of this problem is presented, and both necessary and sufficient conditions for the existence of strictly optimal allocation methods are provided. Based on a class of optimal codes, known as maximum distance separable codes, strictly optimal allocation methods are constructed. Using the necessary conditions proved, we argue that the standard definition of strict optimality is too strong and cannot be attained, in general. Hence, we reconsider the definition of optimality. Instead of basing it on an abstract definition that may not be attainable, we propose a new definition based on the best possible allocation method. Using coding theory, allocation methods that are optimal according to our proposed criterion are developed.
Galois field multiplication is central to coding theory. In many applications of finite fields, there is need for a multiplication algorithm which can be realised easily on VLSI chips. In the paper, what is called the...
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Galois field multiplication is central to coding theory. In many applications of finite fields, there is need for a multiplication algorithm which can be realised easily on VLSI chips. In the paper, what is called the Babylonian multiplication algorithm for using tables of squares is applied to the Galois fields GF(q(m)). It is shown that this multiplication method for certain Galois fields eliminates the need for the division operation of dividing by four in the original Babylonian algorithm. Also, it is found that this multiplier can be used to compute complex multiplications defined on the direct sum of two identical copies of these Galois fields.
In this paper, we develop a coding theory approach to error control in residue number system product codes. Based on this coding theory framework, new computationally efficient algorithms are derived for correcting si...
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In this paper, we develop a coding theory approach to error control in residue number system product codes. Based on this coding theory framework, new computationally efficient algorithms are derived for correcting single errors, double errors, multiple errors, and simultaneously detecting multiple errors and additive overflow. These algorithms reduce the computational complexity of previously known algorithms by at least an order of magnitude. In addition, it is worthwhile to mention here that all the literature published thus far deals almost exclusively with single error correction.
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