We derive an upper bound on the size of a block code with prescribed burst-error-correcting capability combining those two ideas underlying the generalized Singleton and sphere-packing bounds. The two ideas are punctu...
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We derive an upper bound on the size of a block code with prescribed burst-error-correcting capability combining those two ideas underlying the generalized Singleton and sphere-packing bounds. The two ideas are puncturing and sphere-packing. We use the burst metric defined by Gabidulin [1], which is suitable for burst error correction and detection. It is demonstrated that the proposed bound improves previously known ones for finite code-length, when minimum distance is greater than 3, as well as in the asymptotic forms.
A partial-sum query obtains the summation over a set of specified cells of a data cube. We establish a connection between the covering problem in the theory of error-correcting codes and the partial-sum problem and us...
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A partial-sum query obtains the summation over a set of specified cells of a data cube. We establish a connection between the covering problem in the theory of error-correcting codes and the partial-sum problem and use this connection to devise algorithms for the partial-sum problem with efficient space-time-trade-offs. For example,using our algorithms, with 44 percent additional storage, the query response time can be improved by about 12 percent;by roughly doubling the storage requirement, the query response time can be improved by about 34 percent.
In digital VCRs for home use, the video signal for each field is recorded on multiple tracks. Thus, it is difficult to reproduce the video signal smoothly in high-speed trick playback, where the signal is restored by ...
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This paper reports a novel approach for designing byte error-correcting codes using cellular automata (CA), A simple scheme for generation and decoding of single-byte error-correcting and double-byte error-detecting c...
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This paper reports a novel approach for designing byte error-correcting codes using cellular automata (CA), A simple scheme for generation and decoding of single-byte error-correcting and double-byte error-detecting codes, referred to as CA-SbEC-DbED, is presented, Extension of the scheme to locate/correct larger number of information byte errors has been also included. The encoding and decoding algorithms have been designed with tbe help of a linear operator that can be conveniently realized with a maximum length group CA, The regular, modular and cascadable structure of CA can be economically built with VLSI technology, Compared to the existing architecture of the Reed-Solomon decoder chip, CA-based implementation of the proposed decoding scheme provides a simple cost effective solution.
This paper investigates methods to locate system resources, such as expensive hardware or software modules, to provide the most effective cost/performance trade-offs in a torus parallel machine. This paper contains so...
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This paper investigates methods to locate system resources, such as expensive hardware or software modules, to provide the most effective cost/performance trade-offs in a torus parallel machine. This paper contains some solutions to perfect distance-t and perfect/quasi-perfect j-adjacency placement in a k-ary n-cube and a torus using Lee distance error-correcting codes. It also presents generalized resource placement (j-adjacency with distance-t placement) methods based on the concept of covering radius of Lee distance codes.
Reed-Solomon (RS) codes have been widely used in a variety of communication systems to protect digital data against errors occurring in the transmission process. Since the decoding profess for RS codes is rather compu...
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Reed-Solomon (RS) codes have been widely used in a variety of communication systems to protect digital data against errors occurring in the transmission process. Since the decoding profess for RS codes is rather computation-extensive, special-purpose hardware structures are often necessary for it to meet the real-time requirements. In this paper, an area-efficient pipelined very large scale integration (VLSI) architecture is proposed for RS decoding. The architecture is developed based on a time-domain algorithm using the remainder decoding concept. A prominent feature of the proposed system is that, for a t-error-correcting RS code with block length n, it involves only 2t consecutive symbols to compute a discrepancy value in the decoding process, instead of n consecutive symbols used in the previous RS decoders based on the same algorithm without using the remainder decoding concept. The proposed RS decoder can process one data block every n clerk cycles, i.e., the average decoding rate is one symbol per clock cycle. As compared to a similar pipelined RS decoder with the same decoding rate, it gains significant improvements in hardware complexity and latency.
In digital VCRs for home use, the video signal for each field is recorded on multiple tracks. Thus, it is difficult to reproduce the video signal smoothly in high-speed trick playback, where the signal is restored by ...
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In digital VCRs for home use, the video signal for each field is recorded on multiple tracks. Thus, it is difficult to reproduce the video signal smoothly in high-speed trick playback, where the signal is restored by scanning across the tracks. This paper intends to realize a satisfactory high-speed reproduction, and discusses the improvement of the head scanning trajectory, a high-speed trick playback error-control method, and a data coding method for the highspeed trick playback. In the base-band recording VCR, there is a problem that the fixed position of the image frame cannot be restored in integer-multiple speed playback. In order to cope with this problem, a method to adjust the drum rotation speed is considered, and the relation between the variation of the drum rotation and the period of the image presentation is derived. In the high-speed playback, only the C1 code can be restored among the error-correcting codes. For this problem, it is shown that the C3 code can be added and the error-correcting capability can be improved when a data area for high-speed trick playback is provided as in the bit-stream recording VCR. The requantization coding and the data-division coding methods are proposed as data coding methods for the high-speed trick playback. The effectiveness of those methods is demonstrated by image simulation. (C) 1997 Scripta Technica, Inc.
In the ATM system, all multimedia information, such as voice, picture and data, is divided into packets with the fixed length of 53 bytes, called cells, and the cells are transferred. Intensive studies have been made ...
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In the ATM system, all multimedia information, such as voice, picture and data, is divided into packets with the fixed length of 53 bytes, called cells, and the cells are transferred. Intensive studies have been made on the performance of the system, where such multimedia information is multiplexed in the network switch. In the ATM network, the cell loss is not compensated, and it is necessary that the end-user should recover from the errors in order to realize highly reliable data transfer among computers. As one such approach, the error-correcting cone (FEC) has been considered interesting. From such a viewpoint, this paper evaluates analytically the data transfer performance when FEC is used. When FEC is used, the redundant cell produces an overhead, which may enhance congestion when the traffic in the network is high and deteriorate the performance. Also, from this viewpoint, this paper considers the priority control, where the redundant cells are discarded positively when the network is congested. The effectiveness of the approach is examined, as in the data transfer performance for the case where the video and the data exist together in the traffic, and it is demonstrated that the control parameters in the priority control are especially important in that case.
The main construction for resilient functions uses linear error-correcting codes;a resilient function constructed in this way is said to be linear. It has been conjectured that if a resilient function exists, then a l...
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The main construction for resilient functions uses linear error-correcting codes;a resilient function constructed in this way is said to be linear. It has been conjectured that if a resilient function exists, then a linear function with the same parameters exists. In this note we construct infinite classes of nonlinear resilient functions from the Kerdock and Preparata codes. We also show that linear resilient functions having the same parameters as the functions that we construct from the Kerdock codes do not exist. Thus, the aforementioned conjecture is disproved.
Allocation methods for Cartesian product files on multiple disks by using linear error-correcting codes are proposed. This allocation methods can be applied to queries in which the characteristic of each attribute is ...
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ISBN:
(纸本)0780321294
Allocation methods for Cartesian product files on multiple disks by using linear error-correcting codes are proposed. This allocation methods can be applied to queries in which the characteristic of each attribute is not uniform. The structure of Reed-Solomon codes over GF(pm), which give the strictly optimal allocation when all possible partial match queries are equiprobable, and the mapping by the basis for GF(pm) over the subfields is used. As a result, it is shown that a file is constructed by records which has the attributes in which the domain is partitioned by different number. The properties of this method are described.
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