A simplified parallel step-by-step decoding algorithm is proposed for decoding Reed-Solomon (RS) codes. It uses new method to calculate the determinants of the temporarily changed syndrome matrices, based on the prope...
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A simplified parallel step-by-step decoding algorithm is proposed for decoding Reed-Solomon (RS) codes. It uses new method to calculate the determinants of the temporarily changed syndrome matrices, based on the property of these matrices determined in this paper. By using the proposed method, the calculations of the determinants of the temporarily changed syndrome matrices become much simpler and thus the computational complexity of the step-by-step decoding algorithm is significantly reduced.
An [] code is a binary linear code of block length , dimension and minimum Hamming distance . Since the minimum distance determines the error detection or correction capability, it is desired that is as large as possi...
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An [] code is a binary linear code of block length , dimension and minimum Hamming distance . Since the minimum distance determines the error detection or correction capability, it is desired that is as large as possible for the given block length and dimension . One of the most fundamental problems in coding theory is to construct codes with best possible minimum distances. This problem is very difficult in both theory and practice. During the last decades, it has proved that the class of quasi-cyclic (QC) codes contain many such codes. In this paper, augmentation of binary QC codes is studied. A new augmentation algorithm is presented, and 10 new -generator QC codes that are better than previously known code have been constructed. Furthermore, Construction X has been applied to obtain another 18 new improved binary linear codes. With the standard construction techniques, a total of 124 new binary linear codes that improve the lower bound on the minimum distance have been obtained.
This paper describes the implementation of polycomp, a open-sourced, publicly available program for compressing one-dimensional data series in tabular format. The program is particularly suited for compressing smooth,...
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This paper describes the implementation of polycomp, a open-sourced, publicly available program for compressing one-dimensional data series in tabular format. The program is particularly suited for compressing smooth, noiseless streams of data like pointing information, as one of the algorithms it implements applies a combination of least squares polynomial fitting and discrete Chebyshev transforms that is able to achieve a compression ratio C-r up to approximate to 40 in the examples discussed in this work. This performance comes at the expense of a loss of information, whose upper bound is configured by the user. I show two areas in which the usage of polycomp is interesting. In the first example, I compress the ephemeris table of an astronomical object (Ganymede), obtaining C-r approximate to 20, with a compression error on the x, y, z coordinates smaller than 1 m. In the second example, I compress the publicly available timelines recorded by the Low Frequency Instrument (LFI), an array of microwave radiometers onboard the ESA Planck spacecraft. The compression reduces the needed storage from similar to 6.5 TB to approximate to 0.75 TB (C-r approximate to 9), thus making them small enough to be kept in a portable hard drive. (C) 2016 Elsevier B.V. All rights reserved.
In this study, the 'THORS (Thermal-Hydraulic Out-of-Reactor Safety) bundle 2B' test data in ORNL (Oak Ridge National Laboratory, US) were used to supplement a qualification of the MATRA-LMR-FB code. The code w...
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In this study, the 'THORS (Thermal-Hydraulic Out-of-Reactor Safety) bundle 2B' test data in ORNL (Oak Ridge National Laboratory, US) were used to supplement a qualification of the MATRA-LMR-FB code. The code was developed to analyze a sub-channel blockage accident in a Sodium cooled Fast Reactor (SFR), as an effort to enhance its reliability for an analysis of a blockage disturbance. The 'THORS bundle 2B' test was conducted to investigate the thermal-hydraulic effects of 24% and 45% sub-channel inlet blockages with a 19-pin bundle. The test covered several flow rates at the bundle inlet with different bundle powers. The MATRA-LMR-FB predictions were compared with not only the CFX simulation results but also the test data. As a result, most of the comparative results between the MATRA-LMR-FB predictions and the test data lay within a range of +/- 15 degrees C. Such differences were not usually derailed much from other predictions found in a literature survey. The code, however, is slightly biased toward an under-prediction, with the most probable difference occurring at around -2 to -4 degrees C. Nevertheless, it was anticipated that the comparison will supplement the applicability of the MATRA-LMR-FB to a partial flow blockage accident in a subassembly of an SFR. The CFX simulation results mostly agreed with the MATRA-LMR-FB predictions. (C) 2014 Elsevier B.V. All rights reserved.
The distance distribution of a code is the vector whose ith entry is the number of pairs of codewords with distance i. We investigate the structure of the distance distribution for cyclic orbit codes, which are subspa...
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The distance distribution of a code is the vector whose ith entry is the number of pairs of codewords with distance i. We investigate the structure of the distance distribution for cyclic orbit codes, which are subspace codes generated by the action of F-qn* on an F-q-subspace U of F-qn. Note that F-qn* is a Singer cycle in the general linear group of all F-q-automorphisms of F-qn. We show that for full-length orbit codes with maximal possible distance the distance distribution depends only on q,n, and the dimension of U. For full-length orbit codes with lower minimum distance, we provide partial results towards a characterization of the distance distribution, especially in the case that any two codewords intersect in a space of dimension at most 2. Finally, we briefly address the distance distribution of a union of full-length orbit codes with maximum distance.
Due to the growing popularity of Internet of People (IoP) and its impacts on human activity, it has quickly become an important research field and hot subject. Since one purpose of IoP is to connect people to people, ...
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Due to the growing popularity of Internet of People (IoP) and its impacts on human activity, it has quickly become an important research field and hot subject. Since one purpose of IoP is to connect people to people, personal live video delivery that has been popular recently can also be regarded as an important application of IoP. For improving the video quality of video communication services, Raptor code has been adopted in various broadband communication systems. In this paper, we propose a systematic Raptor code decoder based on the group parameters for a group of encoding symbols. For a Raptor code application that can frequently use one or several fixed source block lengths (i.e., the number of source symbols in a source block), we could produce the corresponding group parameters in advance and use them to decode the received encoding symbols more efficiently. For personal live video delivery scenario based on the IPTV delivery, the simulation results show that our decoder is faster than the conventional Raptor code decoder which is adopted by the DVB and 3GPP specifications.
Maximally recoverable codes are codes designed for distributed storage which combine quick recovery from single node failure and optimal recovery from catastrophic failure. Gopalan et al. [Maximally recoverable codes ...
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Maximally recoverable codes are codes designed for distributed storage which combine quick recovery from single node failure and optimal recovery from catastrophic failure. Gopalan et al. [Maximally recoverable codes for grid-like topologies, in Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, 2017, pp. 2092-2108] studied the alphabet size needed for such codes in grid topologies and gave a combinatorial characterization for it. Consider a labeling of the edges of the complete bipartite graph K-n,K-n, with labels coming from F-2(d), that satisfies the following condition: for any simple cycle, the sum of the labels over its edges is nonzero. The minimal d where this is possible controls the alphabet size needed for maximally recoverable codes in n x n grid topologies. Prior to the current work, it was known that d is between (logn)(2) and n log n. We improve both bounds and show that d is linear in n. The upper bound is a recursive construction which beats the random construction. The lower bound follows by first relating the problem to the independence number of the Birkhoff polytope graph, and then providing tight bounds for it using the representation theory of the symmetric group.
In this paper, we give several new constructions of write-once-memory (WOM) codes. The novelty in our constructions is the use of the so-called Wozencraft ensemble of linear codes. Specifically, we obtain the followin...
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In this paper, we give several new constructions of write-once-memory (WOM) codes. The novelty in our constructions is the use of the so-called Wozencraft ensemble of linear codes. Specifically, we obtain the following results. We give an explicit construction of a two-write WOM code that approaches capacity, over the binary alphabet. More formally, for every epsilon > 0, 0 < p < 1, and n = (1/epsilon)(O(1/p epsilon)), we give a construction of a two-write WOM code of length n and capacity H(p) + 1 - p - epsilon. Since the capacity of a two-write WOM code is max(p)(H(p) + 1 - p), we get a code that is epsilon-close to capacity. Furthermore, encoding and decoding can be done in time O(n(2) . poly(log n)) and time O(n . poly(log n)), respectively, and in logarithmic space. In addition, we exhibit an explicit randomized encoding scheme of a two-write capacity-achieving WOM code of block length polynomial in 1/epsilon (again, epsilon is the gap to capacity), with a polynomial time encoding and decoding. We obtain a new encoding scheme for three-write WOM codes over the binary alphabet. Our scheme achieves rate 1.809 - epsilon, when the block length is exp(1/epsilon). This gives a better rate than what could be achieved using previous techniques. We highlight a connection to linear seeded extractors for bit-fixing sources. In particular, we show that obtaining such an extractor with seed length O(log n) can lead to improved parameters for two-write WOM codes. We then give an application of existing constructions of extractors to the problem of designing encoding schemes for memory with defects.
The Delsarte linear program is used to bound the size of codes given their block length n and minimal distance d by taking a linear relaxation from codes to quasicodes. We study for which values of (n, d) this linear ...
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The Delsarte linear program is used to bound the size of codes given their block length n and minimal distance d by taking a linear relaxation from codes to quasicodes. We study for which values of (n, d) this linear program has a unique optimum: while we show that it does not always have a unique optimum, we prove that it does if d > n/2 or if d <= 2. Introducing the Krawtchouk decomposition of a quasicode, we prove there exist optima to the (n, 2e) and (n - 1, 2e - 1) linear programs that have essentially identical Krawtchouk decompositions, revealing a parity phenomenon among the Delsarte linear programs. We generalize the notion of extending and puncturing codes to quasicodes, from which we see that this parity relationship is given by extending/puncturing. We further characterize these pairs of optima, in particular demonstrating that they exhibit a symmetry property, effectively halving the number of decision variables.
The study of self-testing and self-correcting programs leads to the search for robust characterizations of functions. Here the authors make this notion precise and show such a characterization for polynomials. From th...
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The study of self-testing and self-correcting programs leads to the search for robust characterizations of functions. Here the authors make this notion precise and show such a characterization for polynomials. From this characterization, the authors get the following applications. Simple and efficient self-testers for polynomial functions are constructed. The characterizations provide results in the area of coding theory by giving extremely fast and efficient error-detecting schemes for some well-known codes. This error-detection scheme plays a crucial role in subsequent results on the hardness of approximating some NP-optimization problems.
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