This work is a connecting link between the field of digital transmission and (3 Dimension) 3D watermarking. In fact, we propose in this paper a blind and robust watermarking algorithm for 3D multiresolution meshes. Th...
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This work is a connecting link between the field of digital transmission and (3 Dimension) 3D watermarking. In fact, we propose in this paper a blind and robust watermarking algorithm for 3D multiresolution meshes. This data type, before being watermarked, is divided into GOTs (Group Of Triangles) using a spiral scanning method. At every instant, only one GOT is loaded into memory. It undergoes a wavelet transform. Embedding modifies the wavelet coefficients vector thus generated after being presented in a cylindrical coordinate system. After being watermarked, the current GOT will be released from memory to upload the next GOT. Information is coded using a turbo encoder to generate the codeword to be inserted. Once the entire mesh is scanned, the watermarked mesh is reconstructed. During extraction, the same steps are applied only on the watermarked mesh: our algorithm is then blind. Extracted data are decoded using error-correcting code (turbocode) to correct errors that occurred. The results show that our algorithm preserves mesh quality even with a very large insertion rate while significantly minimizing used memory. Data extraction was done correctly despite the application of various attacks. Our algorithm is robust against most popular attacks such as similarity transformation, noise addition, smoothing, coordinate quantization, simplification and compression.
codes over large fields can be used to construct codes over subfields. Such constructions of covering and error-correcting codes are discussed. In particular, packings and coverings with spheres of radius two are cons...
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codes over large fields can be used to construct codes over subfields. Such constructions of covering and error-correcting codes are discussed. In particular, packings and coverings with spheres of radius two are considered. A new construction of binary two-error-correcting codes from quaternary two-error-correcting codes is presented. This construction maintains the density, showing that such binary codes are at least as good as quaternary codes. The same construction is used to arrive at a similar conclusion for covering codes.
It is almost evident that SRAM-based cache memories will be subject to a significant degree of parametric random defects if one wants to leverage the technology scaling to its full extent. Although strong multibit err...
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It is almost evident that SRAM-based cache memories will be subject to a significant degree of parametric random defects if one wants to leverage the technology scaling to its full extent. Although strong multibit error-correcting codes (ECC) appear to be a natural choice to handle a large number of random defects, investigation of their applications in cache remains largely missing arguably because it is commonly believed that multibit ECC may incur prohibitive performance degradation and silicon/energy cost. By developing a cost-effective L2 cache architecture using multibit ECC, this paper attempts to show that, with appropriate cache architecture design, this common belief may not necessarily hold true for L2 cache. The basic idea is to supplement a conventional L2 cache core with several special-purpose small caches/buffers, which can greatly reduce the silicon cost and minimize the probability of explicitly executing multibit ECC decoding on the cache read critical path, and meanwhile, maintain soft error tolerance. Experiments show that, at the random defect density of 0.5 percent, this design approach can maintain almost the same instruction per cycle (IPC) performance over a wide spectrum of benchmarks compared with ideal defect-free L2 cache, while only incurring less than 3 percent of silicon area overhead and 36 percent power consumption overhead.
The condition-based approach identifies sets of input vectors, called conditions, for which it is possible to design an asynchronous protocol solving a distributed problem despite process crashes. This paper establish...
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The condition-based approach identifies sets of input vectors, called conditions, for which it is possible to design an asynchronous protocol solving a distributed problem despite process crashes. This paper establishes a direct correlation between distributed agreement problems and error-correcting codes. In particular, crash failures in distributed agreement problems correspond to erasure failures in error-correcting codes and Byzantine and value domain faults correspond to corruption errors. This correlation is exemplified by concentrating on two well-known agreement problems, namely, consensus and interactive consistency, in the context of the condition-based approach. Specifically, the paper presents the following results: First, it shows that the conditions that allow interactive consistency to be solved despite f(c) crashes and f(e) value domain faults correspond exactly to the set of error- correctingcodes capable of recovering from f(c) erasures and f(e) corruptions. Second, the paper proves that consensus can be solved despite f(c) crash failures iff the condition corresponds to a code whose Hamming distance is f(c) + 1 and Byzantine consensus can be solved despite f(b) Byzantine faults iff the Hamming distance of the code is 2f(b) + 1. Finally, the paper uses the above relations to establish several results in distributed agreement that are derived from known results in error-correcting codes and vice versa.
Best and Brouwer [2] proved that triply-shortened and doubly-shortened binary Hamming codes (which have length 2(m) - 4 and 2(m) - 3, respectively) are optimal. Properties of such codes are here studied, determining a...
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Best and Brouwer [2] proved that triply-shortened and doubly-shortened binary Hamming codes (which have length 2(m) - 4 and 2(m) - 3, respectively) are optimal. Properties of such codes are here studied, determining among other things parameters of certain subcodes. A utilization of these properties makes a computer-aided classification of the optimal binary one-error-correcting codes of lengths 12 and 13 possible;there are 237 610 and 117 823 such codes, respectively (with 27 375 and 17 513 inequivalent extensions). This completes the classification of optimal binary one-error-correcting codes for all lengths up to 15. Some properties of the classified codes are further investigated. Finally, it is proved that for any m >= 4, there are optimal binary one-error-correcting codes of length 2(m) - 4 and 2(m) - 3 and that cannot be lengthened to perfect codes of length 2(m) - 1.
A new method for error-correcting coding is proposed. It is based on processing information messages by finite automata and using a two-base numeral system. The two-level structure of an encoder provides powerful erro...
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A new method for error-correcting coding is proposed. It is based on processing information messages by finite automata and using a two-base numeral system. The two-level structure of an encoder provides powerful error-correcting capabilities. On the first (internal) level, an input message is considered as a binary number represented as a lower (2,3) code that has some redundancy and error-correcting properties. The noise-resistant properties are strengthened on the external level where the code is processed by a special finite automaton. It is a variable-length code, i.e., the codeword length depends not only on the length of an input message but also on the message content. However, the average code rate equals 1/2.
Galois hulls are generalizations of Euclidean and Hermitian hulls, which have attracted interest because of their important applications in determining the complexity of some algorithms about linear codes and in const...
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Galois hulls are generalizations of Euclidean and Hermitian hulls, which have attracted interest because of their important applications in determining the complexity of some algorithms about linear codes and in constructing entanglement-assisted quantum errorcorrectingcodes (EAQECCs). In this paper, the whole contribution is two-folded. On one hand, we propose explicit methods to construct linear codes of larger lengths with Galois hulls of arbitrary dimensions from given Galois self-orthogonal codes. Conditions required in our approach are proven to be relatively weak. On the other hand, we apply these results to construct EAQECCs. Two bounds for EAQECCs constructed from linear codes with prescribed dimensional Galois hull are given and EAQECCs with rates greater than or equal to 12 and positive net rates can be obtained. We also present many interesting examples to explain visually how these two aspects work. (c) 2023 Elsevier B.V. All rights reserved.
This correspondence shows that there is a flaw in the results presented in [1]. A large family of the codes constructed in [1] are not double byte error-correcting codes as originally claimed.
This correspondence shows that there is a flaw in the results presented in [1]. A large family of the codes constructed in [1] are not double byte error-correcting codes as originally claimed.
Here we apply the so-called Horace method for zero-dimensional schemes to error-correcting codes on complete intersections. In particular, we obtain sharper estimates on the minimum distance.
Here we apply the so-called Horace method for zero-dimensional schemes to error-correcting codes on complete intersections. In particular, we obtain sharper estimates on the minimum distance.
One of the important open problems in the theory of central simple algebras is to compute the essential dimension of GL(n)/mu(m), i.e., the essential dimension of a generic division algebra of degree n and exponent di...
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One of the important open problems in the theory of central simple algebras is to compute the essential dimension of GL(n)/mu(m), i.e., the essential dimension of a generic division algebra of degree n and exponent dividing m. In this paper we study the essential dimension of groups of the form G = (GL(n1) x ... x GL(nr))/C, where C is a central subgroup of GL(n1) x ... x GL(nr) GLnr. Equivalently, we are interested in the essential dimension of a generic r-tuple (A(1), ... , A(r)) of central simple algebras such that deg (A(i)) = n(i) and the Brauer classes of A(1), ... , A(r). satisfy a system of homogeneous linear equations in the Brauer group. The equations depend on the choice of C via the error -correctingcodecode(C) which we naturally associate to C. We focus on the case where n(1), ... , n(r) are powers of the same prime. The upper and lower bounds on ed(G) we obtain are expressed in terms of coding -theoretic parameters of code(C), such as its weight distribution. Surprisingly, for many groups of the above form the essential dimension becomes easier to estimate when r >= 3;in some cases we even compute the exact value. The Appendix by Athena Nguyen contains an explicit description of the Galois cohomology of groups of the form (GL(n1) x ... x GL(nr))/C. This description and its corollaries are used throughout the paper.
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