We consider the quadratic Gaussian CEO problem, where the goal is to estimate a measure based on several Gaussian noisy observations which must be encoded and sent to a centralized receiver using limited transmission ...
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We consider the quadratic Gaussian CEO problem, where the goal is to estimate a measure based on several Gaussian noisy observations which must be encoded and sent to a centralized receiver using limited transmission rate. For real applications, besides minimizing the average distortion, given the transmission rate, it is important to take into account memory and processing constraints. Considering these motivations, we present a low complexity coding and decoding strategy, which exploits the correlation between the measurements to reduce the number of bits to be transmitted by refining the output of the quantization stage. The CEO makes an estimate using a decoder based on a process similar to majority voting. We derive explicit expression for the CEO's error probability and compare numerical simulations with known achievability results and bounds. (C) 2016 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
One of the main challenges of coding theory is to construct linear codes with the best possible parameters. Various algebraic and combinatorial methods along with computer searches are used to construct codes with bet...
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One of the main challenges of coding theory is to construct linear codes with the best possible parameters. Various algebraic and combinatorial methods along with computer searches are used to construct codes with better parameters. Given the computational complexity of determining the minimum distance of a code, exhaustive searches are not feasible for all but small parameter sets. Therefore, codes with certain algebraic structures are preferred for both theoretical and practical reasons. In this work we focus on the class of constacyclic codes to first generate all constacyclic codes exhaustively over small finite fields of order up to 9 to create a database of best constacyclic codes. We will then use this database as a building block for a search algorithm for new quasi-twisted codes. Our search on constacyclic codes has revealed 16 new codes, i.e. codes with better parameters than currently best-known linear codes. Given that constacyclic codes are well known, this is a surprising result. Moreover, using the standard constructions of puncturing, shortening or extending a given code, we also derived 55 additional new codes from these constacyclic codes. Hence, we achieved improvements on 71 entries in the database of best-known codes. We use a search strategy that is comprehensive, i.e. it computes every constacyclic code for a given length and shift constant, and it avoids redundantly examining constacyclic codes that are equivalent to either cyclic codes or other constacyclic codes. (C) 2013 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
The total information content of a composite system consisting of k qubits can either be completely encoded in a specific computational basis, or alternatively it can be partially encoded in a number of different base...
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The total information content of a composite system consisting of k qubits can either be completely encoded in a specific computational basis, or alternatively it can be partially encoded in a number of different bases. In that case the information encoded in a complete set of mutually complementary bases is again k bits. Using only two single-qubit gates and the controlled-NOT gate, one can implement coding and decoding in such a complete set. The total information content is then invariant under the particular choice of a complete set of mutually complementary bases. For maximally entangled states the k bits of information are not encoded into the k qubits separately but only into their joint properties.
In this study, an efficient and fast algebraic decoding algorithm (ADA) for the binary systematic quadratic residue (QR) code of length 73 with the reducible generator polynomial to correct up to six errors is propose...
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In this study, an efficient and fast algebraic decoding algorithm (ADA) for the binary systematic quadratic residue (QR) code of length 73 with the reducible generator polynomial to correct up to six errors is proposed. The S(I, J) matrix method given by He et al. (2001) is utilised to compute the unknown syndromes S-5. A technique called swap base is proposed to correct the weight-4 error patterns. To correct the weight-5 error patterns, the new error-locator polynomials for decoding the five errors are derived. Finally, the modified shift-search algorithm (SSA) developed by Lin et al. (2010) is applied to correct the weight-6 error patterns. Moreover, the computations of all syndromes are achieved in a small finite field. Simulation results show that the proposed ADA is practical.
As the size of large-scale computer systems increases, their mean-time-between-failures are becoming significantly shorter than the execution time of many current scientific applications. Fault-tolerant parallel algor...
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As the size of large-scale computer systems increases, their mean-time-between-failures are becoming significantly shorter than the execution time of many current scientific applications. Fault-tolerant parallel algorithm (FTPA) is an application-level fault-tolerant approach that can achieve fast self-recovery by parallel recomputing. The method of parallelizing the loops has been used to design the parallel recomputing code for FTPA in our prior work. In the present paper, we first propose a new parallel recomputing code design methodology. Second, the parallel recomputing code design methodology is automated by exploring the use of compiler technology. Finally, we evaluate the performance of our approach with five programs on Tianhe-1A. The experimental results show that the parallel recomputing code generated by the new method has a higher efficiency of parallel recomputing. (C) 2013 Elsevier Ltd. All rights reserved.
A two-level batch chromosome coding scheme is proposed to solve the lot splitting problem with equipment capacity constraints in flexible job shop scheduling, which includes a lot splitting chromosome and a lot schedu...
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A two-level batch chromosome coding scheme is proposed to solve the lot splitting problem with equipment capacity constraints in flexible job shop scheduling, which includes a lot splitting chromosome and a lot scheduling chromosome. To balance global search and local exploration of the differential evolution algorithm, a hybrid discrete differential evolution algorithm (HDDE) is presented, in which the local strategy with dynamic random searching based on the critical path and a random mutation operator is developed. The performance of HDDE was experimented with 14 benchmark problems and the practical dye vat scheduling problem. The simulation results showed that the proposed algorithm has the strong global search capability and can effectively solve the practical lot splitting problems with equipment capacity constraints.
Reed-Muller codes are error-correcting codes used in many areas related to coding theory, such as electrical engineering and computer science. The binary rth-order Reed-Muller code RM (r, n) can be viewed as the set o...
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Reed-Muller codes are error-correcting codes used in many areas related to coding theory, such as electrical engineering and computer science. The binary rth-order Reed-Muller code RM (r, n) can be viewed as the set of all n-variable Boolean functions of algebraic degree at most r. Despite the intense work on these codes, many problems are known to be hard (notably, determining their covering radius) and remain open to this day. Fourteen years ago, Carlet and Mesnager improved in [IEEE Transactions on Information theory, "Improving the Upper Bounds on the Covering Radii of Binary Reed-Muller Codes", 53(1), 2007] the upper bound on the covering radius of the Reed-Muller code of order 2, and they deduced improved upper bounds on the covering radii of the Reed-Muller codes of higher orders. Until 2021, these upper bounds remained the best ones in the literature. The Reed-Muller code RM (n - 3, n), which corresponds to the dual of the Reed-Muller code RM (2, n), has attracted much attention. One of the main reasons is that it is precisely the code that has been considered to get the upper bounds derived by Carlet and Mesnager. Those upper bounds have been obtained thanks to the characterization of the codewords of the Reed-Muller code, whose Hamming weights are strictly less than 2.5 times the minimum distance 2(n-r) due to Kasami, Tokura, and Azumi. Despite their impressive work in the seventieth, a more refined study and profound description of those codewords of RM (n - 3, n) whose Hamming weight equals 16, and especially 18, seem necessary, as it could help us significantly in improving the covering radius of Reed-Muller codes. In this paper, we push further the known results on the Reed-Muller codes by focusing on the Reed-Muller code RM (n - 3, n). We provide a classification of the codewords of weights 16 and 18 of the Reed-Muller code RM (n - 3, n). Our algebraic descriptions allow us to count the number of such codewords and to enumerate all of them explicitly.
It is shown that steganography with a given distortion criteria, which we call combinatorial steganography, is equivalent to coverings of Hamming spaces or to so-called centered error-correcting codes, depending on wh...
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It is shown that steganography with a given distortion criteria, which we call combinatorial steganography, is equivalent to coverings of Hamming spaces or to so-called centered error-correcting codes, depending on whether an opponent is passive or active, respectively. A construction of centered error-correcting codes based on Reed-Solomon and algebraic geometry codes is proposed.
Suppose that P is a property that may be satisfied by a random code C subset of Sigma(n). For example, for some p is an element of (0, 1), P might be the property that there exist three elements of C that lie in some ...
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Suppose that P is a property that may be satisfied by a random code C subset of Sigma(n). For example, for some p is an element of (0, 1), P might be the property that there exist three elements of C that lie in some Hamming ball of radius pn. We say that R* is the threshold rate for P if a random code of rate R* + epsilon is very likely to satisfy P, while a random code of rate R* - epsilon is very unlikely to satisfy P. While random codes are well-studied in coding theory, even the threshold rates for relatively simple properties like the one above are not well understood. We characterize threshold rates for a rich class of properties. These properties, like the example above, are defined by the inclusion of specific sets of codewords which are also suitably "symmetric." For properties in this class, we show that the threshold rate is in fact equal to the lower bound that a simple first-moment calculation obtains. Our techniques not only pin down the threshold rate for the property P above, they give sharp bounds on the threshold rate for list-recovery in several parameter regimes, as well as an efficient algorithm for estimating the threshold rates for list-recovery in general.
We classify up to isomorphism optimal (v, 4, 1) binary cyclically permutable constant- weight (CPCW) codes with v (<=) 76 and cyclic 2-(73, 4, 1) and 2-(76, 4, 1) designs. There is a one-to-one correspondence betwe...
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We classify up to isomorphism optimal (v, 4, 1) binary cyclically permutable constant- weight (CPCW) codes with v (<=) 76 and cyclic 2-(73, 4, 1) and 2-(76, 4, 1) designs. There is a one-to-one correspondence between optimal (v, 4, 1) CPCW codes, optimal cyclic binary constant-weight codes with weight 4 and minimum distance 6, (v, 4;left perpendicular(v -1)/12righ perpendicular) difference packings, and optimal (v, 4, 1) optical orthogonal codes. Therefore, the classification of CPCW codes holds for them too. Perfect (v, 4, 1) CPCW codes are equivalent to (v, 4, 1) cyclic difference families, and thus (73, 4, 1) cyclic difference families are classified too.
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