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Artykuły w czasopismach na temat „Error correcting index codes”

Autor: Grafiati

Data publikacji: 6 września 2023

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1

Pedrosa, Valéria G., i Max H. M. Costa. "Index Coding with Multiple Interpretations". Entropy 24, nr 8 (18.08.2022): 1149. http://dx.doi.org/10.3390/e24081149.

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The index coding problem consists of a system with a server and multiple receivers with different side information and demand sets, connected by a noiseless broadcast channel. The server knows the side information available to the receivers. The objective is to design an encoding scheme that enables all receivers to decode their demanded messages with a minimum number of transmissions, referred to as an index code length. The problem of finding the minimum length index code that enables all receivers to correct a specific number of errors has also been studied. This work establishes a connection between index coding and error-correcting codes with multiple interpretations from the tree construction of nested cyclic codes. The notion of multiple interpretations using nested codes is as follows: different data packets are independently encoded, and then combined by addition and transmitted as a single codeword, minimizing the number of channel uses and offering error protection. The resulting packet can be decoded and interpreted in different ways, increasing the error correction capability, depending on the amount of side information available at each receiver. Motivating applications are network downlink transmissions, information retrieval from datacenters, cache management, and sensor networks.

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2

Hawkins, John A., Stephen K. Jones, Ilya J. Finkelstein i William H. Press. "Indel-correcting DNA barcodes for high-throughput sequencing". Proceedings of the National Academy of Sciences 115, nr 27 (20.06.2018): E6217—E6226. http://dx.doi.org/10.1073/pnas.1802640115.

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Many large-scale, high-throughput experiments use DNA barcodes, short DNA sequences prepended to DNA libraries, for identification of individuals in pooled biomolecule populations. However, DNA synthesis and sequencing errors confound the correct interpretation of observed barcodes and can lead to significant data loss or spurious results. Widely used error-correcting codes borrowed from computer science (e.g., Hamming, Levenshtein codes) do not properly account for insertions and deletions (indels) in DNA barcodes, even though deletions are the most common type of synthesis error. Here, we present and experimentally validate filled/truncated right end edit (FREE) barcodes, which correct substitution, insertion, and deletion errors, even when these errors alter the barcode length. FREE barcodes are designed with experimental considerations in mind, including balanced guanine-cytosine (GC) content, minimal homopolymer runs, and reduced internal hairpin propensity. We generate and include lists of barcodes with different lengths and error correction levels that may be useful in diverse high-throughput applications, including >106 single-error–correcting 16-mers that strike a balance between decoding accuracy, barcode length, and library size. Moreover, concatenating two or more FREE codes into a single barcode increases the available barcode space combinatorially, generating lists with >1015 error-correcting barcodes. The included software for creating barcode libraries and decoding sequenced barcodes is efficient and designed to be user-friendly for the general biology community.

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3

Karat, Nujoom Sageer, Simon Samuel i B. Sundar Rajan. "Optimal Error Correcting Index Codes for Some Generalized Index Coding Problems". IEEE Transactions on Communications 67, nr 2 (luty 2019): 929–42. http://dx.doi.org/10.1109/tcomm.2018.2878566.

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4

Thomas, Anoop, i B. Sundar Rajan. "A Discrete Polymatroidal Framework for Differential Error-Correcting Index Codes". IEEE Transactions on Communications 67, nr 7 (lipiec 2019): 4593–604. http://dx.doi.org/10.1109/tcomm.2019.2910266.

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5

Yao, Yu, Yuena Ma, Husheng Li i Jingjie Lv. "An explicit construction of quantum codes from one-generator generalized quasi-cyclic codes". MATEC Web of Conferences 336 (2021): 04001. http://dx.doi.org/10.1051/matecconf/202133604001.

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In this paper, we take advantage of a class of one-generator generalized quasi-cyclic (GQC) codes of index 2 to construct quantum error-correcting codes. By studying the form of Hermitian dual codes and their algebraic structure, we propose a sufficient condition for self-orthogonality of GQC codes with Hermitian inner product. By comparison, the quantum codes we constructed have better parameters than known codes.

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6

Kadiev, I. P., P. A. Kadiev i B. R. Kudaev. "INTERLEAVING BURST ERROR ELEMENTS IN INFORMATION ARRAYS USING THE METHOD OF INDEX STRUCTURISATION". Herald of Dagestan State Technical University. Technical Sciences 46, nr 4 (2.01.2020): 84–90. http://dx.doi.org/10.21822/2073-6185-2019-46-4-84-90.

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Objectives. “Burst errors” representing groups of accidentally or intentionally distorted or “erased” characters in blocks of information arrays violate the integrity of their content. However, the use of special codes for detecting and correcting such errors significantly reduces the speed of information transfer due to the need to introduce redundancy in the form of a large number of control characters. Therefore, this study sets out to develop a method for correcting burst errors.Method. A possible approach for correcting burst errors consists in interleaving preliminary permutations of information array elements between different array blocks. After eliminating the results of element permutations, these procedures cause the interleaving of distorted elements occurring during the transfer or storage of the information array between its various blocks, causing single or minor fold errors.Result. For solving problems of this class, a new method of permuting elements of an nxnset of finite sets is proposed based on the index structuring of the formed configurations. These sets are interpreted as information arrays of the same configuration, and the permutation – interleaving – of their elements is carried out according to the method of configuration formed by the index structuring of their location.Conclusion. Three methods for interleaving elements of the original information in arrays are proposed: between rows, between columns and combined – between rows and columns. The proposed interleaving methods based on the preliminary conversion of information arrays by permuting elements according to given algorithms allow their distortions under the influence of burst errors to be corrected. Thus, the task of combating the burst errors leading to the destruction of individual groups of characters can be reduced to solving a simpler problem of minor fold error correction.

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7

Sageer Karat, Nujoom, Anoop Thomas i Balaji Sundar Rajan. "Optimal Linear Error Correcting Delivery Schemes for Two Optimal Coded Caching Schemes". Entropy 22, nr 7 (13.07.2020): 766. http://dx.doi.org/10.3390/e22070766.

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For coded caching problems with small buffer sizes and the number of users no less than the amount of files in the server, an optimal delivery scheme was proposed by Chen, Fan, and Letaief in 2016. This scheme is referred to as the CFL scheme. In this paper, an extension to the coded caching problem where the link between the server and the users is error prone, is considered. The closed form expressions for average rate and peak rate of error correcting delivery scheme are found for the CFL prefetching scheme using techniques from index coding. Using results from error correcting index coding, an optimal linear error correcting delivery scheme for caching problems employing the CFL prefetching is proposed. Another scheme that has lower sub-packetization requirement as compared to CFL scheme for the same cache memory size was considered by J. Gomez-Vilardebo in 2018. An optimal linear error correcting delivery scheme is also proposed for this scheme.

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8

LIU, TAILIN, FENGTONG WEN i QIAOYAN WEN. "ON THE AUTOMORPHISM GROUPS OF A FAMILY OF BINARY QUANTUM ERROR-CORRECTING CODES". International Journal of Quantum Information 04, nr 06 (grudzień 2006): 1013–22. http://dx.doi.org/10.1142/s0219749906002377.

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Based on the classical binary simplex code [Formula: see text] and any fixed-point-free element f of [Formula: see text], Calderbank et al. constructed a binary quantum error-correcting code [Formula: see text]. They proved that [Formula: see text] has a normal subgroup H, which is a semidirect product group of the centralizer Z(f) of f in GLm(2) with [Formula: see text], and the index [Formula: see text] is the number of elements of Ff = {f, 1 - f, 1/f, 1 - 1/f, 1/(1 - f), f/(1 - f)} that are conjugate to f. In this paper, a theorem to describe the relationship between the quotient group [Formula: see text] and the set Ff is presented, and a way to find the elements of Ff that are conjugate to f is proposed. Then we prove that [Formula: see text] is isomorphic to S3 and H is a semidirect product group of [Formula: see text] with [Formula: see text] in the linear case. Finally, we generalize a result due to Calderbank et al.

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9

Indoonundon, Deevya, Tulsi Pawan Fowdur i Sunjiv Soyjaudah. "A Concealment Aware UEP scheme for H.264 using RS Codes". Indonesian Journal of Electrical Engineering and Computer Science 6, nr 3 (1.06.2017): 671. http://dx.doi.org/10.11591/ijeecs.v6.i3.pp671-681.

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<p>H.264/AVC is currently the most widely adopted video coding standard due to its high compression capability and flexibility. However, compressed videos are highly vulnerable to channel errors which may result in severe quality degradation of a video. This paper presents a concealment aware Unequal Error Protection (UEP) scheme for H.264 video compression using Reed Solomon (RS) codes. The proposed UEP technique assigns a code rate to each Macroblock (MB) based on the type of concealment and a Concealment Dependent Index (CDI). Two interleaving techniques, namely Frame Level Interleaving (FLI) and Group Level Interleaving (GLI) have also been employed. Finally, prioritised concealment is applied in cases where error correction is beyond the capability of the RS decoder. Simulation results have demonstrated that the proposed framework provides an average gain of 2.96 dB over a scheme that used Equal Error Protection (EEP).</p>

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10

Haeupler, Bernhard, i Amirbehshad Shahrasbi. "Synchronization Strings: Codes for Insertions and Deletions Approaching the Singleton Bound". Journal of the ACM 68, nr 5 (31.10.2021): 1–39. http://dx.doi.org/10.1145/3468265.

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We introduce synchronization strings , which provide a novel way to efficiently deal with synchronization errors , i.e., insertions and deletions. Synchronization errors are strictly more general and much harder to cope with than more commonly considered Hamming-type errors , i.e., symbol substitutions and erasures. For every ε > 0, synchronization strings allow us to index a sequence with an ε -O(1) -size alphabet, such that one can efficiently transform k synchronization errors into (1 + ε)k Hamming-type errors . This powerful new technique has many applications. In this article, we focus on designing insdel codes , i.e., error correcting block codes (ECCs) for insertion-deletion channels. While ECCs for both Hamming-type errors and synchronization errors have been intensely studied, the latter has largely resisted progress. As Mitzenmacher puts it in his 2009 survey [30]: “ Channels with synchronization errors...are simply not adequately understood by current theory. Given the near-complete knowledge, we have for channels with erasures and errors...our lack of understanding about channels with synchronization errors is truly remarkable. ” Indeed, it took until 1999 for the first insdel codes with constant rate, constant distance, and constant alphabet size to be constructed and only since 2016 are there constructions of constant rate insdel codes for asymptotically large noise rates. Even in the asymptotically large or small noise regimes, these codes are polynomially far from the optimal rate-distance tradeoff. This makes the understanding of insdel codes up to this work equivalent to what was known for regular ECCs after Forney introduced concatenated codes in his doctoral thesis 50 years ago. A straightforward application of our synchronization strings-based indexing method gives a simple black-box construction that transforms any ECC into an equally efficient insdel code with only a small increase in the alphabet size. This instantly transfers much of the highly developed understanding for regular ECCs into the realm of insdel codes. Most notably, for the complete noise spectrum, we obtain efficient “near-MDS” insdel codes, which get arbitrarily close to the optimal rate-distance tradeoff given by the Singleton bound. In particular, for any δ ∈ (0,1) and ε > 0, we give a family of insdel codes achieving a rate of 1 - δ - ε over a constant-size alphabet that efficiently corrects a δ fraction of insertions or deletions.

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11

Gao, Youtao, Guocang Dong i Limin Jin. "Design of An Intelligent Demodulation Method for X-ray Spectrum Communication". Journal of Physics: Conference Series 2447, nr 1 (1.03.2023): 012001. http://dx.doi.org/10.1088/1742-6596/2447/1/012001.

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Abstract X-ray communication based on X-ray spectrum modulation information is a novel communication method, which can effectively improve communication ability and anti-interference ability. In this paper, four characteristic X-rays are chosen to modulate information. The influence of channel attenuation, random noise in space, and miss-shooting rate caused by adjacent targets are discussed. Based on error-correcting output codes and a 10-fold cross-validation method, a neural network intelligent classifier is designed to realize intelligent information demodulation. Simulation results show that if the miss-shooting rate is lower than 0.4 and the photon retention rate after channel attenuation is higher than 0.0008, then the classifier can achieve a recognition success rate of more than 99%. This study provides reliable index requirements for the performance of the four-target material source equipment to be designed next. This paper also provides a theoretical basis for the subsequent further realization of space communication capabilities.

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12

Ghosh, Prabir Kumar, i Soumyananda Dinda. "Revisited the Relationship Between Economic Growth and Transport Infrastructure in India: An Empirical Study". Indian Economic Journal 70, nr 1 (21.12.2021): 34–52. http://dx.doi.org/10.1177/00194662211063535.

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This study empirically re-examines the relationship between transport infrastructure and economic growth in India for the period 1990–2017. Multivariate dynamic models are applied to estimate the relationship between economic growth and different modes of transport infrastructure namely road, rail and air transports in the vector error correction model framework. The results reveal that road and air transports have significant positive contribution to economic growth in the long-run while rail transport is insignificant. This study further examines the said issue using unit free index variables and has constructed a composite index of transport infrastructure using principal component analysis to analyse the nexus between aggregate transport infrastructure and economic growth in India in the post globalisation era. The results of the study indicate the bidirectional causality between aggregate transport infrastructure and economic growth. Results of this study suggest incorporating feedback issue in policy formulations. JEL Codes: C22, O18, R4

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13

Hannah, J. "Error Correcting Codes". Irish Mathematical Society Bulletin 0022 (1989): 60–65. http://dx.doi.org/10.33232/bims.0022.60.65.

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14

Shankar, Priti. "Error correcting codes". Resonance 2, nr 1 (styczeń 1997): 34–43. http://dx.doi.org/10.1007/bf02838778.

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15

Shankar, Priti. "Error correcting codes". Resonance 2, nr 3 (marzec 1997): 33–47. http://dx.doi.org/10.1007/bf02838967.

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Shankar, Priti. "Error correcting codes". Resonance 1, nr 10 (październik 1996): 26–36. http://dx.doi.org/10.1007/bf02839095.

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17

Belhamra, Mohamed Amine, i El Mamoun Souidi. "Error Correcting Network Codes". Computer Networks 197 (październik 2021): 108277. http://dx.doi.org/10.1016/j.comnet.2021.108277.

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18

Ahlswede, R., B. Balkenhol i Ning Cai. "Parallel error correcting codes". IEEE Transactions on Information Theory 48, nr 4 (kwiecień 2002): 959–62. http://dx.doi.org/10.1109/18.992800.

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19

Zemor, G., i G. D. Cohen. "Error-correcting WOM-codes". IEEE Transactions on Information Theory 37, nr 3 (maj 1991): 730–34. http://dx.doi.org/10.1109/18.79943.

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20

Roth, Ron M. "Analog Error-Correcting Codes". IEEE Transactions on Information Theory 66, nr 7 (lipiec 2020): 4075–88. http://dx.doi.org/10.1109/tit.2020.2977918.

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21

Sabin, Roberta Evans, i Samuel J. Lomonaco. "Metacyclic error-correcting codes". Applicable Algebra in Engineering, Communication and Computing 6, nr 3 (maj 1995): 191–210. http://dx.doi.org/10.1007/bf01195337.

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Haider, Salman, Aadil Ahmad Ganaie i Bandi Kamaiah. "Total Factor Productivity and Openness in Indian Economy: 1970–2011". Foreign Trade Review 54, nr 1 (24.12.2018): 46–57. http://dx.doi.org/10.1177/0015732518810835.

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The present article aims to explore the causal link between total factor productivity (TFP) and openness in the Indian economy during the period 1970–2011. The study employs the cointegration and error-correction approach, along with Granger causality test. The TFP index used in the study is based on the Tornqvist index and export plus import as a percentage of GDP is used as a measure of openness. It is found that trade openness is cointegrated with TFP using the autoregressive distributed lag (ARDL) method. In the short run, there is evidence of unidirectional Granger causality running from trade openness to total factor productivity. The finding suggests that heavy protection for the domestic industry would deprive the country of efficiency gains in the long run. The resultant effect would be the wastage of resources. For a developing country, lower efficiency levels will halt the process of development. However, enhancement of TFP can not only be due to increase in trade, along with it, the investment in human and physical capital are also better avenues to be taken care of. JEL Codes: F10 O40 O33 C22

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23

Duan, Lu-Ming, i Guang-Can Guo. "Quantum error avoiding codes verses quantum error correcting codes". Physics Letters A 255, nr 4-6 (maj 1999): 209–12. http://dx.doi.org/10.1016/s0375-9601(99)00183-8.

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24

Misra, Rekha, i Sonam Choudhry. "Trade War: Likely Impact on India". Foreign Trade Review 55, nr 1 (13.01.2020): 93–118. http://dx.doi.org/10.1177/0015732519886793.

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The global financial crisis triggered the built up of domestic pressure in some countries to introduce protectionist measures against imports. The present discussion regarding the ‘trade war’ and ‘de-globalisation’ intensified after both the US and China escalated the tariff rates on imports originating in the US and China. This study evaluates the potential economic effects of the substantial tariff hikes by these two major economies on Brazil, Russia, India, China and South Africa, particularly for India. The study adds to the existing literature on the trade war by examining potential impact on India’s exports, that is, both direct and indirect losses as well as benefits arising due to the trade war using the economic model based on the trend in trade flows, similarity index and supply chain networks using World Input-Output tables. The study uses the Vector Error Correction Model to empirically evaluate the pass-through of the tariff hike on Indian exports using bilateral real effective exchange rate (REER)-consumer price index and REER-product price index. The study finds that the US–China trade tussle may provide some opportunities in short to medium run for India as gains through trade deflection would be higher than the losses due to trade reduction. However, in the long-run, further escalation of tariffs will have negative impact at the global level. JEL Codes: F1, F62, F68

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25

van Tilborg, H., i M. Blaum. "On error-correcting balanced codes". IEEE Transactions on Information Theory 35, nr 5 (1989): 1091–95. http://dx.doi.org/10.1109/18.42227.

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26

Ostergard, P. R. J., i M. K. Kaikkonen. "New single-error-correcting codes". IEEE Transactions on Information Theory 42, nr 4 (lipiec 1996): 1261–62. http://dx.doi.org/10.1109/18.508854.

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Rattan, S. S. "Transparency of Error Correcting Codes". IETE Journal of Education 36, nr 2-3 (kwiecień 1995): 85–91. http://dx.doi.org/10.1080/09747338.1995.11415619.

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28

Köppłer, Ulrike. "3 Error- Correcting Goppa Codes". Journal of Information and Optimization Sciences 7, nr 2 (maj 1986): 227–34. http://dx.doi.org/10.1080/02522667.1986.10698854.

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29

Buttigieg, V., i P. G. Farrell. "Variable-length error-correcting codes". IEE Proceedings - Communications 147, nr 4 (2000): 211. http://dx.doi.org/10.1049/ip-com:20000407.

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30

Cohn, Henry, i Yufei Zhao. "Energy-Minimizing Error-Correcting Codes". IEEE Transactions on Information Theory 60, nr 12 (grudzień 2014): 7442–50. http://dx.doi.org/10.1109/tit.2014.2359201.

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31

Chau, H. F. "Quantum convolutional error-correcting codes". Physical Review A 58, nr 2 (1.08.1998): 905–9. http://dx.doi.org/10.1103/physreva.58.905.

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32

Weber, Jos H., Kees A. Schouhamer Immink i Hendrik C. Ferreira. "Error-Correcting Balanced Knuth Codes". IEEE Transactions on Information Theory 58, nr 1 (styczeń 2012): 82–89. http://dx.doi.org/10.1109/tit.2011.2167954.

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33

Yaakobi, Eitan, Paul H. Siegel, Alexander Vardy i Jack K. Wolf. "Multiple Error-Correcting WOM-Codes". IEEE Transactions on Information Theory 58, nr 4 (kwiecień 2012): 2220–30. http://dx.doi.org/10.1109/tit.2011.2176465.

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Sethi, Amita. "Mixed Burst Error Correcting Codes". International Journal of Mathematics Trends and Technology 46, nr 1 (25.06.2017): 22–28. http://dx.doi.org/10.14445/22315373/ijmtt-v46p505.

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35

Windridge, David, Riccardo Mengoni i Rajagopal Nagarajan. "Quantum error-correcting output codes". International Journal of Quantum Information 16, nr 08 (grudzień 2018): 1840003. http://dx.doi.org/10.1142/s0219749918400038.

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Quantum machine learning is the aspect of quantum computing concerned with the design of algorithms capable of generalized learning from labeled training data by effectively exploiting quantum effects. Error-correcting output codes (ECOC) are a standard setting in machine learning for efficiently rendering the collective outputs of a binary classifier, such as the support vector machine, as a multi-class decision procedure. Appropriate choice of error-correcting codes further enables incorrect individual classification decisions to be effectively corrected in the composite output. In this paper, we propose an appropriate quantization of the ECOC process, based on the quantum support vector machine. We will show that, in addition to the usual benefits of quantizing machine learning, this technique leads to an exponential reduction in the number of logic gates required for effective correction of classification error.

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36

Ruján, Pál. "Finite temperature error-correcting codes". Physical Review Letters 70, nr 19 (10.05.1993): 2968–71. http://dx.doi.org/10.1103/physrevlett.70.2968.

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Escalera, Sergio, David Masip, Eloi Puertas, Petia Radeva i Oriol Pujol. "Online error correcting output codes". Pattern Recognition Letters 32, nr 3 (luty 2011): 458–67. http://dx.doi.org/10.1016/j.patrec.2010.11.005.

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38

Lalam, Massinissa, Karine Amis i Dominique Leroux. "Space-time error correcting codes". IEEE Transactions on Wireless Communications 7, nr 5 (maj 2008): 1472–76. http://dx.doi.org/10.1109/twc.2008.060866.

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Munuera, C. "Steganography and error-correcting codes". Signal Processing 87, nr 6 (czerwiec 2007): 1528–33. http://dx.doi.org/10.1016/j.sigpro.2006.12.008.

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40

Tonchev, Vladimir D. "Error-correcting codes from graphs". Discrete Mathematics 257, nr 2-3 (listopad 2002): 549–57. http://dx.doi.org/10.1016/s0012-365x(02)00513-7.

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41

Steane, A. M. "Simple quantum error-correcting codes". Physical Review A 54, nr 6 (1.12.1996): 4741–51. http://dx.doi.org/10.1103/physreva.54.4741.

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42

Hilden, H. M., D. G. Howe i E. J. Weldon. "Shift error correcting modulation codes". IEEE Transactions on Magnetics 27, nr 6 (listopad 1991): 4600–4605. http://dx.doi.org/10.1109/20.278897.

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Hwang, Tzonelih, i T. R. N. Rao. "Secret Error-Correcting Codes (SECC)". IETE Journal of Research 36, nr 5-6 (wrzesień 1990): 362–67. http://dx.doi.org/10.1080/03772063.1990.11436907.

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Imai, Hideki, i Manabu Hagiwara. "Error-correcting codes and cryptography". Applicable Algebra in Engineering, Communication and Computing 19, nr 3 (2.04.2008): 213–28. http://dx.doi.org/10.1007/s00200-008-0074-0.

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45

Parthasarathy, K. R. "An inducing construction of quantum codes from classical error correcting codes". Journal of Applied Probability 38, A (2001): 27–32. http://dx.doi.org/10.1239/jap/1085496587.

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The aim of the present paper is to construct error correcting quantum codes from classical error correcting group codes by using the Schur orthogonality relations for characters of a finite abelian group and the Knill–Laflamme criterion for a quantum code to correct a pre-assigned family of errors. This is an abstraction and generalization of Shor's example of a nine qubit single error correcting quantum code.

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46

Parthasarathy, K. R. "An inducing construction of quantum codes from classical error correcting codes". Journal of Applied Probability 38, A (2001): 27–32. http://dx.doi.org/10.1017/s002190020011263x.

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The aim of the present paper is to construct error correcting quantum codes from classical error correcting group codes by using the Schur orthogonality relations for characters of a finite abelian group and the Knill–Laflamme criterion for a quantum code to correct a pre-assigned family of errors. This is an abstraction and generalization of Shor's example of a nine qubit single error correcting quantum code.

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47

Conway, J., i N. Sloane. "Lexicographic codes: Error-correcting codes from game theory". IEEE Transactions on Information Theory 32, nr 3 (maj 1986): 337–48. http://dx.doi.org/10.1109/tit.1986.1057187.

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48

QIAN, JIANFA, WENPING MA i XINMEI WANG. "QUANTUM ERROR-CORRECTING CODES FROM QUASI-CYCLIC CODES". International Journal of Quantum Information 06, nr 06 (grudzień 2008): 1263–69. http://dx.doi.org/10.1142/s0219749908004444.

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Quasi-cyclic codes form a generalization of cyclic codes, and contain a large number of record breaking codes. In this paper, we provide a method for constructing self-orthogonal quasi-cyclic codes, and obtain a large number of new quantum quasi-cyclic codes by CSS construction.

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QIAN, JIANFA, WENPING MA i WANGMEI GUO. "QUANTUM CODES FROM CYCLIC CODES OVER FINITE RING". International Journal of Quantum Information 07, nr 06 (wrzesień 2009): 1277–83. http://dx.doi.org/10.1142/s0219749909005560.

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A new method to obtain self-orthogonal codes over finite field F2 is presented. Based on this method, we provide a construction for quantum error-correcting codes starting from cyclic codes over finite ring R = F2 + uF2. As an example, we present infinite families of quantum error-correcting codes which are derived from cyclic codes over the ring R = F2 + uF2.

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Beniwal, Gaurav. "Capacity Achieving Forward Error Correcting Codes". International Journal for Research in Applied Science and Engineering Technology 6, nr 5 (31.05.2018): 638–43. http://dx.doi.org/10.22214/ijraset.2018.5107.

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