Relevant bibliographies by topics / Lattice code

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Lattice code'

Author: Grafiati
Published: 4 June 2021
Last updated: 6 February 2022

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Journal articles on the topic "Lattice code"

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Damen, O., A. Chkeif, and J. C. Belfiore. "Lattice code decoder for space-time codes." IEEE Communications Letters 4, no. 5 (May 2000): 161–63. http://dx.doi.org/10.1109/4234.846498.

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Mathis, Alexander, Andreas V. M. Herz, and Martin Stemmler. "Optimal Population Codes for Space: Grid Cells Outperform Place Cells." Neural Computation 24, no. 9 (September 2012): 2280–317. http://dx.doi.org/10.1162/neco_a_00319.

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Rodents use two distinct neuronal coordinate systems to estimate their position: place fields in the hippocampus and grid fields in the entorhinal cortex. Whereas place cells spike at only one particular spatial location, grid cells fire at multiple sites that correspond to the points of an imaginary hexagonal lattice. We study how to best construct place and grid codes, taking the probabilistic nature of neural spiking into account. Which spatial encoding properties of individual neurons confer the highest resolution when decoding the animal's position from the neuronal population response? A priori, estimating a spatial position from a grid code could be ambiguous, as regular periodic lattices possess translational symmetry. The solution to this problem requires lattices for grid cells with different spacings; the spatial resolution crucially depends on choosing the right ratios of these spacings across the population. We compute the expected error in estimating the position in both the asymptotic limit, using Fisher information, and for low spike counts, using maximum likelihood estimation. Achieving high spatial resolution and covering a large range of space in a grid code leads to a trade-off: the best grid code for spatial resolution is built of nested modules with different spatial periods, one inside the other, whereas maximizing the spatial range requires distinct spatial periods that are pairwisely incommensurate. Optimizing the spatial resolution predicts two grid cell properties that have been experimentally observed. First, short lattice spacings should outnumber long lattice spacings. Second, the grid code should be self-similar across different lattice spacings, so that the grid field always covers a fixed fraction of the lattice period. If these conditions are satisfied and the spatial “tuning curves” for each neuron span the same range of firing rates, then the resolution of the grid code easily exceeds that of the best possible place code with the same number of neurons.
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KENDZIORRA, ANDREAS, and STEFAN E. SCHMIDT. "NETWORK CODING WITH MODULAR LATTICES." Journal of Algebra and Its Applications 10, no. 06 (December 2011): 1319–42. http://dx.doi.org/10.1142/s0219498811005208.

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Kötter and Kschischang presented in 2008 a new model for error correcting codes in network coding. The alphabet in this model is the subspace lattice of a given vector space, a code is a subset of this lattice and the used metric on this alphabet is the map d : (U, V) ↦ dim (U+V)- dim (U∩V). In this paper we generalize this model to arbitrary modular lattices, i.e. we consider codes, which are subsets of modular lattices. The used metric in this general case is the map d : (u, v) ↦ h(u ∨ v) - h(u ∧ v), where h is the height function of the lattice. We apply this model to submodule lattices. Moreover, we show a method to compute the size of spheres in certain modular lattices and present a sphere packing bound, a sphere covering bound, and a Singleton bound for codes, which are subsets of modular lattices.
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Choi, Sooyoung, Azamat Khassenov, and Deokjung Lee. "ICONE23-1905 RESONANCE INTERFERENCE METHOD IN LATTICE PHYSICS CODE STREAM." Proceedings of the International Conference on Nuclear Engineering (ICONE) 2015.23 (2015): _ICONE23–1—_ICONE23–1. http://dx.doi.org/10.1299/jsmeicone.2015.23._icone23-1_430.

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Jain, Sapna. "Singleton's Bound in Euclidean Codes." Algebra Colloquium 17, spec01 (December 2010): 741–48. http://dx.doi.org/10.1142/s1005386710000714.

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There are three standard weight functions on a linear code viz. the Hamming weight, Lee weight and Euclidean weight. The Euclidean weight function is useful in connection with the lattice constructions, where the minimum norm of vectors in the lattice is related to the minimum Euclidean weight of the code. In this paper, we obtain Singleton's bound for Euclidean codes and introduce maximum Euclidean square distance separable (MESDS) codes.
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Wan, Qian, Kai Niu, and Jia Ru Lin. "K-Best Sphere Decoding of Lattice Codes Based on CRC Code." Applied Mechanics and Materials 321-324 (June 2013): 2864–67. http://dx.doi.org/10.4028/www.scientific.net/amm.321-324.2864.

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This work proposes a CRC-aided K-best sphere decoding scheme to improve the performance of lattice codes. The generator of the lattice is designed as to be an upper triangular, which is naturally suited for sphere decoding. When the K is sufficiently large, the naïve K-best sphere decoding can approach the lower bound of block error rate (BLER) of maximum likelihood (ML). Therefore, the proposed scheme can outperforms the naïve K-best sphere decoding with the assistance of CRC code.
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Conway, J., and N. Sloane. "Soft decoding techniques for codes and lattices, including the Golay code and the Leech lattice." IEEE Transactions on Information Theory 32, no. 1 (January 1986): 41–50. http://dx.doi.org/10.1109/tit.1986.1057135.

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Krause, Mathias J., Adrian Kummerländer, Samuel J. Avis, Halim Kusumaatmaja, Davide Dapelo, Fabian Klemens, Maximilian Gaedtke, et al. "OpenLB—Open source lattice Boltzmann code." Computers & Mathematics with Applications 81 (January 2021): 258–88. http://dx.doi.org/10.1016/j.camwa.2020.04.033.

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Harada, Masaaki, and Masaaki Kitazume. "Z6-Code Constructions of the Leech Lattice and the Niemeier Lattices." European Journal of Combinatorics 23, no. 5 (July 2002): 573–81. http://dx.doi.org/10.1006/eujc.2002.0557.

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Horsman, Clare, Austin G. Fowler, Simon Devitt, and Rodney Van Meter. "Surface code quantum computing by lattice surgery." New Journal of Physics 14, no. 12 (December 7, 2012): 123011. http://dx.doi.org/10.1088/1367-2630/14/12/123011.

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Dissertations / Theses on the topic "Lattice code"

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Prahatheesan, Vicknarajah. "A lattice filter for CDMA overlay." Thesis, Hong Kong : University of Hong Kong, 1998. http://sunzi.lib.hku.hk/hkuto/record.jsp?B20665684.

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Landelius, Kim. "Qualification of WestinghouseBWR lattice physics methods againstcritical experiments." Thesis, Uppsala universitet, Institutionen för fysik och astronomi, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-310815.

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This thesis is part of a larger qualification effortperformed at Westinghouse Electric Sweden AB of the PHOENIX5 latticephysics code. The aim of the thesis is to validate PHOENIX5 withregards to cold criticality tests performed at the Toshiba NCAfacility in 2010-2011. For this, 26 different models were built torepresent the experiments performed by Toshiba in PHOENIX5. As anindependent reference, models were also built for the probabilisticMonte Carlo code SERPENT. The parameters examined in this thesis arethe criticality of the system, as well as the pin fission rates forselected experiments. Two different PHOENIX5 libraries were utilized,along with a HELIOS library. The results show that there is a Kinf trend between the differentlibraries. Furthermore, a void trend was found. This void trend waspresent for all models, including the SERPENT models. Pin fissionrate predictions give results close to those of the experiments forboth PHOENIX5 libraries. The system also proved sensitive to meshingchanges, as well as for the chosen water reflector width.
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Flygare, Mattias. "Non-abelian braiding in abelian lattice models from lattice dislocations." Thesis, Karlstads universitet, Institutionen för ingenjörsvetenskap och fysik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-31690.

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Topological order is a new field of research involving exotic physics. Among other things it has been suggested as a means for realising fault-tolerant quantum computation. Topological degeneracy, i.e. the ground state degeneracy of a topologically ordered state, is one of the quantities that have been used to characterize such states. Topological order has also been suggested as a possible quantum information storage. We study two-dimensional lattice models defined on a closed manifold, specifically on a torus, and find that these systems exhibit topological degeneracy proportional to the genus of the manifold on which they are defined. We also find that the addition of lattice dislocations increases the ground state degeneracy, a behaviour that can be interpreted as artificially increasing the genus of the manifold. We derive the fusion and braiding rules of the model, which are then used to calculate the braiding properties of the dislocations themselves. These turn out to resemble non-abelian anyons, a property that is important for the possibility to achieve universal quantum computation. One can also emulate lattice dislocations synthetically, by adding an external field. This makes them more realistic for potential experimental realisations.
Topologisk ordning är ett nytt område inom fysik som bland annat verkar lovande som verktyg för förverkligandet av kvantdatorer. En av storheterna som karakteriserar topologiska tillstånd är det totala antalet degenererade grundtillstånd, den topologiska degenerationen. Topologisk ordning har också föreslagits som ett möjligt sätt att lagra kvantdata. Vi undersöker tvådimensionella gittermodeller definierade på en sluten mångfald, specifikt en torus, och finner att dessa system påvisar topologisk degeneration som är proportionerlig mot mångfaldens topologiska genus. När dislokationer introduceras i gittret finner vi att grundtillståndets degeneration ökar, något som kan ses som en artificiell ökning av mångfaldens genus. Vi härleder sammanslagningsregler och flätningsregler för modellen och använder sedan dessa för att räkna ut flätegenskaperna hos själva dislokationerna. Dessa visar sig likna icke-abelska anyoner, en egenskap som är viktiga för möjligheten att kunna utföra universella kvantberäkningar. Det går också att emulera dislokationer i gittret genom att lägga på ett yttre fält. Detta gör dem mer realistiska för eventuella experimentella realisationer.
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Pedersen, Daniel. "Development of a Kinetic Monte Carlo Code." Thesis, Uppsala universitet, Materialteori, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-202711.

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A framework for constructing kinetic monte carlo (KMC) simulations of diffusive events on a lattice was developed. This code was then tested by running simulations of Fe adatom diffusion on graphene and graphene-boron nitride surfaces. The results from these simulations was then used to show that the modeled diffusion adheres to the laws of brownian motion and generates results similar to recent research findings.
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Ferdinand, N. S. (Nuwan Suresh). "Low complexity lattice codes for communication networks." Doctoral thesis, Oulun yliopisto, 2016. http://urn.fi/urn:isbn:9789526210964.

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Abstract Lattice codes achieve AWGN capacity and naturally fit in many multi-terminal networks because of their inherited structure. Although extensive information theoretic research has been done to prove the importance of lattice codes for these networks, the progress in finding practical low-complexity lattice schemes is limited. Hence, the motivation of this thesis is to develop several methods to make lattice codes practical for communication networks. First, we propose an efficient lattice coding scheme for real-valued, full-duplex one- and two-way relay channels. Lattice decomposition, superposition, and block Markov encoding are used to propose a simple, yet near capacity achieving encoding/decoding schemes for these relay channels. By using information theoretic tools, we prove the achievable rates of these schemes, which are equal to the best known rates. Then, we construct practical, low-complexity implementations of the proposed relay schemes using low-density lattice codes. Numerical evaluation is presented and they show that our schemes achieve performance as close as 2.5dB away from theoretical limits. The effect of shaping/coding loss on the performance of relay channels is studied. Then, we propose a low complexity lattice code construction that provides high shaping and coding gains. First, integer information is encoded to shaped integers. Two methods are proposed for this task: ''Voronoi integers'' and ''non uniform integers''. These shaped integers have shaping gains over the integer lattice. Then for the second step, we present a general framework to systematically encode these integers, using any high dimensional lattice with lower-triangular generator or parity check matrices, retaining the same shaping gain. The proposed scheme can be used to shape high dimensional lattices such as low density lattice codes, LDA-lattice, etc. Comprehensive analysis is presented using low density lattice codes. By using E8 and BW16 as shaping lattices, we numerically show the Voronoi integers result in the shaping gain of these lattices, that is, as much as 0.65dB and 0.86dB. It is numerically observed that non-uniform integers have shaping gains of up to 1.25dB. These shaping operations can be implemented with less complexity than previous low density lattice codes shaping approaches and shaping gains are higher than in previously reported cases, which are in the order of 0.4dB. Lastly, we propose a low complexity practical code construction for compute-and-forward. A novel code construction called ''mixed nested lattice code construction'' is developed. This code construction uses a pair of distinct nested lattices to encode the integers where shaping is provided by a small dimensional lattice with high shaping gain and coding is performed using a high coding gain and a high dimensional lattice. This construction keeps the shaping and the coding gains of respective shaping and coding lattices. Further, we prove an existence of an isomorphism in this construction such that linear combination of lattice codes can be mapped to a linear combination of integers over a finite field. Hence, this construction can be readily used for any compute-and-forward applications. A modified LDLC decoder is proposed to estimate a linear combination of messages. Performance is numerically evaluated
Tiivistelmä Hilakoodit saavuttavat AWGN kapasiteetin ja sopivat luonnollisesti moniin monen päätelaitteen verkkoihin niihin sisältyvän rakenteen vuoksi. Vaikka lukuisat informaatioteoreettiset tutkimustyöt todistavat hilakoodien tärkeyden näille verkoille, käytännössä alhaisen kompleksisuuden hilajärjestelmiä on vielä vähän. Näin ollen tämän tutkielman tarkoitus on kehittää useita metodeja, jotta hilakoodeista saadaan käytännöllisiä viestintäverkkoihin. Aluksi, ehdotamme tehokkaan hilakoodausjärjestelmän reaaliarvoisille, full duplexisille yksi- ja kaksisuuntaisille välittäjäkanaville. Käytämme hilan hajottamista, superpositiota ja lohko-Markov -koodausta ehdottaessamme yksinkertaiset ja siltikin kapasiteetin saavuttavat koodaus- ja dekoodausjärjestelmät näihin välityskanaviin. Käyttämällä informaatioteoreettisia työkaluja, osoitamme näiden järjestelmien saavutettavat nopeudet, jotka ovat yhtä suuret kuin parhaimmat tunnetut nopeudet. Sitten rakennamme käytännölliset ja alhaisen monimutkaisuuden toteutukset ehdotetuille välitysjärjestelmille käyttäen alhaisen tiheyden hilakoodeja. Esitämme näille järjestelmille numeeriset arvioinnit, jotka näyttävät että nämä toteutukset saavuttavat tehokkuuden, joka on 2.5dB:n päässä teoreettisista rajoista. Tutkimme muotoilu- ja koodaushäviön vaikutusta välityskanavien tehokkuuteen. Sitten, ehdotamme alhaisen monimutkaisuuden hilakoodirakenteen, joka tarjoaa korkean muotoilu- ja koodausvahvistuksen. Ensin, kokonaislukuinformaatio on koodattu muotoiltuihin kokonaislukuihin. Esitämme kaksi metodia tähän tehtävään; 'Voronoi kokonaisluvut' ja 'ei yhtenäiset kokonaisluvut'. Näillä muotoilluilla kokonaisluvuilla on muotoiluvahvistusta kokonaislukuhilalle. Toisena askeleena, esitämme yleiset puitteet systemaattiseen kokonaislukujen koodaukseen käyttäen korkeaulotteisia hiloja alhaisen kolmiogeneraattori- tai pariteettivarmistusmatriiseja, jotka säilyttävät samalla muotoiluvahvistuksen. Ehdotettua järjestelmää voidaan käyttää muotoilemaan korkeaulotteisia hiloja kuten alhaisen tiheyden hilakoodeja, LDA-hiloja, jne. Esitämme kattavan analyysin käyttäen alhaisen tiheyden hilakoodeja. Käyttämällä muotoiluhiloina E8aa ja BW16a, näytämme numeerisesti 'Voronoi kokonaislukujen' käyttämisen seurauksena saavutettavat hilojen muotoiluvahvistukset, jotka ovat jopa 0.65dB ja 0.86dB. Näytämme myös numeerisesti että 'ei yhtenäisillä kokonaisluvuilla' on muotoiluvahvistusta jopa 1.25dB. Nämä muotoiluoperaatiot voidaan toteuttaa alhaisemmalla monimutkaisuudella kuin aikaisemmat 'alhaisen tiheyden hilakoodien muotoilumenetelmät' ja muotoiluvahvistukset ovat suuremmat kuin aikaisemmin raportoidut tapaukset, jotka ovat suuruusluokaltaan 0.4dB. Viimeiseksi, ehdotamme käytännöllisen koodikonstruktion alhaisella monimutkaisuudella 'laske ja lähetä' -menetelmään. Kehitämme uuden koodikonstruktion, jota kutsumme 'sekoitetuksi sisäkkäiseksi hilakoodikonstruktioksi'. Tämä koodikonstruktio käyttää kahta eroteltavissa olevaa sisäkkäistä hilaa koodaamaan kokonaisluvut siellä, missä muotoilu tehdään pienen ulottuvuuden hiloilla korkean muotoiluvahvistuksella ja koodaus toteutetaan käyttäen korkean koodausvahvistuksen omaavaa korkeaulottuvuuksista hilaa. Tämä konstruktio säilyttää muotoilu- ja koodausvahvistukset kullekin muotoilu- ja koodaushilalle. Lisäksi, todistamme isomorfismin olemassaolon tässä konstruktiossa siten, että lineaarisen hilakoodien kombinaatio voidaan kuvata lineaarisena kokonaislukujen kombinaationa äärellisessä kunnassa. Näin ollen tätä konstruktiota voidaan helposti käyttää missä tahansa 'laske ja lähetä' -sovelluksessa. Esitämme muokatun LDLC dekooderin lineaarisen viestikombinaation estimointiin. Arvioimme tehon numeerisesti
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Boufatah, Samir. "Effects of Code Dimension in Lattice-Reduction-Aided MIMO Receivers : Optimality in Diversity-Multiplexing Tradeoff." Thesis, KTH, Signalbehandling, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-53770.

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Junla, Nakorn. "Classification of certain genera of codes, lattices and vertex operator algebras." Diss., Kansas State University, 2014. http://hdl.handle.net/2097/18181.

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Doctor of Philosophy
Department of Mathematics
Gerald H. Höhn
We classify the genera of doubly even binary codes, the genera of even lattices, and the genera of rational vertex operator algebras (VOAs) arising from the modular tensor categories (MTCs) of rank up to 4 and central charges up to 16. For the genera of even lattices, there are two types of the genera: code type genera and non code type genera. The number of the code type genera is finite. The genera of the lattices of rank larger than or equal to 17 are non code type. We apply the idea of a vector valued modular form and the representation of the modular group SL[subscript]2(Z) in [Bantay2007] to classify the genera of the VOAs arising from the MTCs of ranks up to 4 and central charges up to 16.
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Tulip, Paul Robert. "Dielectric and lattice dynamical properties of molecular crystals via density functional perturbation theory : implementation within a first principles code." Thesis, Durham University, 2004. http://etheses.dur.ac.uk/2969/.

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Organic molecular crystals form a condensed solid phase offering a rich vein of physical phenomena which are open to investigation. The desire to harness these properties for technological and biological purposes has led to extensive experimental and theoretical investigations. The naturally occurring ɑ-amino acids form molecular crystals in the solid state; to date there have been very few studies of these systems. The work in this thesis is concerned with attempting to understand the relationship between the properties of the molecular crystal, and how these relate to the properties of the constituent molecules in isolation. To this end, density functional calculations of the structural and electronic properties of amino acids in both the crystalline and gaseous states are performed, and the results reported. The bonding mechanisms responsible for the crystal being stable are elucidated, and used to explain the zwitterionisation of the molecules upon formation of the solid state. In order to investigate the lattice dynamical and dielectric properties, the implementation of a variational density functional perturbation theory (DFPT) scheme within the plane wave pseudopotential formalism is described in detail. This scheme is fully self-consistent, and its computational cost is comparable to that of a single-point self-consistent total energy calculation. The long wave method is used to alleviate well-known problems associated with the application of homogeneous fields to crystal systems, viz. that such fields break the crystal symmetry, and the adequate treatment of electronic screening. Calculation of the first order perturbed wavefunctions and the second order change in the Kohn-Sham functional allows properties such as the polarisability, dielectric matrix, dynamical matrix and Born effective charge tensors to be determined. The treatment of crystalline symmetries is described in detail. The DFPT formalism is extended to allow IR absorption spectra to be obtained. The lattice dynamical and dielectric behaviour of the isolated molecules and the molecular crystals are obtained; calculation of the IR spectra facilitates an insight into the effects of the crystalline environment and zwitterionisation upon the lattice dynamics. Results indicate the importance of the molecular shape and structure upon the intermolecular interactions, and hence the crystal structure formed. It is these intermolecular interactions that are found to play the major part in modification of the lattice dynamical and dielectric behaviour.
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Corlay, Vincent. "Decoding algorithms for lattices." Electronic Thesis or Diss., Institut polytechnique de Paris, 2020. http://www.theses.fr/2020IPPAT050.

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Cette thèse aborde deux problèmes liés aux réseaux de points, un vieux problème et un nouveau.Tous deux sont des problèmes de décodage de réseaux de points : À savoir, étant donné un point dans l'espace, trouver le point du réseau le plus proche.Le premier problème est lié au codage de canal en dimensions intermédiaires. Alors que des systèmes efficaces basés sur les réseaux de points existent dans les petites dimensions n < 30 et les grandes dimensions n > 1000, ce n'est pas le cas des dimensions intermédiaires. Nous étudions le décodage de réseaux de points intéressants dans ces dimensions intermédiaires. Nous introduisons de nouvelles familles de réseaux de points obtenues en appliquant le contrôle de parité de manière récursive. Ces familles comprennent des réseaux de points célèbres, tels que les réseaux Barnes-Wall, les réseaux Leech et Nebe, ainsi que de nouveaux réseaux de parité.Nous montrons que tous ces réseaux de points peuvent être décodés efficacement avec un nouveau décodeur récursif par liste.Le deuxième problème concerne les réseaux de neurones. Depuis 2016, d'innombrables articles ont tenté d'utiliser l'apprentissage profond pour résoudre le problème de décodage/détection rencontré dans les communications numériques. Nous proposons d'étudier la complexité du problème que les réseaux de neurones doivent résoudre. Nous introduisons une nouvelle approche du problème de décodage afin de l'adapter aux opérations effectuées par un réseau de neurones. Cela permet de mieux comprendre ce qu'un réseau de neurones peut et ne peut pas faire dans le cadre de ce problème, et d'obtenir des indications concernant la meilleure architecture du réseau de neurones. Des simulations informatiques validant notre analyse sont fournies
This thesis discusses two problems related to lattices, an old problem and a new one.Both of them are lattice decoding problems: Namely, given a point in the space, find the closest lattice point.The first problem is related to channel coding in moderate dimensions. While efficient lattice schemes exist in low dimensions n < 30 and high dimensions n > 1000, this is not the case of intermediate dimensions. We investigate the decoding of interesting lattices in these intermediate dimensions. We introduce new families of lattices obtained by recursively applying parity checks. These families include famous lattices, such as Barnes-Wall lattices, the Leech and Nebe lattices, as well as new parity lattices.We show that all these lattices can be efficiently decoded with an original recursive list decoder.The second problem involves neural networks. Since 2016 countless papers tried to use deep learning to solve the decoding/detection problem encountered in digital communications. We propose to investigate the complexity of the problem that neural networks should solve. We introduce a new approach to the lattice decoding problem to fit the operations performed by a neural network. This enables to better understand what a neural network can and cannot do in the scope of this problem, and get hints regarding the best architecture of the neural network. Some computer simulations validating our analysis are provided
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Jimenez, Juan Pablo Ibieta. "Campos de Gauge e matéria na rede - generalizando o Toric Code." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-16072015-144543/.

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Fases topológicas da matéria são caracterizadas por terem uma degenerescên- cia do estado fundamental que depende da topologia da variedade em que o sistema físico é definido, além disso apresentam estados excitados no interior do sistema que são interpretados como sendo quase-partículas com estatística de tipo anyonica. Estes sistemas apresentam também excitações sem gap de energia em sua borda. Fases topologicamente ordenadas distintas não podem ser distinguidas pelo esquema usual de quebra de simetria de Ginzburg-Landau. Nesta dissertação apresentamos como exemplo o modelo mais simples de um sistema com Ordem Topológica, a saber, o Toric Code (TC), introduzido originalmente por A. Kitaev em [1]. O estado fundamental deste modelo ap- resenta degenerescência igual a 4 quando incorporado à superfície de um toro. As excitações elementares são interpretadas como sendo quase-partículas com estatística do tipo anyonica. O TC é um caso especial de uma classe mais geral de models chamados de Quantum Double Models (QDMs), estes modelos podem ser entendidos como sendo uma implementação de Teorias de gauge na rede em (2 + 1) dimensões na formulação Hamiltoniana, em que os graus de liberdade vivem nas arestas da rede e são elementos do grupo de gauge G. Nós generalizamos estes modelos com a inclusão de campos de matéria nos vértices da rede. Também apresentamos uma construção detalhada de tais modelos e mostramos que eles são exatamente solúveis. Em particular, exploramos o modelo que corresponde à escolher o grupo de gauge como sendo o grupo cíclico Z2 e os graus de liberdade de matéria como sendo elementos de um espaço vetorial bidimensional V2. Além disso, mostramos que a degenerescência do estado fundamental não depende da topologia da variedade e obtemos os estados excitados mais elementares deste modelo.
Topological phases of matter are characterized for having a topologically dependent ground state degeneracy, anyonic quasi-particle bulk excitations and gapless edge excitations. Different topologically ordered phases of matter can not be distinguished by te usual Ginzburg-Landau scheme of symmetry breaking. Therefore, a new mathematical framework for the study of such phases is needed. In this dissertation we present the simplest example of a topologically ordered system, namely, the \\Toric Code (TC) introduced by A. Kitaev in [1]. Its ground state is 4-fold degenerate when embedded on the surface of a torus and its elementary excited states are interpreted as quasi-particle anyons. The TC is a particular case of a more general class of lattice models known as Quantum Double Models (QDMs) which can be interpreted as an implementation of (2+1) Lattice Gauge Theories in the Hamiltonian formulation with discrete gauge group G. We generalize these models by the inclusion of matter fields at the vertices of the lattice. We give a detailed construction of such models, we show they are exactly solvable and explore the case when the gauge group is set to be the abelian Z_2 cyclic group and the matter degrees of freedom to be elements of a 2-dimensional vector space V_2. Furthermore, we show that the ground state degeneracy is not topologically dependent and obtain the most elementary excited states.
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Books on the topic "Lattice code"

1

Rouben, B. Description of the lattice code POWDERPUFS-V. Mississauga, Ont: AECL, 1995.

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Oggier, Frédérique. Algebraic number theory and code design for Rayleigh fading channels. Hanover, MA: Now, 2004.

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Ebeling, Wolfgang. Lattices and Codes. Wiesbaden: Springer Fachmedien Wiesbaden, 2013. http://dx.doi.org/10.1007/978-3-658-00360-9.

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Ebeling, Wolfgang. Lattices and Codes. Wiesbaden: Vieweg+Teubner Verlag, 1994. http://dx.doi.org/10.1007/978-3-322-96879-1.

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Ebeling, Wolfgang. Lattices and Codes. Wiesbaden: Vieweg+Teubner Verlag, 2002. http://dx.doi.org/10.1007/978-3-322-90014-2.

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Friedrich, Hirzebruch, ed. Lattices and codes: A course partially based on lectures by F. Hirzebruch. Braunschweig/Wiesbaden: Vieweg, 1994.

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Friedrich, Hirzebruch, ed. Lattices and codes: A course partially based on lectures by F. Hirzebruch. 2nd ed. Braunschweig/Wiesbaden: Vieweg, 2002.

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Constellation shaping, nonlinear precoding, and trellis coding for voiceband telephone channel modems with emphasis on ITU-T recommendation V.34. Boston: Kluwer Academic Publishers, 2002.

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Bianca come il latte, rossa come il sangue: Romanzo. Milano: Mondadori, 2011.

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Mohamad, A. A. Lattice Boltzmann method: Fundamentals and engineering applications with computer codes / A. A. Mohamad. London: Springer, 2011.

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Book chapters on the topic "Lattice code"

1

Pivanti, Marcello, Filippo Mantovani, Sebastiano Fabio Schifano, Raffaele Tripiccione, and Luca Zenesini. "An Optimized Lattice Boltzmann Code for BlueGene/Q." In Parallel Processing and Applied Mathematics, 385–94. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-55195-6_36.

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Bruno, E., and B. Ginatempo. "A KKR And KKR-CPA Code for any Bravais Lattice." In Properties of Complex Inorganic Solids, 441–46. Boston, MA: Springer US, 1997. http://dx.doi.org/10.1007/978-1-4615-5943-6_53.

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Biferale, Luca, Filippo Mantovani, Marcello Pivanti, Fabio Pozzati, Mauro Sbragaglia, Andrea Scagliarini, Sebastiano Fabio Schifano, Federico Toschi, and Raffaele Tripiccione. "A Multi-GPU Implementation of a D2Q37 Lattice Boltzmann Code." In Parallel Processing and Applied Mathematics, 640–50. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-31464-3_65.

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Amrani, Ofer, Yair Be'ery, and Alexander Vardy. "Bounded-distance decoding of the Leech lattice and the Golay code." In Algebraic Coding, 236–48. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/3-540-57843-9_24.

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Attig, N., S. Güsken, P. Lacock, Th Lippert, K. Schilling, P. Ueberholz, and J. Viehoff. "Running a code for lattice quantum chromodynamics efficiently on CRAY T3E systems." In High-Performance Computing and Networking, 183–92. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0037145.

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Calore, Enrico, Sebastiano Fabio Schifano, and Raffaele Tripiccione. "On Portability, Performance and Scalability of an MPI OpenCL Lattice Boltzmann Code." In Lecture Notes in Computer Science, 438–49. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-14313-2_37.

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Lammers, Peter, Kamen N. Beronov, Gunther Brenner, and Franz Durst. "Direct Simulation with the Lattice Boltzmann Code BEST of Developed Turbulence in Channel Flows." In High Performance Computing in Science and Engineering, Munich 2002, 43–58. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55526-8_4.

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Imparato, Alberto, Maurizio Giordano, and Mario Mango Furnari. "Parallelization and vectorization effects on a code simulating a vitreous lattice model with constrained dynamics." In Lecture Notes in Computer Science, 145–56. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/bfb0094918.

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Guo, Qian, Thomas Johansson, and Paul Stankovski. "Coded-BKW: Solving LWE Using Lattice Codes." In Lecture Notes in Computer Science, 23–42. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-47989-6_2.

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Thomas, Christopher E. "Meson Spectroscopy from Lattice QCD." In Light Cone 2016, 55–62. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-65732-5_9.

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Conference papers on the topic "Lattice code"

1

Brambilla, Michele, Dirk Hesse, and Francesco Di Renzo. "Code development (not only) for NSPT." In 31st International Symposium on Lattice Field Theory LATTICE 2013. Trieste, Italy: Sissa Medialab, 2014. http://dx.doi.org/10.22323/1.187.0418.

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Cossu, Guido, Junichi Noaki, Shoji Hashimoto, Takashi Kaneko, Hidenori Fukaya, Peter A. Boyle, and Jun Doi. "JLQCD IroIro++ lattice code on BG/Q." In 31st International Symposium on Lattice Field Theory LATTICE 2013. Trieste, Italy: Sissa Medialab, 2014. http://dx.doi.org/10.22323/1.187.0482.

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Ueda, Satoru. "Bridge++: an object-oriented C++ code for lattice simulations." In 31st International Symposium on Lattice Field Theory LATTICE 2013. Trieste, Italy: Sissa Medialab, 2014. http://dx.doi.org/10.22323/1.187.0412.

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Zhang, Hongbo, Chuntao Tang, Weiyan Yang, Guangwen Bi, and Bo Yang. "Development and Verification of the PWR Lattice Code PANDA." In 2017 25th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/icone25-66573.

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Abstract:
Lattice code generates homogenized few-group cross sections for core neutronics code. It is an important component of the nuclear design code system. The development and improvement of lattice codes are always significant topics in reactor physics. The PANDA code is a PWR lattice code developed by Shanghai Nuclear Engineering Research and Design Institute (SNERDI). It starts from the 70-group library, and performs the resonance calculation based on the Spatially Dependent Dancoff Method (SDDM). The 2D heterogeneous transport calculation is performed without any group collapse and cell homogenization by MOC with two-level Coarse Mesh Finite Difference (CMFD) acceleration. Matrix exponential methods are used to solve the Bateman depletion equation. Based on the methodologies, the PANDA code is developed. The verifications on different levels preliminarily demonstrate the ability of the PANDA code.
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Matsumine, Toshiki, Brian M. Kurkoski, and Hideki Ochiai. "Construction D Lattice Decoding and Its Application to BCH Code Lattices." In GLOBECOM 2018 - 2018 IEEE Global Communications Conference. IEEE, 2018. http://dx.doi.org/10.1109/glocom.2018.8647232.

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Ueda, Satoru, Sinya Aoki, Tatsumi Aoyama, Kazuyuki Kanaya, Hideo Matsufuru, Shinji Motoki, Yusuke Namekawa, Hidekatsu Nemura, Yusuke Taniguchi, and Naoya Ukita. "Lattice QCD code Bridge++ on multi-thread and many core accelerators." In The 32nd International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2015. http://dx.doi.org/10.22323/1.214.0036.

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Osborn, James. "The FUEL code project." In The 32nd International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2015. http://dx.doi.org/10.22323/1.214.0028.

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Gottlieb, Steven, Ronald Babich, Richard C. Brower, Michael A. Clark, Balint Joo, and Guochun Shi. "Progress on the QUDA code suite." In XXIX International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2012. http://dx.doi.org/10.22323/1.139.0033.

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Belfiore, Jean-Claude, and Frederique Oggier. "Secrecy gain: A wiretap lattice code design." In Its Applications (Isita2010). IEEE, 2010. http://dx.doi.org/10.1109/isita.2010.5650095.

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Darte, Alain, Alexandre Isoard, and Tomofumi Yuki. "Extended lattice-based memory allocation." In CGO '16: 14th Annual IEEE/ACM International Symposium on Code Generation and Optimization. New York, NY, USA: ACM, 2016. http://dx.doi.org/10.1145/2892208.2892213.

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Reports on the topic "Lattice code"

1

Jessee, Matthew, Jinan Yang, Ugur Mertyurek, William B. J. Marshall, and Andrew Holcomb. SCALE Lattice Physics Code Assessments of Accident Tolerant Fuel. Office of Scientific and Technical Information (OSTI), February 2020. http://dx.doi.org/10.2172/1606738.

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Pattison, Martin J., Kannan N. Premnath, Sanjoy Banerjee, and Vinay Dwivedi. Development of a Prototype Lattice Boltzmann Code for CFD of Fusion Systems. Office of Scientific and Technical Information (OSTI), February 2007. http://dx.doi.org/10.2172/901573.

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Stockman, H. W. A 3D Lattice Boltzmann Code for Modeling Flow and Multi-Component Dispersion. Office of Scientific and Technical Information (OSTI), February 1999. http://dx.doi.org/10.2172/4090.

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Na, H., and J. Osborn. Lattice Quantum Chromodynamics (SPI, mapping, site ordering, and QPX in Lattice QCD code on Mira): ALCF-2 Early Science Program Technical Report. Office of Scientific and Technical Information (OSTI), May 2013. http://dx.doi.org/10.2172/1079769.

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Milutinovic, J., and A. G. Ruggiero. Comparison of accelerator codes for a RHIC lattice. Office of Scientific and Technical Information (OSTI), May 1988. http://dx.doi.org/10.2172/1118919.

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Milutinovic, J., and A. G. Ruggiero. Comparison of Accelerator Codes for a RHIC Lattice. Office of Scientific and Technical Information (OSTI), March 1989. http://dx.doi.org/10.2172/1119306.

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Weinstein, Marvin. CORE: A New Method for Solving Hamiltonian Lattice Systems. Office of Scientific and Technical Information (OSTI), July 2003. http://dx.doi.org/10.2172/813289.

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Rouxelin, Pascal Nicolas, and Gerhard Strydom. IAEA CRP on HTGR Uncertainties in Modeling: Assessment of Phase I Lattice to Core Model Uncertainties. Office of Scientific and Technical Information (OSTI), September 2016. http://dx.doi.org/10.2172/1364525.

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Wen, Qingsong, Minzhen Ren, and Xiaoli Ma. Fixed-point Design of the Lattice-reduction-aided Iterative Detection and Decoding Receiver for Coded MIMO Systems. Fort Belvoir, VA: Defense Technical Information Center, January 2011. http://dx.doi.org/10.21236/ada586964.

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Hiroshi Takahashi, Upendra Rohatgi, and T.J. Downar. A proliferation resistant hexagonal tight lattice BWR fueled core for increased burnup and reduced fuel storage requirements. Annual progress report: August, 1999 to July, 2000 [DOE NERI]. Office of Scientific and Technical Information (OSTI), August 2000. http://dx.doi.org/10.2172/761537.

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