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Relevant bibliographies by topics / Non binary stabilizer codes

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Academic literature on the topic 'Non binary stabilizer codes'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 February 2022

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Journal articles on the topic "Non binary stabilizer codes"

1

Naghipour, Avaz, Mohammad Ali Jafarizadeh, and Sedaghat Shahmorad. "Quantum stabilizer codes from Abelian and non-Abelian groups association schemes." International Journal of Quantum Information 13, no. 03 (2015): 1550021. http://dx.doi.org/10.1142/s0219749915500215.

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A new method for the construction of the binary quantum stabilizer codes is provided, where the construction is based on Abelian and non-Abelian groups association schemes. The association schemes based on non-Abelian groups are constructed by bases for the regular representation from U6n, T4n, V8n and dihedral D2n groups. By using Abelian group association schemes followed by cyclic groups and non-Abelian group association schemes a list of binary stabilizer codes up to 40 qubits is given in tables 4, 5 and 10. Moreover, several binary stabilizer codes of minimum distances 5, 7 and 8 with goo

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2

Nguyen, Duc Manh, and Sunghwan Kim. "New construction of binary and nonbinary quantum stabilizer codes based on symmetric matrices." International Journal of Modern Physics B 33, no. 24 (2019): 1950274. http://dx.doi.org/10.1142/s0217979219502746.

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In this paper, we propose two construction methods for binary and nonbinary quantum stabilizer codes based on symmetric matrices. In the first construction, we use the identity and symmetric matrices to generate parity-check matrices that satisfy the symplectic inner product (SIP) for the construction of quantum stabilizer codes. In the second construction, we modify the first construction to generate parity-check matrices based on the Calderbank–Shor–Stean structure for the construction of quantum stabilizer codes. The binary and nonbinary quantum stabilizer codes whose parameters achieve equ

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3

Arvind, V., P. P. Kurur, and K. R. Parthasarathy. "Non-stabilizer quantum codes from Abelian subgroups of the error group." Quantum Information and Computation 4, no. 6&7 (2004): 411–35. http://dx.doi.org/10.26421/qic4.6-7-2.

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This paper is motivated by the computer-generated nonadditive code described in Rains et al\cite{rains97nonadditive}. We describe a theory of non-stabilizer codes of which the nonadditive code of Rains et al is an example. Furthermore, we give a general strategy of constructing good nonstabilizer codes from good stabilizer codes and give some explicit constructions and asymptotically good nonstabilizer codes. Like in the case of stabilizer codes, we can design fairly efficient encoding and decoding procedures.

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Nguyen, Duc Manh, and Sunghwan Kim. "Quantum stabilizer codes based on a new construction of self-orthogonal trace-inner product codes over GF(4)." International Journal of Modern Physics B 34, no. 05 (2020): 2050017. http://dx.doi.org/10.1142/s0217979220500174.

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In this paper, we propose quantum stabilizer codes based on a new construction of self-orthogonal trace-inner product codes over the Galois field with 4 elements (GF(4)). First, from any two binary vectors, we construct a generator matrix of linear codes whose components are over GF(4). We prove that the proposed linear codes comply with the self-orthogonal, trace-inner product. Then, we propose mapping tables to construct new quantum stabilizer codes by using linear codes. Comparison results show that our proposed quantum codes have various dimensions for any code length with the capacity for

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Nguyen, Duc Manh, and Sunghwan Kim. "A novel construction for quantum stabilizer codes based on binary formalism." International Journal of Modern Physics B 34, no. 08 (2020): 2050059. http://dx.doi.org/10.1142/s0217979220500599.

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In this research, we propose a novel construction of quantum stabilizer code based on a binary formalism. First, from any binary vector of even length, we generate the parity-check matrix of the quantum code from a set composed of elements from this vector and its relations by shifts via subtraction and addition. We prove that the proposed matrices satisfy the condition constraint for the construction of quantum codes. Finally, we consider some constraint vectors which give us quantum stabilizer codes with various dimensions and a large minimum distance with code length from six to twelve digi

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6

Wu, Yansheng, and Yoonjin Lee. "Self-Orthogonal Codes Constructed from Posets and Their Applications in Quantum Communication." Mathematics 8, no. 9 (2020): 1495. http://dx.doi.org/10.3390/math8091495.

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It is an important issue to search for self-orthogonal codes for construction of quantum codes by CSS construction (Calderbank-Sho-Steane codes); in quantum error correction, CSS codes are a special type of stabilizer codes constructed from classical codes with some special properties, and the CSS construction of quantum codes is a well-known construction. First, we employ hierarchical posets with two levels for construction of binary linear codes. Second, we find some necessary and sufficient conditions for these linear codes constructed using posets to be self-orthogonal, and we use these se

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Hwang, Yongsoo, Byung-Soo Choi, and Moongu Jeon. "On the construction of stabilizer codes with an arbitrary binary matrix." Quantum Information Processing 12, no. 1 (2012): 467–79. http://dx.doi.org/10.1007/s11128-012-0394-7.

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Magdalena de la Fuente, Julio Carlos, Nicolas Tarantino, and Jens Eisert. "Non-Pauli topological stabilizer codes from twisted quantum doubles." Quantum 5 (February 17, 2021): 398. http://dx.doi.org/10.22331/q-2021-02-17-398.

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It has long been known that long-ranged entangled topological phases can be exploited to protect quantum information against unwanted local errors. Indeed, conditions for intrinsic topological order are reminiscent of criteria for faithful quantum error correction. At the same time, the promise of using general topological orders for practical error correction remains largely unfulfilled to date. In this work, we significantly contribute to establishing such a connection by showing that Abelian twisted quantum double models can be used for quantum error correction. By exploiting the group coho

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Luo, Lan, and Zhi Ma. "Non-Binary Quantum Synchronizable Codes From Repeated-Root Cyclic Codes." IEEE Transactions on Information Theory 64, no. 3 (2018): 1461–70. http://dx.doi.org/10.1109/tit.2018.2795479.

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Tyagi, Vinod, and Tarun Lata. "bi-Byte correcting non-binary perfect codes." Discrete Mathematics, Algorithms and Applications 11, no. 02 (2019): 1950018. http://dx.doi.org/10.1142/s1793830919500186.

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Etzion [T. Etzion, Perfect byte correcting codes, IEEE Trans. Inform. Theory 44 (1998) 3140–3146.] has classified byte error correcting binary codes into five different categories with respect to the size of the byte. If a code is partitioned into [Formula: see text] equal byte of size say [Formula: see text] then [Formula: see text] or the size of bytes is [Formula: see text]. Alternatively if bytes are of different size say, [Formula: see text] then [Formula: see text]. The result was further modified by Tyagi and Sethi [V. Tyagi and A. Sethi, [Formula: see text]-Byte correcting perfect code

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Dissertations / Theses on the topic "Non binary stabilizer codes"

1

Gilra, Deepak. "A class of non-binary LDPC codes." Texas A&M University, 2003. http://hdl.handle.net/1969/67.

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Chilumuru, Suma Namuduri Kameswara. "Distributed video coding using non-binary LDPC codes." Diss., A link to full text of this thesis in SOAR, 2006. http://soar.wichita.edu/dspace/handle/10057/619.

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Thesis (M.S.)--Wichita State University, College of Engineering, Dept. of Electrical and Computer Engineering.<br>"December 2006." Title from PDF title page (viewed on Oct. 29, 2007). Thesis adviser: Kamesh Namuduri. Includes bibliographic references (leaves 47-50).

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Reid, Andrew Carey. "Turbo codes: convergence phenomena & non-binary constructions." Thesis, University of Canterbury. Electrical and Electronic Engineering, 2002. http://hdl.handle.net/10092/5462.

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The introduction of turbo codes in 1993 provided a code structure that could approach Shannon limit performance whilst remaining practically decodeable. Much subsequent work has focused on this remarkable structure, attempting to explain its performance and to extend or modify it. This thesis builds on this research providing insights into the convergence behaviour of the iterative decoder for turbo codes and examining the potential of turbo codes constructed from non-binary component codes. The first chapter of this thesis gives a brief history of coding theory, providing context for the wor

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Ciobanu, Alexandru. "Adaptive multiset stochastic decoding of non-binary LDPC codes." Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=106390.

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In this thesis, we propose a new stochastic decoding algorithm for non-binary LDPC codes with d_v = 2, which is based on the concept of a mutliset, a generalization of the set that allows for multiple occurrences of the same element. The algorithm is called Adaptive Multiset Stochastic Algorithm (AMSA) and represents probability mass functions as multisets, which simplifies the structure of the variable node. AMSA reduces the run-time complexity of one decoding cycle to O(q) for regular memory architectures, and to O(1) if a custom SRAM architecture is used. Two fully-parallel AMSA decoders ar

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García, Herrero Francisco Miguel. "Architectures for soft-decision decoding of non-binary codes." Doctoral thesis, Universitat Politècnica de València, 2013. http://hdl.handle.net/10251/33753.

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En esta tesis se estudia el dise¿no de decodificadores no-binarios para la correcci'on de errores en sistemas de comunicaci'on modernos de alta velocidad. El objetivo es proponer soluciones de baja complejidad para los algoritmos de decodificaci'on basados en los c'odigos de comprobaci'on de paridad de baja densidad no-binarios (NB-LDPC) y en los c'odigos Reed-Solomon, con la finalidad de implementar arquitecturas hardware eficientes. En la primera parte de la tesis se analizan los cuellos de botella existentes en los algoritmos y en las arquitecturas de decodificadores NB-LDPC y se pro

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Shams, Bilal. "Codes LDPC non-binaire de nouvelle generation." Phd thesis, Université de Cergy Pontoise, 2010. http://tel.archives-ouvertes.fr/tel-00766409.

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Dans cette thèse, nous présentons nos travaux dans le domaine des algorithmes de décodage des codes LDPC non-binaires généralisés. Les codes LDPC binaires ont été initialement proposés par Gallager en 1963, et après quelques avancées théoriques fondamentales, ils ont été proposés dans des standards tels que DVB-S2, WI-MAX, DSL, W-LAN etc. Plus tard, les codes LDPC non-binaires (NB-LDPC) ont été pro- posés dans la littérature, et ont montré une meilleure performance pour de petites tailles de code ou lorsqu'ils sont utilisés sur des canaux non-binaires. Cependant, les avan- tages de l'utilisati

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Bhutto, Tarique Inayat. "Root LDPC Codes for Non Ergodic Transmission Channels." Thesis, Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-5938.

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4 ABSTRACT Tremendous amount of research has been conducted in modern coding theory in the past few years and much of the work has been done in developing new coding techniques. Low density parity check (LDPC) codes are class of linear block error correcting codes which provide capacity performance on a large collection of data transmission and storage channels while Root LDPC codes in this thesis work are admitting implementable decoders with manageable complexity. Furthermore, work has been conducted to develop graphical methods to represent LDPC codes. This thesis implement one of the LDPC

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Cai, Fang. "Low-complexity Decoding Algorithms and Architectures for Non-binary LDPC Codes." Case Western Reserve University School of Graduate Studies / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=case1372338108.

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Garrammone, Giuliano [Verfasser]. "Non-Binary Codes with Applications to Satellite and Space Communications / Giuliano Garrammone." München : Verlag Dr. Hut, 2015. http://d-nb.info/1074063392/34.

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Uzunoglu, Cihan. "Performance Comparison Of Message Passing Decoding Algorithms For Binary And Non-binary Low Density Parity Check (ldpc) Codes." Master's thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/2/12609072/index.pdf.

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In this thesis, we investigate the basics of Low-Density Parity-Check (LDPC) codes over binary and non-binary alphabets. We especially focus on the message passing decoding algorithms, which have different message definitions such as a posteriori probabilities, log-likelihood ratios and Fourier transforms of probabilities. We present the simulation results that compare the performances of small block length binary and non-binary LDPC codes, which have regular and irregular structures over GF(2),GF(4) and GF(8) alphabets. We observe that choosing non-binary alphabets improve the performance wit

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Books on the topic "Non binary stabilizer codes"

1

1977-, Johnston Martin, ed. Non-binary error control coding for wireless communication and data storage. Wiley, 2008.

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Carrasco, Rolando Antonio, and Martin Johnston. Non-Binary Error Control Coding for Wireless Communication and Data Storage. Wiley & Sons, Incorporated, John, 2008.

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Book chapters on the topic "Non binary stabilizer codes"

1

Ma, Zhi, Xin Lu, Keqin Feng, and Dengguo Feng. "On Non-binary Quantum BCH Codes." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11750321_63.

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Lev, Alexandr Y., Yuliy A. Lev, and Vyacheslav N. Okhrymenko. "Non-binary Block Inseparable Errors Control Codes." In Cryptography and Coding. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-45325-3_37.

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Alzubi, Jafar A., Omar A. Alzubi, and Thomas M. Chen. "Algebraic-Geometric Non-binary Block Turbo Codes." In SpringerBriefs in Electrical and Computer Engineering. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08293-6_4.

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Wolfmann, J. "Weights of Primitive Binary Cyclic Codes from Non-Primitive Codes." In Eurocode ’92. Springer Vienna, 1993. http://dx.doi.org/10.1007/978-3-7091-2786-5_10.

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Divya, I., and M. Anbuselvi. "Protograph-Based Design of Non-Binary LDPC Codes." In Advances in Intelligent Systems and Computing. Springer India, 2014. http://dx.doi.org/10.1007/978-81-322-2135-7_39.

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Yang, Leilei, Fei Liu, and Haitao Li. "Min–Max Decoding for Non-Binary LDPC Codes." In Lecture Notes in Electrical Engineering. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-34528-9_14.

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Gashkov, Igor. "Non Binary Codes and “Mathematica” Calculations: Reed-Solomon Codes Over GF (2n)." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11428862_90.

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Yasodha, T., I. Jocobraglend, and K. Meena Alias Jeyanthi. "Energy Efficient Decoder Design for Non-binary LDPC Codes." In Lecture Notes in Electrical Engineering. Springer India, 2014. http://dx.doi.org/10.1007/978-81-322-2119-7_146.

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Zhibin, Deng, Meng Jiahui, Wang Ziyong, Zhang Liang, and Gao Jingpeng. "FPGA Implementation of Rate Compatible Non-binary LDPC Codes." In Advances in Intelligent Systems and Computing. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-00214-5_7.

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M’rabet, Zakaria, Fouad Ayoub, and Mostafa Belkasmi. "A Threshold Decoding Algorithm for Non-binary OSMLD Codes." In Communications in Computer and Information Science. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-61143-9_11.

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Conference papers on the topic "Non binary stabilizer codes"

1

Lv, Jingjie, Xi Zhang, and Ruihu Li. "New Non-Binary Stabilizer Quantum Codes Derived from Quasi-Negacyclic Codes." In 2019 12th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics (CISP-BMEI). IEEE, 2019. http://dx.doi.org/10.1109/cisp-bmei48845.2019.8965879.

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MANABU, HAGIWARA, and HIDEKI IMAI. "A CONSTRUCTION FOR NON-STABILIZER CLIFFORD CODES." In Proceedings of the International Symposium on Mesoscopic Superconductivity and Spintronics — In the Light of Quantum Computation. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701619_0047.

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Voicila, Adrian, David Declercq, Francois Verdier, Marc Fossorier, and Pascal Urard. "Split non-binary LDPC codes." In 2008 IEEE International Symposium on Information Theory - ISIT. IEEE, 2008. http://dx.doi.org/10.1109/isit.2008.4595128.

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Behgoo, Arash, and Ali Aghagolzadeh. "Non-binary Irregular Repeat Codes." In 2006 40th Annual Conference on Information Sciences and Systems. IEEE, 2006. http://dx.doi.org/10.1109/ciss.2006.286692.

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Andriyanova, Iryna, Vishwambhar Rathi, and Jean-Pierre Tillich. "Binary weight distribution of non-binary LDPC codes." In 2009 IEEE International Symposium on Information Theory - ISIT. IEEE, 2009. http://dx.doi.org/10.1109/isit.2009.5205662.

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Bhatia, A., A. R. Iyengar, and P. H. Siegel. "Enhancing Binary Images of Non-Binary LDPC Codes." In 2011 IEEE Global Communications Conference (GLOBECOM 2011). IEEE, 2011. http://dx.doi.org/10.1109/glocom.2011.6134315.

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Bo Zhou, Li Zhang, Jingyu Kang, et al. "Non-binary LDPC codes vs. Reed-Solomon codes." In 2008 Information Theory and Applications Workshop (ITA). IEEE, 2008. http://dx.doi.org/10.1109/ita.2008.4601044.

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Boutros, Joseph J., Fanny Jardel, and Cyril Measson. "Probabilistic shaping and non-binary codes." In 2017 IEEE International Symposium on Information Theory (ISIT). IEEE, 2017. http://dx.doi.org/10.1109/isit.2017.8006941.

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Briffa, Johann A., and Hans Georg Schaathun. "Non-binary turbo codes and applications." In 2008 5th International Symposium on Turbo Codes and Related Topics. IEEE, 2008. http://dx.doi.org/10.1109/turbocoding.2008.4658714.

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Gao, You, and Ya-Yuan Tao. "Non-binary quantum codes constructed from classical BCH codes." In 2010 International Conference on Machine Learning and Cybernetics (ICMLC). IEEE, 2010. http://dx.doi.org/10.1109/icmlc.2010.5580593.

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Reports on the topic "Non binary stabilizer codes"

1

Knill, E. Non-binary unitary error bases and quantum codes. Office of Scientific and Technical Information (OSTI), 1996. http://dx.doi.org/10.2172/373768.

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