Academic literature on the topic 'Non-binary codes'

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Journal articles on the topic "Non-binary codes"

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Tyagi, Vinod, and Tarun Lata. "bi-Byte correcting non-binary perfect codes." Discrete Mathematics, Algorithms and Applications 11, no. 02 (April 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 codes, Asian-Eur. J. Math. 7(1) (2014) 1–8.] and the classification of bytes was given with respect to size of the byte as well as length of the burst. We call such codes as [Formula: see text]-byte correcting perfect codes. Our aim in this paper is to find the possibilities for the existence of [Formula: see text]-byte correcting non-binary perfect codes.
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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 (March 2018): 1461–70. http://dx.doi.org/10.1109/tit.2018.2795479.

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Yang, Min, Wen-yan Zhang, Jie Zhong, and Jie Wu. "Construction of Non-binary QC-LDPC Codes." Journal of Electronics & Information Technology 35, no. 2 (February 18, 2014): 297–302. http://dx.doi.org/10.3724/sp.j.1146.2012.00403.

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KASAI, Kenta, Charly POULLIAT, David DECLERCQ, and Kohichi SAKANIWA. "Weight Distributions of Non-binary LDPC Codes." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E94-A, no. 4 (2011): 1106–15. http://dx.doi.org/10.1587/transfun.e94.a.1106.

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Berrou, C., and M. Jézéquel. "Non-binary convolutional codes for turbo coding." Electronics Letters 35, no. 1 (1999): 39. http://dx.doi.org/10.1049/el:19990059.

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Borges, J., J. Rifà, and V. A. Zinoviev. "On non-antipodal binary completely regular codes." Discrete Mathematics 308, no. 16 (August 2008): 3508–25. http://dx.doi.org/10.1016/j.disc.2007.07.008.

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Wang, Liqi, and Shixin Zhu. "On non-binary quantum repeated-root cyclic codes." International Journal of Quantum Information 12, no. 03 (April 2014): 1450010. http://dx.doi.org/10.1142/s0219749914500105.

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In this paper, based on the Steane's enlargement construction, three classes of non-binary quantum codes are constructed from classical repeated-root cyclic codes of length 2ps over 𝔽q with odd characteristic p. The exact minimum distances of these quantum codes are determined. This construction yields a quantum MDS code with parameters [[2p, 2p - 4, 3]]p and two good quantum codes with parameters [[2p, 2p - 7, 4]]p and [[2p, 2p - 10, 5]]p.
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Yu, Qingping, Zhiping Shi, Xingwang Li, Jianhe Du, Jiayi Zhang, and Khaled M. Rabie. "On the Concatenations of Polar Codes and Non-Binary LDPC Codes." IEEE Access 6 (2018): 65088–97. http://dx.doi.org/10.1109/access.2018.2877178.

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Bag, Tushar, Hai Q. Dinh, Ashish Kumar Upadhyay, and Woraphon Yamaka. "New Non-Binary Quantum Codes from Cyclic Codes Over Product Rings." IEEE Communications Letters 24, no. 3 (March 2020): 486–90. http://dx.doi.org/10.1109/lcomm.2019.2959529.

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Shi, Minjia, Yan Liu, and Patrick Solé. "Optimal binary codes from trace codes over a non-chain ring." Discrete Applied Mathematics 219 (March 2017): 176–81. http://dx.doi.org/10.1016/j.dam.2016.09.050.

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

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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.
"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 work. Chapter two explains in detail both the turbo encoding and decoding structures considered. Chapter three presents new work on convergence phenomena observed in the iterative decoding process. These results emphasise the dynamic nature of the decoder and allow for both a stopping criteria and ARQ scheme to be proposed. Chapters four and five present the work on non-binary turbo codes. First the problem of choosing good component codes is discussed and an achievability bound on the dominant parameter affecting their performance is derived. Searches for good component codes over a number of small rings are then conducted, and simulation results presented. The new results, and suggestions for further work are summarised in the conclusion of Chapter six.
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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 are implemented on FPGA for two versions of a (192,96) (2,4)-regular code, one over GF(64) and the other over GF(256), both achieving a maximum clock frequency of 108 MHz and a throughput of 65 Mbit/s at E_b/N_0 = 2.4 dB. We also propose an SRAM architecture for ASIC implementations that reduces the run-time complexity of a decoding cycle to O(1) and achieves a throughput of 698 Mbit/s at the same noise level. The algorithm has a frame error rate (FER) of 3.5 x 10^-7 at E_b/N_0 = 2.4 dB when using the GF(256) version of the code. To the best of our knowledge, the implemented decoders are the first fully-parallel non-binary LDPC decoders over GF(64) and GF(256) reported in the literature.
Dans cette thèse, nous proposons un nouvel algorithme de décodage stochastique pour des codes LDPC non-binaires avec d_v = 2, qui est basé sur le concept de multiensemble, une généralisation de l'ensemble où un élément peut apparaître plusieurs fois. L'algorithme est appelé Algorithme Stochastique à Multiensembles Adaptifs (ASMA) et représente des fonctions de masse comme multiensembles, ce qui simplifie la structure du nœud de variable. ASMA réduit la complexité d'exécution d'une itération de décodage à O(q) pour les architectures de mémoire ordinaire, et O(1) si une architecture SRAM personnalisée est utilisée. Deux décodeurs ASMA tout-parallèles sont mis en œuvre sur FPGA pour deux versions d'un code (192,96) (2,4)-réguliers, l'un sur GF(64) et le l'autre sur GF(256), et tous les deux atteignent une fréquence d'horloge maximale de 108 MHz et un débit de 65 Mbit/s à E_b/N_0 = 2.4 dB. Nous proposons aussi une architecture SRAM pour les implémentations ASIC qui réduit la complexité d'exécution d'un cycle de décodage à O(1) et atteint 698 Mbit/s au même niveau de bruit. L'algorithme a un taux d'erreur de trame de 3.5 x 10^-7 à E_b/N_0 = 2.4 dB pour la version GF(256) du code. Au meilleur de notre connaissance, les décodeurs présentés ici sont les premiers décodeurs LDPC non-binaires opérant sur GF(64) et GF(256) et tout-parallèles rapportés dans la littérature.
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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 proponen soluciones de baja complejidad y de alta velocidad basadas en el volteo de s'¿mbolos. En primer lugar, se estudian las soluciones basadas en actualizaci'on por inundaci 'on con el objetivo de obtener la mayor velocidad posible sin tener en cuenta la ganancia de codificaci'on. Se proponen dos decodificadores diferentes basados en clipping y t'ecnicas de bloqueo, sin embargo, la frecuencia m'axima est'a limitada debido a un exceso de cableado. Por este motivo, se exploran algunos m'etodos para reducir los problemas de rutado en c'odigos NB-LDPC. Como soluci'on se propone una arquitectura basada en difusi'on parcial para algoritmos de volteo de s'¿mbolos que mitiga la congesti'on por rutado. Como las soluciones de actualizaci 'on por inundaci'on de mayor velocidad son sub-'optimas desde el punto de vista de capacidad de correci'on, decidimos dise¿nar soluciones para la actualizaci'on serie, con el objetivo de alcanzar una mayor velocidad manteniendo la ganancia de codificaci'on de los algoritmos originales de volteo de s'¿mbolo. Se presentan dos algoritmos y arquitecturas de actualizaci'on serie, reduciendo el 'area y aumentando de la velocidad m'axima alcanzable. Por 'ultimo, se generalizan los algoritmos de volteo de s'¿mbolo y se muestra como algunos casos particulares puede lograr una ganancia de codificaci'on cercana a los algoritmos Min-sum y Min-max con una menor complejidad. Tambi'en se propone una arquitectura eficiente, que muestra que el 'area se reduce a la mitad en comparaci'on con una soluci'on de mapeo directo. En la segunda parte de la tesis, se comparan algoritmos de decodificaci'on Reed- Solomon basados en decisi'on blanda, concluyendo que el algoritmo de baja complejidad Chase (LCC) es la soluci'on m'as eficiente si la alta velocidad es el objetivo principal. Sin embargo, los esquemas LCC se basan en la interpolaci'on, que introduce algunas limitaciones hardware debido a su complejidad. Con el fin de reducir la complejidad sin modificar la capacidad de correcci'on, se propone un esquema de decisi'on blanda para LCC basado en algoritmos de decisi'on dura. Por 'ultimo se dise¿na una arquitectura eficiente para este nuevo esquema
García Herrero, FM. (2013). Architectures for soft-decision decoding of non-binary codes [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/33753
TESIS
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Zhou, Biyun. "Non-binary cyclic codes and its applications in decoding of high dimensional trellis-coded modulation." Ohio : Ohio University, 2000. http://www.ohiolink.edu/etd/view.cgi?ohiou1173380815.

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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'utilisation de codes NB-LDPC impliquent une augmentation importante de la complexité de décodage. Pour un code défini dans un corps de Galois GF (q), la complexité est d'ordre O (q2). De même, la mémoire requise pour le stockage des messages est d'ordre O (q). Ainsi, l'implémentation d'un décodeur LDPC défini sur un corps de Galois pour q > 64 devient impossible dans la pratique. L'objectif prin- cipal de cette thèse est de développer des algorithmes avec une bonne performance et complexité réduite de sorte qu'ils deviennent implémentables. Pour une performance de décodage optimisée, non seulement l'algorithme est important, mais également la structure du code joue un rôle clé. Avec cet objectif à l'esprit, une nouvelle famille de codes appelés " cluster-NB-LDPC codes " a été élaborée ainsi que des améliorations spécifiques du décodeur non-binaire pour ces codes. Le résultat principal est que nous avons pu proposer des décodeurs pour les codes cluster-NB-LDPC avec une complex- ité réduite par rapport aux décodeurs classiques pour les codes NB-LDPC définis sur les corps de Galois, sans aucune perte de performance dans la capacité de correction vi Résumé d'erreur. Dans la première partie de la thèse, nous avons modifié l'algorithme EMS pour les cluster-codes. La généralisation directe de l'algorithme EMS aux codes cluster-NB- LDPC n'est pas réaliste . Il y a une perte de performance et une augmentation de la complexité. Par conséquent, nous proposons quelques modifications dans la procé- dure, qui non seulement améliore considérablement les performances de décodage, mais diminue également la complexité. Au niveau des noeuds de parité, cet algo- rithme conserve les mêmes limites sur le nombre d'opérations que l'algorithme EMS pour GF (q)-codes, O (nmlognm) avec nm << q. Nous proposons ensuite une autre méthode, basée sur la diversité des codes cluster, afin d'améliorer les performances de l'algorithme EMS pour les codes cluster-LDPC. Il contribue également à réduire la complexité globale du décodeur. Finalement, nous comparons les performances de décodage en utilisant cette méthode et analysons l'effet sur la complexité de décodage. Dans la dernière partie du chapitre, nous proposons une nouvelle direction pour le décodage des codes LDPC. Elle est basée sur la création des listes des mots de code qui correspondent à des noeuds de parité. Les listes sont construite de manière récur- sive dans une structure en arbre, ce qui en fait un bon candidat pour l'implémentation matérielle. Il s'agit d'une méthode nouvelle et doit encore être améliorée mais à pre- miére vue nous avons obtenu de bons résultats avec un nombre réduit d'operations.
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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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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 kind “Root LDPC code” using iterative method and calculate its threshold level for binary and non-binary Root LDPC code. This threshold value can serve as a starting point for further study on this topic. We use C++ as tool to simulate the code structure and parameters. The results show that non-binary Root LDPC code provides higher threshold value as compare to binary Root LDPC code.
postal address: Björnkullaringen 26, LGH 1029 14151 Huddinge Stockholm Sweden. Mobile: +46-720 490 967
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Books on the topic "Non-binary codes"

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1977-, Johnston Martin, ed. Non-binary error control coding for wireless communication and data storage. Chichester, West Sussex, U.K: 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 codes"

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Ma, Zhi, Xin Lu, Keqin Feng, and Dengguo Feng. "On Non-binary Quantum BCH Codes." In Lecture Notes in Computer Science, 675–83. Berlin, Heidelberg: 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, 395–401. Berlin, Heidelberg: 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, 41–55. Cham: 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, 107–17. Vienna: 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, 363–69. New Delhi: 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, 125–34. Berlin, Heidelberg: 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, 663–66. Berlin, Heidelberg: 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, 1497–507. New Delhi: 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, 57–64. Cham: 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, 121–33. Cham: 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 codes"

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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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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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Bo Zhou, Li Zhang, Jingyu Kang, Qin Huang, Ying Y. Tai, Shu Lin, and Meina Xu. "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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Changcai Han and Si Li. "Coded cooperation with non-binary codes for wireless networks." In 2012 IEEE 14th International Conference on Communication Technology (ICCT). IEEE, 2012. http://dx.doi.org/10.1109/icct.2012.6511379.

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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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Sassatelli, Lucile, David Declercq, and Charly Poulliat. "Low-rate non-binary hybrid LDPC codes." In 2008 5th International Symposium on Turbo Codes and Related Topics. IEEE, 2008. http://dx.doi.org/10.1109/turbocoding.2008.4658702.

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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 codes"

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

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