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Journal articles on the topic 'Non-binary codes'

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Author: Grafiati

Published: 4 June 2021

Last updated: 19 February 2022

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Beeharry, Yogesh, Tulsi P. Fowdur, and Krishnaraj M. S. Soyjaudah. "Performance of Hybrid Binary and Non-Binary Turbo Decoding Schemes for LTE and DVB-RCS Standards." ECTI Transactions on Electrical Engineering, Electronics, and Communications 17, no. 1 (September 9, 2019): 1–13. http://dx.doi.org/10.37936/ecti-eec.2019171.215363.

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Binary and Non-Binary Turbo codes have been deployed in several digital communication standards to perform error correction. In order to enhance their error performance, several schemes such as Joint Source Channel Decoding (JSCD), extrinsic information scaling mechanisms, and prioritized QAM constellation mapping have been proposed for improving the error performance of error correcting codes. In this paper, hybrid schemes comprising of JSCD, regression based extrinsic information scaling, and prioritized 16-Quadrature Amplitude Modulation (QAM) with binary and non-binary Turbo codes have been presented. Significant improvement in error performance has been observed with the proposed scheme as compared to the conventional one. The hybrid scheme in the case of binary symmetric and asymmetric LTE Turbo codes, and triple binary Turbo codes outperform the conventional scheme by 0.8 dB on average. With duo-binary Turbo codes for the DVB-RCS standard, the hybrid scheme outperforms the conventional one with an average gain of 0.9 dB in BER performance.

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12

Zhi, Ma, Leng Riguang, Wei Zhengchao, and Zhong Shuqin. "Constructing non-binary asymmetric quantum codes via graphs." China Communications 10, no. 2 (February 2013): 33–41. http://dx.doi.org/10.1109/cc.2013.6472857.

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13

Ge, X., and S. T. Xia. "Structured non-binary LDPC codes with large girth." Electronics Letters 43, no. 22 (2007): 1220. http://dx.doi.org/10.1049/el:20072120.

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14

Tyagi, Vinod, and Tarun Lata. "Restricted bi-byte correcting non-binary optimal codes." Discrete Mathematics, Algorithms and Applications 11, no. 02 (April 2019): 1950019. http://dx.doi.org/10.1142/s1793830919500198.

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In this paper, we have introduced the idea of restricted burst, which is the modification of the classical definition of burst. We show the existence of [Formula: see text]-restricted burst correcting non-binary optimal codes for byte-oriented memories with different possibilities of size of the bytes [Formula: see text] and length of burst [Formula: see text] for [Formula: see text].

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15

Gao, Jian, and Yongkang Wang. "New Non-Binary Quantum Codes Derived From a Class of Linear Codes." IEEE Access 7 (2019): 26418–21. http://dx.doi.org/10.1109/access.2019.2899383.

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16

Yu, Yang, Wen Chen, and Lili Wei. "Design of Convergence-Optimized Non-Binary LDPC Codes over Binary Erasure Channel." IEEE Wireless Communications Letters 1, no. 4 (August 2012): 336–39. http://dx.doi.org/10.1109/wcl.2012.050112.120297.

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17

Fan, Wei Wei, Bo Li, You Wen Zhang, and Da Jun Sun. "Research of FH-MFSK Underwater Acoustic Communication Based on Non-Binary LDPC Codes." Applied Mechanics and Materials 519-520 (February 2014): 945–52. http://dx.doi.org/10.4028/www.scientific.net/amm.519-520.945.

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Compared with binary-modulation, Multiple-modulation can obtain higher rate of transmission in the condition of same symbol-rate. If using binary channel codes with multiple-modulation, there exists an problem of information-loss of the probability from bit to symbol conversion. Underwater acoustic channel is an multipath, time-variation, high-noise and strong doppler-effect wireless channel, which leads to high error-rate caused by signal distortion. To solve the problems above, we adopt FH-MFSK modulation to overcome the inter-symbol interference by multipath. The PN sequence is used as a frame synchronization signal and frequency energy accumulation method is used to detect the frame-synchronization. PN hopping signal is chosen to estimate the doppler frequency-shift and using non-binary LDPC codes based on symbol for channel error codes. Finally, We perform numerical simulations and the experiments on the lake to show that compared with binary LDPC codes, non-binary LDPC codes for multiple-modulation can achieve same error-rate under lower SNR.

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18

Timakul, Sekson, and Somsak Choomchuay. "A Construction of Non Binary LDPC Codes by Circular Matrices." Advanced Materials Research 909 (March 2014): 338–41. http://dx.doi.org/10.4028/www.scientific.net/amr.909.338.

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In LDPC code, the structure of code's parity check matrix plays the crucial role in code performance. In this paper proposes the preliminary investigation of a designed parity check matrix from Tanner. We modify this technique in to non binary LDPC structure and decoding with FFT-SPA. We take into high code rate application more than 0.8. The result has shown that in bit error rate (BER) compare between non-binary LDPC and binary LDPC. In our results, the performance of non binary LDPC has better than binary LDPC.

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19

Weng, Zhenyu, and Yuesheng Zhu. "Efficient Querying from Weighted Binary Codes." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 07 (April 3, 2020): 12346–53. http://dx.doi.org/10.1609/aaai.v34i07.6919.

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Binary codes are widely used to represent the data due to their small storage and efficient computation. However, there exists an ambiguity problem that lots of binary codes share the same Hamming distance to a query. To alleviate the ambiguity problem, weighted binary codes assign different weights to each bit of binary codes and compare the binary codes by the weighted Hamming distance. Till now, performing the querying from the weighted binary codes efficiently is still an open issue. In this paper, we propose a new method to rank the weighted binary codes and return the nearest weighted binary codes of the query efficiently. In our method, based on the multi-index hash tables, two algorithms, the table bucket finding algorithm and the table merging algorithm, are proposed to select the nearest weighted binary codes of the query in a non-exhaustive and accurate way. The proposed algorithms are justified by proving their theoretic properties. The experiments on three large-scale datasets validate both the search efficiency and the search accuracy of our method. Especially for the number of weighted binary codes up to one billion, our method shows a great improvement of more than 1000 times faster than the linear scan.

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20

Hassani, Sanae El, Frederic Guilloud, Ramesh Pyndiah, Marie-Helene Hamon, and Pierre Penard. "New Optimizations for Layered Non-Binary LDPC Codes Decoding." International Journal of Applied Research on Information Technology and Computing 3, no. 1 (2012): 46. http://dx.doi.org/10.5958/j.0975-8070.3.1.005.

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21

Al-Hilali, Riyadh A., Abdulkareem S. Abdallah, and Raad H. Thaher. "A Novel Decoding Method for Non-Binary TCM Codes." Communications and Network 06, no. 01 (2014): 22–28. http://dx.doi.org/10.4236/cn.2014.61004.

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22

Zhang, Xinmiao, and Fang Cai. "Reduced-Complexity Decoder Architecture for Non-Binary LDPC Codes." IEEE Transactions on Very Large Scale Integration (VLSI) Systems 19, no. 7 (July 2011): 1229–38. http://dx.doi.org/10.1109/tvlsi.2010.2047956.

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23

Huang, Qin, and Shuai Yuan. "Bit Reliability-Based Decoders for Non-Binary LDPC Codes." IEEE Transactions on Communications 64, no. 1 (January 2016): 38–48. http://dx.doi.org/10.1109/tcomm.2015.2501298.

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24

Zhao, Shancheng, Xiujie Huang, and Xiao Ma. "Structural Analysis of Array-Based Non-Binary LDPC Codes." IEEE Transactions on Communications 64, no. 12 (December 2016): 4910–22. http://dx.doi.org/10.1109/tcomm.2016.2609906.

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25

Zhao, Shancheng, and Xiao Ma. "Extended construction of array‐based non‐binary LDPC codes." Electronics Letters 55, no. 4 (February 2019): 196–98. http://dx.doi.org/10.1049/el.2018.7527.

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26

Chao-Cheng Huang, Chi-Jen Wu, Chao-Yu Chen, and Chi-chao Chao. "Parallel Symbol-Flipping Decoding for Non-Binary LDPC Codes." IEEE Communications Letters 17, no. 6 (June 2013): 1228–31. http://dx.doi.org/10.1109/lcomm.2013.051313.130303.

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27

Paluncic, Filip, and B. T. Maharaj. "Capacity-Approaching Non-Binary Balanced Codes Using Auxiliary Data." IEEE Transactions on Information Theory 65, no. 1 (January 2019): 159–73. http://dx.doi.org/10.1109/tit.2018.2844834.

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28

Kasai, Kenta, David Declercq, and Kohichi Sakaniwa. "Fountain Coding via Multiplicatively Repeated Non-Binary LDPC Codes." IEEE Transactions on Communications 60, no. 8 (August 2012): 2077–83. http://dx.doi.org/10.1109/tcomm.2012.061112.110177.

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29

Ciobanu, Alexandru, Saied Hemati, and Warren J. Gross. "Adaptive Multiset Stochastic Decoding of Non-Binary LDPC Codes." IEEE Transactions on Signal Processing 61, no. 16 (August 2013): 4100–4113. http://dx.doi.org/10.1109/tsp.2013.2264813.

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30

Dabak, Beyza, Ahmed Hareedy, and Robert Calderbank. "Non-Binary Constrained Codes for Two-Dimensional Magnetic Recording." IEEE Transactions on Magnetics 56, no. 11 (November 2020): 1–10. http://dx.doi.org/10.1109/tmag.2020.3017511.

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31

Mostari, Latifa, Abdelmalik Taleb-Ahmed, and Abdennacer Bounoua. "Simplified soft output demapper for non-binary LDPC codes." Optik 126, no. 24 (December 2015): 5074–76. http://dx.doi.org/10.1016/j.ijleo.2015.09.210.

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32

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 (April 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 good quantum parameters is presented. The preference of this method specially for Abelian group association schemes is that one can construct any binary quantum stabilizer code with any distance by using the commutative structure of association schemes.

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33

Hartanto, Ari Dwi, and Al Sutjijana. "Binary Cyclic Pearson Codes." Jurnal Matematika MANTIK 7, no. 1 (March 18, 2021): 1–8. http://dx.doi.org/10.15642/mantik.2021.7.1.1-8.

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The phenomena of unknown gain or offset on communication systems and modern storages such as optical data storage and non-volatile memory (flash) becomes a serious problem. This problem can be handled by Pearson distance applied to the detector because it offers immunity to gain and offset mismatch. This distance can only be used for a specific set of codewords, called Pearson codes. An interesting example of Pearson code can be found in T-constrained code class. In this paper, we present binary 2-constrained codes with cyclic property. The construction of this code is adopted from cyclic codes, but it cannot be considered as cyclic codes.

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34

Gierszal, Henryk, Witold Hołubowicz, Łukasz Kiedrowski, and Adam Flizikowski. "Performance of Non-Binary LDPC Codes for Next Generation Mobile Systems." International Journal of Electronics and Telecommunications 56, no. 2 (June 1, 2010): 111–16. http://dx.doi.org/10.2478/v10177-010-0014-3.

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Performance of Non-Binary LDPC Codes for Next Generation Mobile SystemsA new family of non-binary LDPC is presented that are based on a finite field GF(64). They may be successfully implemented in single-carrier and OFDM transmission system. Results prove that DAVINCI codes allow for improving the system performance and may be considered to be applied in the future mobile system.

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35

Blasco, Francisco Lazaro, Giuliano Garrammone, and Gianluigi Liva. "Parallel Concatenation of Non-Binary Linear Random Fountain Codes with Maximum Distance Separable Codes." IEEE Transactions on Communications 61, no. 10 (October 2013): 4067–75. http://dx.doi.org/10.1109/tcomm.2013.090513.120834.

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36

Borissov, Yuri, Nickolai Manev, and Svetla Nikova. "On the non-minimal codewords in binary Reed–Muller codes." Discrete Applied Mathematics 128, no. 1 (May 2003): 65–74. http://dx.doi.org/10.1016/s0166-218x(02)00436-5.

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37

Herbert, Alan. "ALU non-B-DNA conformations, flipons, binary codes and evolution." Royal Society Open Science 7, no. 6 (June 2020): 200222. http://dx.doi.org/10.1098/rsos.200222.

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ALUs contribute to genetic diversity by altering DNA's linear sequence through retrotransposition, recombination and repair. ALUs also have the potential to form alternative non-B-DNA conformations such as Z-DNA, triplexes and quadruplexes that alter the read-out of information from the genome. I suggest here these structures enable the rapid reprogramming of cellular pathways to offset DNA damage and regulate inflammation. The experimental data supporting this form of genetic encoding is presented. ALU sequence motifs that form non-B-DNA conformations under physiological conditions are called flipons. Flipons are binary switches. They are dissipative structures that trade energy for information. By efficiently targeting cellular machines to active genes, flipons expand the repertoire of RNAs compiled from a gene. Their action greatly increases the informational capacity of linearly encoded genomes. Flipons are programmable by epigenetic modification, synchronizing cellular events by altering both chromatin state and nucleosome phasing. Different classes of flipon exist. Z-flipons are based on Z-DNA and modify the transcripts compiled from a gene. T-flipons are based on triplexes and localize non-coding RNAs that direct the assembly of cellular machines. G-flipons are based on G-quadruplexes and sense DNA damage, then trigger the appropriate protective responses. Flipon conformation is dynamic, changing with context. When frozen in one state, flipons often cause disease. The propagation of flipons throughout the genome by ALU elements represents a novel evolutionary innovation that allows for rapid change. Each ALU insertion creates variability by extracting a different set of information from the neighbourhood in which it lands. By elaborating on already successful adaptations, the newly compiled transcripts work with the old to enhance survival. Systems that optimize flipon settings through learning can adapt faster than with other forms of evolution. They avoid the risk of relying on random and irreversible codon rewrites.

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38

Wu, Daolong, Yue Sun, and Ying Li. "Rate assignment for multi-level polarised non-binary polar codes." IET Communications 10, no. 10 (July 1, 2016): 1151–55. http://dx.doi.org/10.1049/iet-com.2015.0738.

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39

Dolecek, Lara, Dariush Divsalar, Yizeng Sun, and Behzad Amiri. "Non-Binary Protograph-Based LDPC Codes: Enumerators, Analysis, and Designs." IEEE Transactions on Information Theory 60, no. 7 (July 2014): 3913–41. http://dx.doi.org/10.1109/tit.2014.2316215.

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40

Le, Tuan A., and Hieu D. Nguyen. "New Multiple Insertion/Deletion Correcting Codes for Non-Binary Alphabets." IEEE Transactions on Information Theory 62, no. 5 (May 2016): 2682–93. http://dx.doi.org/10.1109/tit.2016.2541139.

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41

Deka, Kuntal, A. Rajesh, and Prabin Kumar Bora. "EXIT Chart Analysis of Puncturing for Non-Binary LDPC Codes." IEEE Communications Letters 18, no. 12 (December 2014): 2089–92. http://dx.doi.org/10.1109/lcomm.2014.2366119.

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42

Baldi, Marco, Franco Chiaraluce, Nicola Maturo, Gianluigi Liva, and Enrico Paolini. "A Hybrid Decoding Scheme for Short Non-Binary LDPC Codes." IEEE Communications Letters 18, no. 12 (December 2014): 2093–96. http://dx.doi.org/10.1109/lcomm.2014.2367097.

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43

Arul Murugan, C., B. Banuselvasaraswathy, K. Gayathree, and M. Ishwarya Niranjana. "Efficient high throughput decoding architecture for non-binary LDPC codes." International Journal of Engineering & Technology 7, no. 2.8 (March 19, 2018): 195. http://dx.doi.org/10.14419/ijet.v7i2.8.10407.

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This article, deals with efficient trellis inbuilt decoding architecture for non-binary Linear Density Parity Check (LDPC) codes. In this decoder, a bidirectional recursion is embedded to enhance the layered scheduling and decoding latency, which in turn is used to minimize the number of iterations compared to existing techniques. Consequently, it is necessary to increase the throughput for improving the efficiency of the system. In addition, a compression technique is implemented for reducing the requirements of memory and the area. Trellis based decoder was used to reinforce the check node processing. The proposed decoder for LDPC codes yields high throughput when compared to other similar decoders presented in preceding works. The designed architecture was implemented using Cadence Virtuoso software. This decoder provides a throughput of about 39.21 Mb/s at clock frequency of 190MHz.

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44

Ashikhmin, Alexey E., and Simon N. Litsyn. "Fast Decoding of Non-Binary First Order Reed-Muller Codes." Applicable Algebra in Engineering, Communication and Computing 7, no. 4 (June 1, 1996): 299–308. http://dx.doi.org/10.1007/s002000050035.

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45

Hou, Xiang-dong. "On the asymptotic number of non-equivalent binary linear codes." Finite Fields and Their Applications 13, no. 2 (April 2007): 318–26. http://dx.doi.org/10.1016/j.ffa.2005.09.002.

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46

Ashikhmin, Alexey E., and Simon N. Litsyn. "Fast decoding of non-binary first order Reed-Muller codes." Applicable Algebra in Engineering, Communication and Computing 7, no. 4 (July 1996): 299–308. http://dx.doi.org/10.1007/bf01195535.

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47

Puppe, V. "Group Actions and Codes." Canadian Journal of Mathematics 53, no. 1 (February 1, 2001): 212–24. http://dx.doi.org/10.4153/cjm-2001-009-0.

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AbstractA 2-action with “maximal number of isolated fixed points” (i.e., with only isolated fixed points such that dimk(⊕iHi (M; k)) = |M2|, k = ) on a 3-dimensional, closed manifold determines a binary self-dual code of length = . In turn this code determines the cohomology algebra H*(M; k) and the equivariant cohomology . Hence, from results on binary self-dual codes one gets information about the cohomology type of 3-manifolds which admit involutions with maximal number of isolated fixed points. In particular, “most” cohomology types of closed 3-manifolds do not admit such involutions. Generalizations of the above result are possible in several directions, e.g., one gets that “most” cohomology types (over ) of closed 3-manifolds do not admit a non-trivial involution.

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48

Ansari, A. S., T. Shah, Zia Ur-Rahman, and Antonio A. Andrade. "Sequences of Primitive and Non-primitive BCH Codes." TEMA (São Carlos) 19, no. 2 (September 12, 2018): 369. http://dx.doi.org/10.5540/tema.2018.019.02.369.

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In this work, we introduce a method by which it is established that; how a sequence of non-primitive BCH codes can be obtained by a given primitive BCH code. For this, we rush to the out of routine assembling technique of BCH codes and use the structure of monoid rings instead of polynomial rings. Accordingly, it is gotten that there is a sequence $\{C_{b^{j}n}\}_{1\leq j\leq m}$, where $b^{j}n$ is the length of $C_{b^{j}n}$, of non-primitive binary BCH codes against a given binary BCH code $C_{n}$ of length $n$. Matlab based simulated algorithms for encoding and decoding for these type of codes are introduced. Matlab provides built in routines for construction of a primitive BCH code, but impose several constraints, like degree $s$ of primitive irreducible polynomial should be less than $16$. This work focuses on non-primitive irreducible polynomials having degree $bs$, which go far more than 16.

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49

M, Sakthivel, Karthick Raja M, Ragupathy KR, and Sathis Kumar K. "Performance Comparison of Eg-Ldpc Codes With Maximum Likelihood Algorithm Over Non-Binary Ldpc Codes." International Journal of Computational Science and Information Technology 2, no. 2 (May 30, 2014): 43–53. http://dx.doi.org/10.5121/ijcsity.2014.2205.

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50

Bezzateev, Sergey V., and Natalia A. Shekhunova. "Lower Bounds on the Covering Radius of the Non-Binary and Binary Irreducible Goppa Codes." IEEE Transactions on Information Theory 64, no. 11 (November 2018): 7171–77. http://dx.doi.org/10.1109/tit.2018.2867839.

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