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Dissertations / Theses on the topic 'Coding theor'

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Published: 4 June 2021

Last updated: 1 February 2022

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1

Pinnawala, Nimalsiri, and nimalsiri pinnawala@rmit edu au. "Properties of Trace Maps and their Applications to Coding Theory." RMIT University. Mathematical and Geospatial Sciences, 2008. http://adt.lib.rmit.edu.au/adt/public/adt-VIT20080515.121603.

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In this thesis we study the application of trace maps over Galois fields and Galois rings in the construction of non-binary linear and non-linear codes and mutually unbiased bases. Properties of the trace map over the Galois fields and Galois rings has been used very successfully in the construction of cocyclic Hadamard, complex Hadamard and Butson Hadamard matrices and consequently to construct linear codes over integers modulo prime and prime powers. These results provide motivation to extend this work to construct codes over integers modulo . The prime factorization of integers paved the way to focus our attention on the direct product of Galois rings and Galois fields of the same degree. We define a new map over the direct product of Galois rings and Galois fields by using the usual trace maps. We study the fundamental properties of the this map and notice that these are very similar to that of the trace map over Galois rings and Galois fields. As such this map called the trace-like map and is used to construct cocyclic Butson Hadamard matrices and consequently to construct linear codes over integers modulo . We notice that the codes construct in this way over the integers modulo 6 is simplex code of type . A further generalization of the trace-like map called the weighted-trace map is defined over the direct product of Galois rings and Galois fields of different degrees. We use the weighted-trace map to construct some non-linear codes and mutually unbiased bases of odd integer dimensions. Further more we study the distribution of over the Galois fields of degree 2 and use it to construct 2-dimensional, two-weight, self-orthogonal codes and constant weight codes over integers modulo prime.

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2

Ryzhikov, Andrew. "Synchronizing automata and coding theory." Thesis, Paris Est, 2020. http://www.theses.fr/2020PESC2030.

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Cette thèse est consacrée a l’étude des mots synchronisant pour les automates finis et les codes. Intuitivement, un mot synchronisant est tel que son application amène le système dans un état indépendant de l'état initial. Un code ou un automate est synchronisant s’il admet un mot synchronisant. Il existe une forte relation entre l’utilisation de cette notion pour les automates ou les codes et son usage est l’un des leitmotifs de cette thèse.Un des principaux outils pour traiter les codes est l’usage d’un automate particulier préservant ses propriétés de synchronisation. Pour les codes préfixes, ceci est obtenu en utilisant un automate déterministe.Nous avons exploré deux problèmes principaux concernant la synchronisation. Le premier consiste à mesurer la longueur du plus court mot synchronisant pour un automate ou un code. Dans le cas d’un automate fini complet et déterministe, un des problèmes les plus anciens de la théorie combinatoire des automates propose une borne quadratique en termes du nombre d'états de l’automate. Nous étendons cette conjecture aux automates partiels non-déterministes. Nous établissons des bornes polynomiales pour ces classes en présence de la forte connexité, et nous discutons leur lien avec la conjecture originale de Černý.La relation avec les codes finis nous permet de prouver l’existence de bornes similaires en termes de la somme des longueurs des mots du code, et aussi de la longueur du plus long mot. Le deuxième cas est lié à une autre importante conjecture, proposée par Restivo. Elle concerne les mots mortels plutôt que synchronisant. Dans la plupart de ces cas, nous examinons aussi la complexité de calcul d’un mot synchronisant court, un deuxième aspect fondamental de cette thèse. Au-delà, nous étudions plusieurs généralisations de la notion de mot synchronisant, qui permettent d’utiliser une information partielle sur sur l’état dans lequel se trouve l’automate. Pour plusieurs de ces généralisations, nous prouvons des bornes inférieures de complexité, même dans ce cas très particuliers<br>This thesis is devoted to studying synchronizing words for finite automata and variable-length codes. Intuitively, a synchronizing word is a word such that its application brings a system into some particular state regardless of its initial state. A code or automaton is synchronizing if it admits a synchronizing word. There is a deep connection between the concrete implementations of this notion for finite automata and variable-length codes, and the use of it is one of the leitmotifs of this thesis.One of the main tools for dealing with variable-length codes is assigning a special automaton preserving many synchronization properties to it. For finite codes, this is done using prefix automata.We investigate two fundamental problems about synchronization. The first one is measuring the length of shortest synchronizing words for synchronizing automata and codes. For the case of complete deterministic finite automata, the Černý conjecture, one of the oldest problems in combinatorial automata theory, proposes a quadratic upper bound in terms of the number of states in the automaton. We broaden this conjecture to partial deterministic finite automata and then to unambiguous non-deterministic finite automata. We show polynomial upper bounds for mentioned classes in the presence of strong connectivity, and discuss their connections with the original Černý conjecture.The relation with finite codes allows us to show similar bounds in terms of the sum of the lengths of the codewords, as well as in terms of the length of the longest codeword. The second case is related to another important conjecture stated by Restivo. It deals with mortal words instead of synchronizing ones, the case which we also investigate. For most of these settings we also examine the computational complexity of finding short synchronizing words, which is the second fundamental question investigated in this thesis. Besides that, we study various generalization of the notion of a synchronizing word, which allow to use some partial information about the current state of an automaton. For several such generalizations we show strong computational complexity lower bounds even in very restricted cases

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3

Redwood-Sawyerr, J. A. S. "Constant envelope modulation coding." Thesis, University of Essex, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.356049.

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4

Chaiyaboonthanit, Thanit. "Image coding using wavelet transform and adaptive block truncation coding /." Online version of thesis, 1991. http://hdl.handle.net/1850/10913.

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5

Cohen, D. A. "A problem in algebraic coding theory." Thesis, University of Oxford, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.380002.

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6

Arslan, Ogul. "Some algebraic problems from coding theory." [Gainesville, Fla.] : University of Florida, 2009. http://purl.fcla.edu/fcla/etd/UFE0024938.

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7

Adistambha, Kevin. "Embedded lossless audio coding using linear prediction and cascade coding." Access electronically, 2005. http://www.library.uow.edu.au/adt-NWU/public/adt-NWU20060724.122433/index.html.

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8

Delopoulos, Athanasios. "Coding techniques for moving images." Thesis, Imperial College London, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338648.

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9

Kaouri, Hussein Ali. "Speech coding using vector quantisation." Thesis, Queen's University Belfast, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.356934.

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10

Allott, David. "Efficient source coding for digital images." Thesis, Loughborough University, 1985. https://dspace.lboro.ac.uk/2134/27563.

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A requirement exists for interactive view-data systems to incorporate some facility for the transmission of good quality multi-level single-frame images (both monochrome and colour) for both general information services and more commercial applications such as mail order catalogues.

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11

Saleemi, Mehwish [Verfasser]. "Coding Theory via Groebner Bases / Mehwish Saleemi." München : Verlag Dr. Hut, 2012. http://d-nb.info/1028785445/34.

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12

Wang, Tsang-Yi Varshney Pramod K. "Distributed fault-tolerant classification using coding theory." Related Electronic Resource: Current Research at SU : database of SU dissertations, recent titles available full text, 2003. http://wwwlib.umi.com/cr/syr/main.

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13

Schmidt, Natalia [Verfasser]. "Gröbner Bases in Coding Theory / Natalia Schmidt." München : Verlag Dr. Hut, 2015. http://d-nb.info/1074063236/34.

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14

Ali, Maaruf. "Fractal image coding techniques and their applications." Thesis, King's College London (University of London), 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.265858.

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15

Dunscombe, Elizabeth Jane. "Some applications of mathematics to coding theory." Thesis, Royal Holloway, University of London, 1988. http://repository.royalholloway.ac.uk/items/a101f1a7-d892-4307-85c4-311c422cdb01/1/.

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This thesis deals with the transmission of data over a channel that is subject to noise, or interference. There are many different methods of trying to achieve reliable communication of data in the presence of noise. This thesis considers some of these methods, in particular, those aspects involving the use of error-correcting codes. A number of specific applications are considered, as well as some more general theory. One general class of codes is that of cyclic codes (where every cyclic shift of a codeword is also a codeword). Chapter 2 of this thesis reviews a decoding scheme for cyclic codes proposed by Professor P.M. Cohn. The scheme is a modification of standard array syndrome decoding. It is shown that Cohn's scheme does not perform as well as the original version of syndrome decoding. Chapter 3 considers Cyclotomically Shortened Reed Solomon codes (a class of codes introduced by J.L. Dornstetter) and their relationship with the Chinese Remainder Theorem codes of J.J. Stone. The blocklength and dimension of these codes is established, together with the best possible lower bound on the minimum distance. The notion of cyclotomic shortening is then extended to Alternant codes. Chapter 4 deals with the subject of interleaving for channels that are subject to bursts of errors. An optimal solution is given to a problem posed by Inmarsat when interleaving is used with a convolutional code. It is shown how to improve the method of interleaving which feeds data column-wise into an array and then transmits row-wise, by careful selection of the order in which the rows are transmitted. The final chapter discusses the concept of an error-correcting code with two different codeword lengths. Some general results about such codes are presented. A method of forming these codes is given for the case when one word length is twice the other. A specific example of this type of code is considered. Both theoretical and simulated performance results are presented for the example.

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16

McEwen, Peter A. "Trellis coding for partial response channels /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 1999. http://wwwlib.umi.com/cr/ucsd/fullcit?p9968170.

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17

Lin, Fu-Huei. "Rate-quality based video coding." Diss., Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/14923.

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18

Cheng, Niann-Tsyr. "Error resilient video coding for noisy channels." Thesis, University of Cambridge, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239176.

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19

Lund, David J. "Reconfigurable channel coding for future communication systems." Thesis, Lancaster University, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.289042.

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20

Suddle, Muhammad Riaz. "Speech coding in private and broadcast networks." Thesis, University of Surrey, 1996. http://epubs.surrey.ac.uk/1019/.

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21

Goh, Kwong Huang. "Wavelet transform based image and video coding." Thesis, University of Strathclyde, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.387720.

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22

Bhagwat, Ashwini. "Methodologies and tools for computation offloading on heterogeneous multicores." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29688.

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Thesis (M. S.)--Computing, Georgia Institute of Technology, 2009.<br>Committee Chair: Pande, Santosh; Committee Member: Clark, Nate; Committee Member: Yalamanchili, Sudhakar. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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23

Kunze, Richard J. "Redundant visual coding of state information /." free to MU campus, to others for purchase, 1997. http://wwwlib.umi.com/cr/mo/fullcit?p9841208.

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24

Yoshida, Beni. "Studying many-body physics through quantum coding theory." Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/77257.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2012.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Cataloged from student-submitted PDF version of thesis.<br>Includes bibliographical references (p. 133-140).<br>The emerging closeness between correlated spin systems and error-correcting codes enables us to use coding theoretical techniques to study physical properties of many-body spin systems. This thesis illustrates the use of classical and quantum coding theory in classifying quantum phases arising in many-body spin systems via a systematic study of stabilizer Hamiltonians with translation symmetries. In the first part, we ask what kinds of quantum phases may arise in gapped spin systems on a D-dimensional lattice. We address this condensed matter theoretical question by giving a complete classification of quantum phases arising in stabilizer Hamiltonians at fixed points of RG transformations for D = 1; 2; 3. We found a certain dimensional duality on geometric shapes of logical operators where m-dimensional and (D m)-dimensional logical operators always form anti-commuting pairs (m is an integer). We demonstrate that quantum phases are completely classified by topological characterizations of logical operators where topological quantum phase transitions are driven by non-analytical changes of geometric shapes of logical operators. As a consequence, we argue that topological order is unstable at any nonzero temperature and self-correcting quantum memory in a strict sense may not exist where the memory time is upper bounded by some constant at a fixed temperature, regardless of the system size. Our result also implies that topological field theory is the universal theory for stabilizer Hamiltonians with continuous scale symmetries. In the second part, we ask the fundamental limit on information storage capacity of discrete spin systems. There is a well-known theoretical limit on the amount of information that can be reliably stored in a given volume of discrete spin systems. Yet, previously known systems were far below this theoretical limit. We propose a construction of classical stabilizer Hamiltonians which asymptotically saturate this limit. Our model borrows an idea from fractal geometries arising in the Sierpinski triangle, and is a rare manifestation of limit cycle behaviors with discrete scale symmetries in real-space RG transformations, which may be beyond descriptions of topological field theory.<br>by Beni Yoshida.<br>Ph.D.

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25

Zhou, Zhi. "Standards conforming video coding optimization /." Thesis, Connect to this title online; UW restricted, 2005. http://hdl.handle.net/1773/5984.

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26

Ahmed, Mohammed Zaki. "Crosstalk-resiliant coding for high density digital recording." Thesis, University of Plymouth, 2003. http://hdl.handle.net/10026.1/2536.

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Increasing the track density in magnetic systems is very difficult due to inter-track interference (ITI) caused by the magnetic field of adjacent tracks. This work presents a two-track partial response class 4 magnetic channel with linear and symmetrical ITI; and explores modulation codes, signal processing methods and error correction codes in order to mitigate the effects of ITI. Recording codes were investigated, and a new class of two-dimensional run-length limited recording codes is described. The new class of codes controls the type of ITI and has been found to be about 10% more resilient to ITI compared to conventional run-length limited codes. A new adaptive trellis has also been described that adaptively solves for the effect of ITI. This has been found to give gains up to 5dB in signal to noise ratio (SNR) at 40% ITI. It was also found that the new class of codes were about 10% more resilient to ITI compared to conventional recording codes when decoded with the new trellis. Error correction coding methods were applied, and the use of Low Density Parity Check (LDPC) codes was investigated. It was found that at high SNR, conventional codes could perform as well as the new modulation codes in a combined modulation and error correction coding scheme. Results suggest that high rate LDPC codes can mitigate the effect of ITI, however the decoders have convergence problems beyond 30% ITI.

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27

Zemouri, Rachid. "Data compression of speech using sub-band coding." Thesis, University of Newcastle Upon Tyne, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.316094.

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28

Lac, Jacquelyn Ha. "Chinese remainder theorem and its applications." CSUSB ScholarWorks, 2008. https://scholarworks.lib.csusb.edu/etd-project/3373.

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29

Cao, Lei. "Error resilient image coding and wireless communications /." free to MU campus, to others for purchase, 2002. http://wwwlib.umi.com/cr/mo/fullcit?p3052160.

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30

Blasco-Serrano, Ricardo. "Coding Strategies for Compress-and-Forward Relaying." Licentiate thesis, KTH, Kommunikationsteori, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-26802.

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The deployment of large communication networks with many autonomous devices has opened new possibilities for transmission. In particular cooperation among the different nodes has been identified as an enabling technology to satisfy the increasing demand of resources. This thesis studies different coding strategies for cooperation in relay channels in the form of compress-and-forward. In the first part of this thesis we consider the application of the newly introduced polar codes for compress-and-forward relaying in relay channels with orthogonal receivers. First we construct polar codes for compress-and-forward relaying based on Slepian-Wolf coding for the scenario where the capacity of the relay-destination channel is large enough. We then consider the more general picture where the capacity of the relay-destination channel is arbitrary. As for Wyner-Ziv coding, we employ nested polar codes for source and channel coding that allow for compression at any desired distortion and exploit the correlation between the observations of the source transmission to minimize the transmission rate over the relay-destination channel. This construction allows for transmission at the prominent compress-and-forward rate under some additional constraints. In the second part of this thesis we propose a new coding strategy for compress-and-forward relaying for half-duplex Gaussian channels. Our code construction is based on simple code concatenation for joint source-channel coding at the relay and iterative decoding at the destination. Finally, we propose several realizations of the structure at the relay and different iterative decoding algorithms in order to adapt the construction to different scenarios. Our simulation results show remarkable performance gains over other cooperation strategies such as decode-and-forward and amplify-and-forward in the scenarios where both source-relay and relay-destination links have low signal-to-noise ratios.<br><p>QC 20101206</p>

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31

Yamazato, Takaya, Iwao Sasase, and Shinsaku Mori. "Interlace Coding System Involving Data Compression Code, Data Encryption Code and Error Correcting Code." IEICE, 1992. http://hdl.handle.net/2237/7844.

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32

Yong, Xuerong. "The channel capacity of one and two-dimensional constrained codes /." View Abstract or Full-Text, 2002. http://library.ust.hk/cgi/db/thesis.pl?COMP%202002%20YONG.

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Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2002.<br>Includes bibliographical references (leaves 105-110). Also available in electronic version. Access restricted to campus users.

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33

Bate, Stephen Donald. "Adaptive coding algorithms for data transmission." Thesis, Coventry University, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.303388.

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34

Pirestani, Shervin. "Source-controlled block turbo coding." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 69 p, 2008. http://proquest.umi.com/pqdlink?did=994238721&sid=2&Fmt=2&clientId=8331&RQT=309&VName=PQD.

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35

Morgenstern, Robert M. "Vector quantization applied to speech coding in the wireless environment." Thesis, This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-07292009-090440/.

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36

Bayrakeri, Sadik. "Scalable video coding using spatio-temporal interpolation." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/15385.

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37

Cesbron, Fred́eŕique Chantal. "Multiresolution fractal coding of still images." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/15508.

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38

Ng, Cheuk-yan, and 吳卓恩. "Rate control algorithms for video coding." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B29729361.

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39

Ng, Cheuk-yan. "Rate control algorithms for video coding /." Hong Kong : University of Hong Kong, 2000. http://sunzi.lib.hku.hk/hkuto/record.jsp?B25151289.

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40

Alexopoulos, Kyriakos. "Phase spectral representation for low bit rate speech coding." Thesis, Imperial College London, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249314.

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41

Fragiacomo, Simon. "Development in channel coding for error and spectral control." Thesis, University College London (University of London), 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.265072.

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42

Easton, Mark. "Fast algorithms for low bit rate digital speech coding." Thesis, University of Liverpool, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.240500.

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43

Kweh, Teck Hock. "Improved quality block-based low bit rate video coding." Thesis, University of Surrey, 1998. http://epubs.surrey.ac.uk/844563/.

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The aim of this research is to develop algorithms for enhancing the subjective quality and coding efficiency of standard block-based video coders. In the past few years, numerous video coding standards based on motion-compensated block-transform structure have been established where block-based motion estimation is used for reducing the correlation between consecutive images and block transform is used for coding the resulting motion-compensated residual images. Due to the use of predictive differential coding and variable length coding techniques, the output data rate exhibits extreme fluctuations. A rate control algorithm is devised for achieving a stable output data rate. This rate control algorithm, which is essentially a bit-rate estimation algorithm, is then employed in a bit-allocation algorithm for improving the visual quality of the coded images, based on some prior knowledge of the images. Block-based hybrid coders achieve high compression ratio mainly due to the employment of a motion estimation and compensation stage in the coding process. The conventional bit-allocation strategy for these coders simply assigns the bits required by the motion vectors and the rest to the residual image. However, at very low bit-rates, this bit-allocation strategy is inadequate as the motion vector bits takes up a considerable portion of the total bit-rate. A rate-constrained selection algorithm is presented where an analysis-by-synthesis approach is used for choosing the best motion vectors in term of resulting bit rate and image quality. This selection algorithm is then implemented for mode selection. A simple algorithm based on the above-mentioned bit-rate estimation algorithm is developed for the latter to reduce the computational complexity. For very low bit-rate applications, it is well-known that block-based coders suffer from blocking artifacts. A coding mode is presented for reducing these annoying artifacts by coding a down-sampled version of the residual image with a smaller quantisation step size. Its applications for adaptive source/channel coding and for coding fast changing sequences are examined.

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44

Liu, Bin. "Dirty paper coding applications in wireless networks /." Thesis, Connect to this title online; UW restricted, 2008. http://hdl.handle.net/1773/5862.

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45

Neeser, Fredy D. "Communication theory and coding for channels with intersymbol interference /." Zürich, 1993. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=10314.

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46

Liu, Youjian. "An algebraic space-time coding theory and its applications /." The Ohio State University, 2001. http://rave.ohiolink.edu/etdc/view?acc_num=osu1488204276534358.

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47

Anim-Appiah, Kofi Dankwa. "Interleaved concalenated coding for input-constrained channels." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/15363.

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48

Andreou, Alexis. "Supports of subcodes and t-designs." Thesis, Queen Mary, University of London, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.321906.

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49

Nikolaidis, Christos. "On binary linear codes with 2-transitive automorphism group and minimum weight four." Thesis, University of Oxford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318832.

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50

Greenough, Philip Peter. "Optimal linear codes over GF(3) and GF(4)." Thesis, University of Salford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.238848.

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