STUDIES on GOPALA-HEMACHANDRA CODES and THEIR APPLICATIONS. by Logan Childers December, 2020
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Error Correction Capacity of Unary Coding
Error Correction Capacity of Unary Coding Pushpa Sree Potluri1 Abstract Unary coding has found applications in data compression, neural network training, and in explaining the production mechanism of birdsong. Unary coding is redundant; therefore it should have inherent error correction capacity. An expression for the error correction capability of unary coding for the correction of single errors has been derived in this paper. 1. Introduction The unary number system is the base-1 system. It is the simplest number system to represent natural numbers. The unary code of a number n is represented by n ones followed by a zero or by n zero bits followed by 1 bit [1]. Unary codes have found applications in data compression [2],[3], neural network training [4]-[11], and biology in the study of avian birdsong production [12]-14]. One can also claim that the additivity of physics is somewhat like the tallying of unary coding [15],[16]. Unary coding has also been seen as the precursor to the development of number systems [17]. Some representations of unary number system use n-1 ones followed by a zero or with the corresponding number of zeroes followed by a one. Here we use the mapping of the left column of Table 1. Table 1. An example of the unary code N Unary code Alternative code 0 0 0 1 10 01 2 110 001 3 1110 0001 4 11110 00001 5 111110 000001 6 1111110 0000001 7 11111110 00000001 8 111111110 000000001 9 1111111110 0000000001 10 11111111110 00000000001 The unary number system may also be seen as a space coding of numerical information where the location determines the value of the number. -
Image Data Compression Introduction to Coding
Image Data Compression Introduction to Coding © 2018-19 Alexey Pak, Lehrstuhl für Interaktive Echtzeitsysteme, Fakultät für Informatik, KIT 1 Review: data reduction steps (discretization / digitization) Continuous 2D siGnal Fully diGital siGnal (liGht intensity on sensor) gq (xa, yb,ti ) Discrete time siGnal (pixel voltaGe readinGs) g(xa, yb,ti ) g(x, y,t) Spatial discretization Temporal discretization and diGitization g(xa, yb,t) g(xa, yb,t) gq (xa, yb,t) Discrete value siGnal AnaloG siGnal Spatially discrete siGnal (e.G., # of electrons at each (liGht intensity at a pixel) (pixel-averaGed intensity) pixel of the CCD matrix) © 2018-19 Alexey Pak, Lehrstuhl für Interaktive Echtzeitsysteme, Fakultät für Informatik, KIT 2 Review: data reduction steps (discretization / digitization) Discretization of 1D continuous-time signals (sampling) • Important signal transformations: up- and down-sampling • Information-preserving down-sampling: rate determined based on signal bandwidth • Fourier space allows simple interpretation of the effects due to decimation and interpolation (techniques of up-/down-sampling) Scalar (one-dimensional) signal quantization of continuous-value signals • Quantizer types: uniform, simple non-uniform (with a dead zone, with a limited amplitude) • Advanced quantizers: PDF-optimized (Max-Lloyd algorithm), perception-optimized, SNR- optimized • Implementation: pre-processing with a compander function + simple quantization Vector (multi-dimensional) signal quantization • Terminology: quantization, reconstruction, codebook, distance metric, Voronoi regions, space partitioning • Relation to the general classification problem (from Machine Learning) • Linde-Buzo-Gray algorithm of constructing (sub-optimal) codebooks (aka k-means) © 2018-19 Alexey Pak, Lehrstuhl für Interaktive Echtzeitsysteme, Fakultät für Informatik, KIT 3 LGB vector quantization – 2D example [Linde, Buzo, Gray ‘80]: 1. -
The Existence of Fibonacci Numbers in the Algorithmic Generator for Combinatoric Pascal Triangle
British Journal of Science 62 September 2014, Vol. 11 (2) THE EXISTENCE OF FIBONACCI NUMBERS IN THE ALGORITHMIC GENERATOR FOR COMBINATORIC PASCAL TRIANGLE BY Amannah, Constance Izuchukwu [email protected]; +234 8037720614 Department of Computer Science, Faculty of Natural and Applied Sciences, Ignatius Ajuru University of Education, P.M.B. 5047, Port Harcourt, Rivers State, Nigeria. & Nanwin, Nuka Domaka Department of Computer Science, Faculty of Natural and Applied Sciences, Ignatius Ajuru University of Education, P.M.B. 5047, Port Harcourt, Rivers State, Nigeria © 2014 British Journals ISSN 2047-3745 British Journal of Science 63 September 2014, Vol. 11 (2) ABSTRACT The discoveries of Leonard of Pisa, better known as Fibonacci, are revolutionary contributions to the mathematical world. His best-known work is the Fibonacci sequence, in which each new number is the sum of the two numbers preceding it. When various operations and manipulations are performed on the numbers of this sequence, beautiful and incredible patterns begin to emerge. The numbers from this sequence are manifested throughout nature in the forms and designs of many plants and animals and have also been reproduced in various manners in art, architecture, and music. This work simulated the Pascal triangle generator to produce the Fibonacci numbers or sequence. The Fibonacci numbers are generated by simply taken the sums of the "shallow" diagonals (shown in red) of Pascal's triangle. The Fibonacci numbers occur in the sums of "shallow" diagonals in Pascal's triangle. This Pascal triangle generator is a combinatoric algorithm that outlines the steps necessary for generating the elements and their positions in the rows of a Pascal triangle. -
The Pillars of Lossless Compression Algorithms a Road Map and Genealogy Tree
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 13, Number 6 (2018) pp. 3296-3414 © Research India Publications. http://www.ripublication.com The Pillars of Lossless Compression Algorithms a Road Map and Genealogy Tree Evon Abu-Taieh, PhD Information System Technology Faculty, The University of Jordan, Aqaba, Jordan. Abstract tree is presented in the last section of the paper after presenting the 12 main compression algorithms each with a practical This paper presents the pillars of lossless compression example. algorithms, methods and techniques. The paper counted more than 40 compression algorithms. Although each algorithm is The paper first introduces Shannon–Fano code showing its an independent in its own right, still; these algorithms relation to Shannon (1948), Huffman coding (1952), FANO interrelate genealogically and chronologically. The paper then (1949), Run Length Encoding (1967), Peter's Version (1963), presents the genealogy tree suggested by researcher. The tree Enumerative Coding (1973), LIFO (1976), FiFO Pasco (1976), shows the interrelationships between the 40 algorithms. Also, Stream (1979), P-Based FIFO (1981). Two examples are to be the tree showed the chronological order the algorithms came to presented one for Shannon-Fano Code and the other is for life. The time relation shows the cooperation among the Arithmetic Coding. Next, Huffman code is to be presented scientific society and how the amended each other's work. The with simulation example and algorithm. The third is Lempel- paper presents the 12 pillars researched in this paper, and a Ziv-Welch (LZW) Algorithm which hatched more than 24 comparison table is to be developed. -
The Deep Learning Solutions on Lossless Compression Methods for Alleviating Data Load on Iot Nodes in Smart Cities
sensors Article The Deep Learning Solutions on Lossless Compression Methods for Alleviating Data Load on IoT Nodes in Smart Cities Ammar Nasif *, Zulaiha Ali Othman and Nor Samsiah Sani Center for Artificial Intelligence Technology (CAIT), Faculty of Information Science & Technology, University Kebangsaan Malaysia, Bangi 43600, Malaysia; [email protected] (Z.A.O.); [email protected] (N.S.S.) * Correspondence: [email protected] Abstract: Networking is crucial for smart city projects nowadays, as it offers an environment where people and things are connected. This paper presents a chronology of factors on the development of smart cities, including IoT technologies as network infrastructure. Increasing IoT nodes leads to increasing data flow, which is a potential source of failure for IoT networks. The biggest challenge of IoT networks is that the IoT may have insufficient memory to handle all transaction data within the IoT network. We aim in this paper to propose a potential compression method for reducing IoT network data traffic. Therefore, we investigate various lossless compression algorithms, such as entropy or dictionary-based algorithms, and general compression methods to determine which algorithm or method adheres to the IoT specifications. Furthermore, this study conducts compression experiments using entropy (Huffman, Adaptive Huffman) and Dictionary (LZ77, LZ78) as well as five different types of datasets of the IoT data traffic. Though the above algorithms can alleviate the IoT data traffic, adaptive Huffman gave the best compression algorithm. Therefore, in this paper, Citation: Nasif, A.; Othman, Z.A.; we aim to propose a conceptual compression method for IoT data traffic by improving an adaptive Sani, N.S. -
Pixel-Based Video Coding
UPTEC IT 14 003 Examensarbete 30 hp Mars 2014 Pixel-based video coding Johannes Olsson Sandgren Abstract Pixel-based video coding Johannes Olsson Sandgren Teknisk- naturvetenskaplig fakultet UTH-enheten This paper studies the possibilities of extending the pixel-based compression algorithm LOCO-I, used by the lossless and near lossless image compression standard Besöksadress: JPEG-LS, introduced by the Joint Photographic Experts Group (JPEG) in 1999, to Ångströmlaboratoriet Lägerhyddsvägen 1 video sequences and very low bit-rates. Bitrates below 1 bit per pixel are achieved Hus 4, Plan 0 through skipping signaling when the prediction of a pixels sufficiently good. The pixels to be skipped are implicitly detected by the decoder, minimizing the overhead. Postadress: Different methods of quantization are tested, and the possibility of using vector Box 536 751 21 Uppsala quantization is investigated, by matching pixel sequences against a dynamically generated vector tree. Several different prediction schemes are evaluated, both linear Telefon: and non-linear, with both static and adaptive weights. Maintaining the low 018 – 471 30 03 computational complexity of LOCO-I has been a priority. The results are compared Telefax: to different HEVC implementations with regards to compression speed and ratio. 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student Handledare: Jonatan Samuelsson Ämnesgranskare: Cris Luengo Examinator: Lars-Åke Nordén ISSN: 1401-5749, UPTEC IT 14 003 Tryckt av: Reprocentralen ITC Sammanfattning på svenska De dominerande videokomprimeringsstandarderna idag, som H.26x, är blockbaserade, och har förhållandevis hög beräkningsmässig komplexitet, framförallt i kodningsfasen. I följande text utforskas möjligheten att utöka en välkänd algoritm, LOCO-I, för pixel- baserad komprimering så att komprimering lägre än 1 bit per pixel blir möjlig. -
The Generalized Principle of the Golden Section and Its Applications in Mathematics, Science, and Engineering
Chaos, Solitons and Fractals 26 (2005) 263–289 www.elsevier.com/locate/chaos The Generalized Principle of the Golden Section and its applications in mathematics, science, and engineering A.P. Stakhov International Club of the Golden Section, 6 McCreary Trail, Bolton, ON, Canada L7E 2C8 Accepted 14 January 2005 Abstract The ‘‘Dichotomy Principle’’ and the classical ‘‘Golden Section Principle’’ are two of the most important principles of Nature, Science and also Art. The Generalized Principle of the Golden Section that follows from studying the diagonal sums of the Pascal triangle is a sweeping generalization of these important principles. This underlies the foundation of ‘‘Harmony Mathematics’’, a new proposed mathematical direction. Harmony Mathematics includes a number of new mathematical theories: an algorithmic measurement theory, a new number theory, a new theory of hyperbolic functions based on Fibonacci and Lucas numbers, and a theory of the Fibonacci and ‘‘Golden’’ matrices. These mathematical theories are the source of many new ideas in mathematics, philosophy, botanic and biology, electrical and computer science and engineering, communication systems, mathematical education as well as theoretical physics and physics of high energy particles. Ó 2005 Elsevier Ltd. All rights reserved. Algebra and Geometry have one and the same fate. The rather slow successes followed after the fast ones at the beginning. They left science at such step where it was still far from perfect. It happened,probably,because Mathematicians paid attention to the higher parts of the Analysis. They neglected the beginnings and did not wish to work on such field,which they finished with one time and left it behind. -
Survey on Inverted Index Compression Over Structured Data
Volume 6, No. 3, May 2015 (Special Issue) ISSN No. 0976-5697 International Journal of Advanced Research in Computer Science RESEARCH PAPER Available Online at www.ijarcs.info Survey on Inverted Index Compression over Structured Data B.Usharani M.TanoojKumar Dept.of Computer Science and Engineering Dept.of ComputerScience and Engineering Andhra Loyola Institute of Engineering and Technology Andhra Loyola Institute of Engineering and Technology India India e-mail:[email protected] e-mail:[email protected] Abstract: A user can retrieve the information by providing a few keywords in the search engine. In the keyword search engines, the query is specified in the textual form. The keyword search allows casual users to access database information. In keyword search, the system has to provide a search over billions of documents stored on millions of computers. The index stores summary of information and guides the user to search for more detailed information. The major concept in the information retrieval(IR) is the inverted index. Inverted index is one of the design factors of the index data structures. Inverted index is used to access the documents according to the keyword search. Inverted index is normally larger in size ,many compression techniques have been proposed to minimize the storage space for inverted index. In this paper we propose the Huffman coding technique to compress the inverted index. Experiments on the performance of inverted index compression using Huffman coding proves that this technique requires minimum storage space as well as increases the key word search performance and reduces the time to evaluate the query. -
Habilitation `A Diriger Des Recherches from Image Coding And
Habilitation `aDiriger des Recherches From image coding and representation to robotic vision Marie BABEL Universit´ede Rennes 1 June 29th 2012 Bruno Arnaldi, Professor, INSA Rennes Committee chairman Ferran Marques, Professor, Technical University of Catalonia Reviewer Beno^ıtMacq, Professor, Universit´eCatholique de Louvain Reviewer Fr´ed´ericDufaux, CNRS Research Director, Telecom ParisTech Reviewer Charly Poulliat, Professor, INP-ENSEEIHT Toulouse Examiner Claude Labit, Inria Research Director, Inria Rennes Examiner Fran¸oisChaumette, Inria Research Director, Inria Rennes Examiner Joseph Ronsin, Professor, INSA Rennes Examiner IRISA UMR CNRS 6074 / INRIA - Equipe Lagadic IETR UMR CNRS 6164 - Equipe Images 2 Contents 1 Introduction 3 1.1 An overview of my research project ........................... 3 1.2 Coding and representation tools: QoS/QoE context .................. 4 1.3 Image and video representation: towards pseudo-semantic technologies . 4 1.4 Organization of the document ............................. 5 2 Still image coding and advanced services 7 2.1 JPEG AIC calls for proposal: a constrained applicative context ............ 8 2.1.1 Evolution of codecs: JPEG committee ..................... 8 2.1.2 Response to the call for JPEG-AIC ....................... 9 2.2 Locally Adaptive Resolution compression framework: an overview . 10 2.2.1 Principles and properties ............................ 11 2.2.2 Lossy to lossless scalable solution ........................ 12 2.2.3 Hierarchical colour region representation and coding . 12 2.2.4 Interoperability ................................. 13 2.3 Quadtree Partitioning: principles ............................ 14 2.3.1 Basic homogeneity criterion: morphological gradient . 14 2.3.2 Enhanced color-oriented homogeneity criterion . 15 2.3.2.1 Motivations .............................. 15 2.3.2.2 Results ................................ 16 2.4 Interleaved S+P: the pyramidal profile ........................ -
Efficient Inverted Index Compression Algorithm Characterized by Faster
entropy Article Efficient Inverted Index Compression Algorithm Characterized by Faster Decompression Compared with the Golomb-Rice Algorithm Andrzej Chmielowiec 1,* and Paweł Litwin 2 1 The Faculty of Mechanics and Technology, Rzeszow University of Technology, Kwiatkowskiego 4, 37-450 Stalowa Wola, Poland 2 The Faculty of Mechanical Engineering and Aeronautics, Rzeszow University of Technology, Powsta´ncówWarszawy 8, 35-959 Rzeszow, Poland; [email protected] * Correspondence: [email protected] Abstract: This article deals with compression of binary sequences with a given number of ones, which can also be considered as a list of indexes of a given length. The first part of the article shows that the entropy H of random n-element binary sequences with exactly k elements equal one satisfies the inequalities k log2(0.48 · n/k) < H < k log2(2.72 · n/k). Based on this result, we propose a simple coding using fixed length words. Its main application is the compression of random binary sequences with a large disproportion between the number of zeros and the number of ones. Importantly, the proposed solution allows for a much faster decompression compared with the Golomb-Rice coding with a relatively small decrease in the efficiency of compression. The proposed algorithm can be particularly useful for database applications for which the speed of decompression is much more important than the degree of index list compression. Citation: Chmielowiec, A.; Litwin, P. Efficient Inverted Index Compression Keywords: inverted index compression; Golomb-Rice coding; runs coding; sparse binary sequence Algorithm Characterized by Faster compression Decompression Compared with the Golomb-Rice Algorithm. -
Image Compression Using Extended Golomb Code Vector Quantization and Block Truncation Coding
ISSN(Online): 2319-8753 ISSN (Print): 2347-6710 International Journal of Innovative Research in Science, Engineering and Technology (A High Impact Factor, Monthly, Peer Reviewed Journal) Visit: www.ijirset.com Vol. 8, Issue 11, November 2019 Image Compression Using Extended Golomb Code Vector Quantization And Block Truncation Coding Vinay Kumar1, Prof. Neha Malviya2 M. Tech. Scholar, Department of Electronics and Communication, Swami Vivekanand College of Science & Technology, Bhopal, India1 Assistant Professor, Department of Electronics and Communication, Swami Vivekanand College of Science & Technology, Bhopal, India 2 ABSTRACT: Text and image data are important elements for information processing almost in all the computer applications. Uncompressed image or text data require high transmission bandwidth and significant storage capacity. Designing an efficient compression scheme is more critical with the recent growth of computer applications. Extended Golomb code, for integer representation is proposed and used as a part of Burrows-Wheeler compression algorithm to compress text data. The other four schemes are designed for image compression. Out of four, three schemes are based on Vector Quantization (VQ) method and the fourth scheme is based on Absolute Moment Block Truncation Coding (AMBTC). The proposed scheme is block prediction-residual block coding AMBTC (BP-RBCAMBTC). In this scheme an image is divided into non-overlapping image blocks of small size (4x4 pixels) each. Each image block is encoded using neighboring image blocks which have high correlation among IX them. BP-RBCAMBTC obtains better image quality and low bit rate than the recently proposed method based on BTC. KEYWORDS: Block Truncation Code (BTC), Vector Quantization, Golomb Code Vector I. -
Techniques for Inverted Index Compression
Techniques for Inverted Index Compression GIULIO ERMANNO PIBIRI, ISTI-CNR, Italy ROSSANO VENTURINI, University of Pisa, Italy The data structure at the core of large-scale search engines is the inverted index, which is essentially a collection of sorted integer sequences called inverted lists. Because of the many documents indexed by such engines and stringent performance requirements imposed by the heavy load of queries, the inverted index stores billions of integers that must be searched efficiently. In this scenario, index compression is essential because it leads to a better exploitation of the computer memory hierarchy for faster query processing and, at the same time, allows reducing the number of storage machines. The aim of this article is twofold: first, surveying the encoding algorithms suitable for inverted index compression and, second, characterizing the performance of the inverted index through experimentation. CCS Concepts: • Information systems → Search index compression; Search engine indexing. Additional Key Words and Phrases: Inverted Indexes; Data Compression; Efficiency ACM Reference Format: Giulio Ermanno Pibiri and Rossano Venturini. 2020. Techniques for Inverted Index Compression. ACM Comput. Surv. 1, 1 (August 2020), 35 pages. https://doi.org/10.1145/nnnnnnn.nnnnnnn 1 INTRODUCTION Consider a collection of textual documents each described, for this purpose, as a set of terms. For each distinct term t appearing in the collection, an integer sequence St is built and lists, in sorted order, all the identifiers of the documents (henceforth, docIDs) where the term appears. The sequence St is called the inverted list, or posting list, of the term t and the set of inverted lists for all the distinct terms is the subject of this article – the data structure known as the inverted index.