DOCSLIB.ORG

Jpeg Image Compression and Decompression

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Jpeg Image Compression and Decompression 1. INTRODUCTION 1.1 GENERAL INTRODUCTION In today’s digital world, when we see digital movie, listen digital music, read digital mail, store documents digitally, making conversation digitally, we have to deal with huge amount of digital data. So, data compression plays a very significant role to keep the digital world realistic. If there were no data compression techniques, we would have not been able to listen to songs over the Internet, see digital pictures or movies, or we would have not heard about video conferencing or telemedicine. How data compression made it possible? What are the main advantages of data compression in digital world? There may be many answers but the three obvious reasons are the saving of memory space for storage, channel bandwidth and the processing time for transmission. Every one of us might have experienced that before the advent MP3, hardly 4 or 5 songs of wav file could be accommodated. And it was not possible to send a wav file through mail because of its tremendous file size. Now, we can easily accommodate 50 to 60 songs of MP3 in a music CD of same capacity. Because, the uncompressed audio files can be compressed 10 to 15 times using MP3 format and we have no problem in sending any of our favorite music to our distant friends in any corner of the world. Also, we can download a song in MP3 in a matter of seconds. Similar compression schemes were developed for other digital data like images and videos. Videos are nothings but the animations of frames of images in a proper sequence at a rate of 30 frames per second or higher. A huge amount of memory is required for storing video files. The possibility of storing 4/5 movies in DVD CD now rather than we used 2/3 CDs for a movie file is because compression. We will consider here mainly the image compression techniques. 1.2 MOTIVATION Image compression is an important issue in digital image processing and finds extensive applications in many fields. This is the basic operation performed frequently by any digital photography technique to capture an image. For longer use of the portable photography device it should consume less power so that battery life will be more. To improve the Conventional techniques of image compressions 1 using the DW T have already been reported and sufficient literatures are available on this.The JPEG is a lossy compression scheme, which employs the DWT as a tool and used mainly in digital cameras for compression of images. In the recent past the demand for low power image compression is growing. As a result various research workers are actively engaged to evolve efficient methods of image compression using latest digital signal processing techniques. The objective is to achieve a reasonable compression ratio as well as better quality of reproduction of image with a low power consumption. Keeping these objectives in mind the research work in the present thesis has been undertaken. In sequel the following problems have been investigated. 1.3 OBJECTIVE OF THE PROJECT Image Compression addresses the problem of reducing the amount of data required to represent the digital image. Compression is achieved by the removal of one or more of three basic data redundancies: (1) Coding redundancy, which is present when less than optimal (i.e.the smallest length) code words are used; (2) Interpixel redundancy, which results from correlations between the pixels of an image; &/or (3) psycho visual redundancy which is due to data that is ignored by the human visual system (i.e. visually nonessential information).Huffman codes contain the smallest possible number of code symbols (e.g., bits) per source symbol (e.g., grey level value) subject to the constraint that the source symbols are coded one at a time. So, Huffman coding when combined with technique of reducing the image redundancies using Discrete Wavelet Transform (DWT) helps in compressing the image data to a very good extent. 1.4 ORGANIZATION OF DOCUMENTATION In this project documentation we have initially put the definition and objective of the project as well as the design of the project which is followed by the implementation and testing phases. Finally the project has been concluded successfully and also the future enhancements of the project were given in this Documentation. 1.5 JPEG IMAGE 2 JPEG is the most common image format used by digital cameras and other photographic image capture devices for storing and transmitting photographic images on the World Wide Web. JPEG compression is used in a number of image file formats these format variations are often not distinguished and are simply called JPEG. The term "JPEG" is an acronym for the Joint Photographic Experts Group which created the standard Image data compression is concerned with minimizing the number of bits required to represent an image with no significant loss of information. Image compression algorithms aim to remove redundancy present in the data (correlation of data) in a way which makes image reconstruction possible; this is called information preserving compression Perhaps the simplest and most dramatic form of data compression is the sampling of band limited images, where an infinite number of pixels per unit area are reduced to one sample without any loss of information. Transform based methods better preserve subjective image quality, and are less sensitive to statistical image property changes both inside a single images and between images. Prediction methods provide higher compression ratios in a much less expensive way. If compressed images are transmitted an important property is insensitivity to transmission channel noise. Transform based techniques are significantly less sensitivity to channel noise. If transform coefficients are corrupted during transmission, the resulting image is spread homogeneously through the image or image part and is not too disturbing. 2. LITERATURE SURVEY 3 2.1 INTRODUCTION For the past few years, a joint ISO/CCITT committee known as JPEG (Joint Photographic Experts Group) has been working to establish the first international compression standard for continuous-tone still images, both grayscale and color. JPEG’s proposed standard aims to be generic support a wide variety of applications for continuous-tone images. To meet the differing needs of many applications, the JPEG standard includes two basic compression methods, each with various modes of operation. A DWT-based method is specified for “lossy’’ compression, and a predictive method for “lossless’’ compression. JPEG features a simple lossy technique known as the Baseline method, a subset of the other DWT-based modes of operation. The Baseline method has been by far the most widely implemented JPEG method to date, and is sufficient in its own right for a large number of applications. This article provides an overview of the JPEG standard, and focuses in detail on the Baseline method. Advances over the past decade in many aspects of digital technology especially devices for image acquisition, data storage, and bitmapped printing and display - have brought about many applications of digital imaging. However, these applications tend to be specialized due to their relatively high cost. With the possible exception of facsimile, digital images are not commonplace in general-purpose computing systems the way text and geometric graphics are. The majority of modern business and consumer usage of photographs and other types of images take place through more traditional analog means. 2.2 EXISTING SYSTEM Discrete cosine transform (DCT) is widely used in image processing, especially for compression. Some of the applications of two-dimensional DCT involve still image compression and compression of individual video frames, while multidimensional DCTis mostly used for compression of video streams. DCT is also useful for transferring multi dimensional data to frequency domain, where different operations, like spread spectrum, data compression, data watermarking, can be performed in easier and more efficient manner. A number of papers discussing DCT algorithms is available in the literature that signifies its importance and application 4 2.3 DISADVANTAGES OF EXISTING SYSTEM 1. Assuming a periodic input, the magnitude of the DFT coefficients is spatially invariant .This is not true for the DCT. 2. Only spatial correlation of the pixels inside the single 2-D block is considered and the correlation from the pixels of the neighboring blocks is neglected 3. Impossible to completely decor relate the blocks at their boundaries using DCT 4. Undesirable blocking artifacts affect the reconstructed images or video frames. (high compression ratios or very low bit rates) 2.4 PROPOSED SYSTEM The Discrete wavelet transform (DWT) has gained widespread acceptance in signal processing and image compression. Because of their inherent multi-resolution nature, wavelet-coding schemes are especially suitable for applications where scalability and tolerable degradation are important. Recently the JPEG committee has released its new image coding standard, JPEG- 2000, which has been based upon DWT . DWT has a good localization property in the time domain and frequency domain. Number of encoding bits is less compare to existing method. 2.5 CONCLUSION Image compression is of prime importance in Real time applications like video conferencing where data are transmitted through a channel.Using JPEG standard DCT is used for mapping which reduces the inter pixel redundancies followed by quantization which reduces the psychovisual redundancies then coding redundancy is reduced by the use of optimal code word having minimum average length. 3. ANALYSIS 3.1 INTRODUCTION 5 The of the project is to compress the image the image by using SPIHT with entrophy encoder. Traditional image coding technology mainly uses the statistical redundancy between pixels to reach the goal of compressing. The research on wavelet transform image coding technology has made a rapid progress. Because of its high speed, low memory requirements and complete reversibility, digital wavelet transform (IWT) has been adopted by new image coding standard, JPEG 2000.
Load more

Recommended publications
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • Lelewer and Hirschberg, "Data Compression"
    Data Compression DEBRA A. LELEWER and DANIEL S. HIRSCHBERG Department of Information and Computer Science, University of California, Irvine, California 92717 This paper surveys a variety of data compression methods spanning almost 40 years of research, from the work of Shannon, Fano, and Huffman in the late 1940s to a technique developed in 1986. The aim of data compression is to reduce redundancy in stored or communicated data, thus increasing effective data density. Data compression has important application in the areas of file storage and distributed systems. Concepts from information theory as they relate to the goals and evaluation of data compression methods are discussed briefly. A framework for evaluation and comparison of methods is constructed and applied to the algorithms presented. Comparisons of both theoretical and empirical natures are reported, and possibilities for future research are suggested Categories and Subject Descriptors: E.4 [Data]: Coding and Information Theory-data compaction and compression General Terms: Algorithms, Theory Additional Key Words and Phrases: Adaptive coding, adaptive Huffman codes, coding, coding theory, tile compression, Huffman codes, minimum-redundancy codes, optimal codes, prefix codes, text compression INTRODUCTION mation but whose length is as small as possible. Data compression has important Data compression is often referred to as application in the areas of data transmis- coding, where coding is a general term en- sion and data storage. Many data process- compassing any special representation of ing applications require storage of large data that satisfies a given need. Informa- volumes of data, and the number of such tion theory is defined as the study of applications is constantly increasing as the efficient coding and its consequences in use of computers extends to new disci- the form of speed of transmission and plines.
    [Show full text]
  • ABSTRACT Title of Thesis: a LOGIC SYSTEM for FIBONACCI
    ABSTRACT Title of Thesis: A LOGIC SYSTEM FOR FIBONACCI NUMBERS EQUIVALENT TO 64-BIT BINARY Jiani Shen, Master of Science, 2018 Thesis Directed By: Professor Robert W. Newcomb, Electrical & Computer Engineering Compared to the most commonly used binary computers, the Fibonacci computer has its own research values. Making study of Fibonacci radix system is of considerable importance to the Fibonacci computer. Most materials only explain how to use binary coefficients in Fibonacci base to represent positive integers and introduce a little about basic arithmetic on positive integers using complicated but incomplete methods. However, rarely have materials expanded the arithmetic to negative integers with an easier way. In this thesis, we first transfer the unsigned binary Fibonacci representation with minimal form(UBFR(min)) into the even-subscripted signed ternary Fibonacci representation(STFRe), which includes the negative integers and doubles the range over UBFR(min). Then, we develop some basic operations on both positive and negative integers by applying various properties of the Fibonacci sequence into arithmetic. We can set the arithmetic range equivalent to 64-bit binary as our daily binary computers, or whatever reasonable ranges we want. A LOGIC SYSTEM FOR FIBONACCI NUMBERS EQUIVALENT TO 64-BIT BINARY by Jiani Shen Thesis submitted to the Faculty of the Graduate School of the University of Maryland, College Park, in partial fulfillment of the requirements for the degree of [Master of Science] [2018] Advisory Committee: Professor [Robert W. Newcomb], Chair Professor A. Yavuz Oruc Professor Gang Qu © Copyright by [Jiani Shen] [2018] Acknowledgements Sincere thanks to dear Professor Robert Newcomb. He guides me to do the thesis and reviews the papers for me diligently.
    [Show full text]
  • Variable-Length Coding: Unary Coding Golomb Coding Elias Gamma and Delta Coding Fibonacci Coding
    www.vsb.cz Analysis and Signal Compression Information and Probability Theory Michal Vašinek VŠB – Technická univerzita Ostrava FEI/EA404 [email protected] 2020, February 12th Content Classes of Codes Variable-length coding: Unary coding Golomb coding Elias Gamma and Delta coding Fibonacci coding Michal Vašinek (VŠB-TUO) Analysis and Signal Compression 1 / 22 Codes Obrázek: Classes of codes, Cover and Thomas, Elements of Information Theory, p. 106. Michal Vašinek (VŠB-TUO) Analysis and Signal Compression 2 / 22 Nonsigular code Let X be a range of random variable X, for instance the alphabet of input data. Let D be d-ary alphabet of output, for instance binary alphabet D = f0; 1g. Nonsingular Code A code is said to be nonsingular if every element of the range of X maps into different string in D∗; that is: x 6= x0 ! C(x) 6= C(x0) Michal Vašinek (VŠB-TUO) Analysis and Signal Compression 3 / 22 Nonsigular code Nonsingular Code A code is said to be nonsingular if every element of the range of X maps into different string in D∗; that is: x 6= x0 ! C(x) 6= C(x0) Let C(’a’) = 0, C(’b’)=00, C(’c’)=01 be codewords of code C. Encode the sequence s = abc, i.e. C(s) = 0 00 01 = 00001. We can decode in many ways: aaac, bac, abc. Can be solved by adding special separating symbol. For instance with code 11. Michal Vašinek (VŠB-TUO) Analysis and Signal Compression 4 / 22 Uniquely Decodable Codes Definition The extension C∗ of a code C is the mapping from finite length strings of X to finite-length strings of D, defined by: C(x1x2; : : : ; xn) = C(x1)C(x2) :::C(xn) For instance, if C(x1) = 00 and C(x2) = 11 then C(x1x2) = 0011.
    [Show full text]
  • New Classes of Random Sequences For
    NEW CLASSES OF RANDOM SEQUENCES FOR CODING AND CRYPTOGRAPHY APPLICATIONS By KIRTHI KRISHNAMURTHY VASUDEVA MURTHY Bachelor of Engineering in Instrumentation Technology Visvesvaraya Technological University Bangalore, Karnataka 2013 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of MASTER OF SCIENCE May, 2016 NEW CLASSES OF RANDOM SEQUENCES FOR CODING AND CRYPTOGRAPHY APPLICATIONS Thesis Approved: Dr. Subhash Kak Thesis Adviser Dr. Keith A Teague Dr. George Scheets ii ACKNOWLEDGEMENTS I would like to express my deep gratitude to my master’s thesis advisor Dr. Subhash Kak. He continually and convincingly conveyed a spirit of adventure and motivation in regard to research with profound patience handling me in all my tough situations. Without his persistent support, this thesis would not have been possible. I render my sincere thanks to my committee members, Dr. Keith Teague and Dr. George Scheets for their support and guidance in final stages of thesis presentation and document review. I thank Oklahoma State University for giving opportunity to utilize and enhance my technical knowledge. Lastly, I would like to thank my parents and friends for constant encouragement emotionally and financially to pursue masters and complete thesis research and document at OSU. iii Acknowledgements reflect the views of the author and are not endorsed by committee members or Oklahoma State University. Name: KIRTHI KRISHNAMURTHY VASUDEVA MURTHY Date of Degree: MAY, 2016 Title of Study: NEW CLASSES OF RANDOM SEQUENCES FOR CODING AND CRYPTOGRAPHY APPLICATIONS Major Field: ELECTRICAL ENGINEERING Abstract: Cryptography is required for securing data in a digital or analog medium and there exists a variety of protocols to encode the data and decrypt them without third party interference.
    [Show full text]
  • Entropy Coding and Different Coding Techniques
    Journal of Network Communications and Emerging Technologies (JNCET) www.jncet.org Volume 6, Issue 5, May (2016) Entropy Coding and Different Coding Techniques Sandeep Kaur Asst. Prof. in CSE Dept, CGC Landran, Mohali Sukhjeet Singh Asst. Prof. in CS Dept, TSGGSK College, Amritsar. Abstract – In today’s digital world information exchange is been 2. CODING TECHNIQUES held electronically. So there arises a need for secure transmission of the data. Besides security there are several other factors such 1. Huffman Coding- as transfer speed, cost, errors transmission etc. that plays a vital In computer science and information theory, a Huffman code role in the transmission process. The need for an efficient technique for compression of Images ever increasing because the is a particular type of optimal prefix code that is commonly raw images need large amounts of disk space seems to be a big used for lossless data compression. disadvantage during transmission & storage. This paper provide 1.1 Basic principles of Huffman Coding- a basic introduction about entropy encoding and different coding techniques. It also give comparison between various coding Huffman coding is a popular lossless Variable Length Coding techniques. (VLC) scheme, based on the following principles: (a) Shorter Index Terms – Huffman coding, DEFLATE, VLC, UTF-8, code words are assigned to more probable symbols and longer Golomb coding. code words are assigned to less probable symbols. 1. INTRODUCTION (b) No code word of a symbol is a prefix of another code word. This makes Huffman coding uniquely decodable. 1.1 Entropy Encoding (c) Every source symbol must have a unique code word In information theory an entropy encoding is a lossless data assigned to it.
    [Show full text]
  • STUDIES on GOPALA-HEMACHANDRA CODES and THEIR APPLICATIONS. by Logan Childers December, 2020
    STUDIES ON GOPALA-HEMACHANDRA CODES AND THEIR APPLICATIONS. by Logan Childers December, 2020 Director of Thesis: Krishnan Gopalakrishnan, PhD Major Department: Computer Science Gopala-Hemachandra codes are a variation of the Fibonacci universal code and have ap- plications in data compression and cryptography. We study a specific parameterization of Gopala-Hemachandra codes and present several results pertaining to these codes. We show that GHa(n) always exists for n ≥ 1 when −2 ≥ a ≥ −4, meaning that these are universal codes. We develop two new algorithms to determine whether a GH code exists for a given a and n, and to construct them if they exist. We also prove that when a = −(4 + k) where k ≥ 1, that there are at most k consecutive integers for which GH codes do not exist. In 2014, Nalli and Ozyilmaz proposed a stream cipher based on GH codes. We show that this cipher is insecure and provide experimental results on the performance of our program that cracks this cipher. STUDIES ON GOPALA-HEMACHANDRA CODES AND THEIR APPLICATIONS. A Thesis Presented to The Faculty of the Department of Computer Science East Carolina University In Partial Fulfillment of the Requirements for the Degree Master of Science in Computer Science by Logan Childers December, 2020 Copyright Logan Childers, 2020 STUDIES ON GOPALA-HEMACHANDRA CODES AND THEIR APPLICATIONS. by Logan Childers APPROVED BY: DIRECTOR OF THESIS: Krishnan Gopalakrishnan, PhD COMMITTEE MEMBER: Venkat Gudivada, PhD COMMITTEE MEMBER: Karl Abrahamson, PhD CHAIR OF THE DEPARTMENT OF COMPUTER SCIENCE: Venkat Gudivada, PhD DEAN OF THE GRADUATE SCHOOL: Paul J. Gemperline, PhD Table of Contents LIST OF TABLES ..................................
    [Show full text]
  • Fibonacci Codes for Crosstalk Avoidance
    IOSR Journal of Electronics and Communication Engineering (IOSR-JECE) e-ISSN: 2278-2834,p- ISSN: 2278-8735.Volume 8, Issue 3 (Nov. - Dec. 2013), PP 09-15 www.iosrjournals.org Fibonacci Codes for Crosstalk Avoidance 1Sireesha Kondapalli, 2Dr. Giri Babu Kande 1PG Student (M.Tech VLSI), Dept. Of ECE, Vasireddy Venkatadri Ins. Tech., Nambur, Guntur, AP, India 2 Professor & Head, Dept. Of ECE, Vasireddy Venkatadri Ins. Tech., Nambur, Guntur, AP, India Abstract: In the deep sub micrometer CMOS process technology, the interconnect resistance, length, and inter- wire capacitance are increasing significantly, which contribute to large on-chip interconnect propagation delay. Data transmitted over interconnect determine the propagation delay and the delay is very significant when adjacent wires are transitioning in opposite directions (i.e., crosstalk transitions) as compared to transitioning in the same direction. Propagation delay across long on-chip buses is significant when adjacent wires are transitioning in opposite direction (i.e., crosstalk transitions) as compared to transitioning in the same direction. By exploiting Fibonacci number system, we propose a family of Fibonacci coding techniques for crosstalk avoidance, relate them to some of the existing crosstalk avoidance techniques, and show how the encoding logic of one technique can be modified to generate code words of the other technique. Keywords: On-chip bus, crosstalk, Fibonacci coding. I. Introduction The advancement of very large scale integration (VLSI) technologies has been following Moore’s law for the past several decades: the number of transistors on an integrated circuit is doubling every two years and the channel length is scaling at the rate of 0.7/3 years.
    [Show full text]