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Data Compression: Dictionary-Based Coding 2 / 37 Dictionary-Based Coding Dictionary-Based Coding
Dictionary-based Coding already coded not yet coded search buffer look-ahead buffer cursor (N symbols) (L symbols) We know the past but cannot control it. We control the future but... Last Lecture Last Lecture: Predictive Lossless Coding Predictive Lossless Coding Simple and effective way to exploit dependencies between neighboring symbols / samples Optimal predictor: Conditional mean (requires storage of large tables) Affine and Linear Prediction Simple structure, low-complex implementation possible Optimal prediction parameters are given by solution of Yule-Walker equations Works very well for real signals (e.g., audio, images, ...) Efficient Lossless Coding for Real-World Signals Affine/linear prediction (often: block-adaptive choice of prediction parameters) Entropy coding of prediction errors (e.g., arithmetic coding) Using marginal pmf often already yields good results Can be improved by using conditional pmfs (with simple conditions) Heiko Schwarz (Freie Universität Berlin) — Data Compression: Dictionary-based Coding 2 / 37 Dictionary-based Coding Dictionary-Based Coding Coding of Text Files Very high amount of dependencies Affine prediction does not work (requires linear dependencies) Higher-order conditional coding should work well, but is way to complex (memory) Alternative: Do not code single characters, but words or phrases Example: English Texts Oxford English Dictionary lists less than 230 000 words (including obsolete words) On average, a word contains about 6 characters Average codeword length per character would be limited by 1 -
Package 'Brotli'
Package ‘brotli’ May 13, 2018 Type Package Title A Compression Format Optimized for the Web Version 1.2 Description A lossless compressed data format that uses a combination of the LZ77 algorithm and Huffman coding. Brotli is similar in speed to deflate (gzip) but offers more dense compression. License MIT + file LICENSE URL https://tools.ietf.org/html/rfc7932 (spec) https://github.com/google/brotli#readme (upstream) http://github.com/jeroen/brotli#read (devel) BugReports http://github.com/jeroen/brotli/issues VignetteBuilder knitr, R.rsp Suggests spelling, knitr, R.rsp, microbenchmark, rmarkdown, ggplot2 RoxygenNote 6.0.1 Language en-US NeedsCompilation yes Author Jeroen Ooms [aut, cre] (<https://orcid.org/0000-0002-4035-0289>), Google, Inc [aut, cph] (Brotli C++ library) Maintainer Jeroen Ooms <[email protected]> Repository CRAN Date/Publication 2018-05-13 20:31:43 UTC R topics documented: brotli . .2 Index 4 1 2 brotli brotli Brotli Compression Description Brotli is a compression algorithm optimized for the web, in particular small text documents. Usage brotli_compress(buf, quality = 11, window = 22) brotli_decompress(buf) Arguments buf raw vector with data to compress/decompress quality value between 0 and 11 window log of window size Details Brotli decompression is at least as fast as for gzip while significantly improving the compression ratio. The price we pay is that compression is much slower than gzip. Brotli is therefore most effective for serving static content such as fonts and html pages. For binary (non-text) data, the compression ratio of Brotli usually does not beat bz2 or xz (lzma), however decompression for these algorithms is too slow for browsers in e.g. -
Annual Report 2016
ANNUAL REPORT 2016 PUNJABI UNIVERSITY, PATIALA © Punjabi University, Patiala (Established under Punjab Act No. 35 of 1961) Editor Dr. Shivani Thakar Asst. Professor (English) Department of Distance Education, Punjabi University, Patiala Laser Type Setting : Kakkar Computer, N.K. Road, Patiala Published by Dr. Manjit Singh Nijjar, Registrar, Punjabi University, Patiala and Printed at Kakkar Computer, Patiala :{Bhtof;Nh X[Bh nk;k wjbk ñ Ò uT[gd/ Ò ftfdnk thukoh sK goT[gekoh Ò iK gzu ok;h sK shoE tk;h Ò ñ Ò x[zxo{ tki? i/ wB[ bkr? Ò sT[ iw[ ejk eo/ w' f;T[ nkr? Ò ñ Ò ojkT[.. nk; fBok;h sT[ ;zfBnk;h Ò iK is[ i'rh sK ekfJnk G'rh Ò ò Ò dfJnk fdrzpo[ d/j phukoh Ò nkfg wo? ntok Bj wkoh Ò ó Ò J/e[ s{ j'fo t/; pj[s/o/.. BkBe[ ikD? u'i B s/o/ Ò ô Ò òõ Ò (;qh r[o{ rqzE ;kfjp, gzBk óôù) English Translation of University Dhuni True learning induces in the mind service of mankind. One subduing the five passions has truly taken abode at holy bathing-spots (1) The mind attuned to the infinite is the true singing of ankle-bells in ritual dances. With this how dare Yama intimidate me in the hereafter ? (Pause 1) One renouncing desire is the true Sanayasi. From continence comes true joy of living in the body (2) One contemplating to subdue the flesh is the truly Compassionate Jain ascetic. Such a one subduing the self, forbears harming others. (3) Thou Lord, art one and Sole. -
Arithmetic Coding
Arithmetic Coding Arithmetic coding is the most efficient method to code symbols according to the probability of their occurrence. The average code length corresponds exactly to the possible minimum given by information theory. Deviations which are caused by the bit-resolution of binary code trees do not exist. In contrast to a binary Huffman code tree the arithmetic coding offers a clearly better compression rate. Its implementation is more complex on the other hand. In arithmetic coding, a message is encoded as a real number in an interval from one to zero. Arithmetic coding typically has a better compression ratio than Huffman coding, as it produces a single symbol rather than several separate codewords. Arithmetic coding differs from other forms of entropy encoding such as Huffman coding in that rather than separating the input into component symbols and replacing each with a code, arithmetic coding encodes the entire message into a single number, a fraction n where (0.0 ≤ n < 1.0) Arithmetic coding is a lossless coding technique. There are a few disadvantages of arithmetic coding. One is that the whole codeword must be received to start decoding the symbols, and if there is a corrupt bit in the codeword, the entire message could become corrupt. Another is that there is a limit to the precision of the number which can be encoded, thus limiting the number of symbols to encode within a codeword. There also exist many patents upon arithmetic coding, so the use of some of the algorithms also call upon royalty fees. Arithmetic coding is part of the JPEG data format. -
Pdflib Text and Image Extraction Toolkit (TET) Manual
ABC Text and Image Extraction Toolkit (TET) Version 5.2 Toolkit for extracting Text, Images, and other items from PDF Copyright © 2002–2019 PDFlib GmbH. All rights reserved. Protected by European and U.S. patents. PDFlib GmbH Franziska-Bilek-Weg 9, 80339 München, Germany www.pdflib.com phone +49 • 89 • 452 33 84-0 If you have questions check the PDFlib mailing list and archive at groups.yahoo.com/neo/groups/pdflib/info Licensing contact: [email protected] Support for commercial PDFlib licensees: [email protected] (please include your license number) This publication and the information herein is furnished as is, is subject to change without notice, and should not be construed as a commitment by PDFlib GmbH. PDFlib GmbH assumes no responsibility or lia- bility for any errors or inaccuracies, makes no warranty of any kind (express, implied or statutory) with re- spect to this publication, and expressly disclaims any and all warranties of merchantability, fitness for par- ticular purposes and noninfringement of third party rights. TET contains modified parts of the following third-party software: CMap resources. Copyright © 1990-2019 Adobe Zlib compression library, Copyright © 1995-2017 Jean-loup Gailly and Mark Adler TIFFlib image library, Copyright © 1988-1997 Sam Leffler, Copyright © 1991-1997 Silicon Graphics, Inc. Cryptographic software written by Eric Young, Copyright © 1995-1998 Eric Young ([email protected]) Independent JPEG Group’s JPEG software, Copyright © Copyright © 1991-2017, Thomas G. Lane, Guido Vollbeding Cryptographic software, Copyright © 1998-2002 The OpenSSL Project (www.openssl.org) Expat XML parser, Copyright © 2001-2017 Expat maintainers ICU International Components for Unicode, Copyright © 1995-2012 International Business Machines Corpo- ration and others OpenJPEG library, Copyright © 2002-2014, Université catholique de Louvain (UCL), Belgium TET contains the RSA Security, Inc. -
CALIFORNIA STATE UNIVERSITY, NORTHRIDGE LOSSLESS COMPRESSION of SATELLITE TELEMETRY DATA for a NARROW-BAND DOWNLINK a Graduate P
CALIFORNIA STATE UNIVERSITY, NORTHRIDGE LOSSLESS COMPRESSION OF SATELLITE TELEMETRY DATA FOR A NARROW-BAND DOWNLINK A graduate project submitted in partial fulfillment of the requirements For the degree of Master of Science in Electrical Engineering By Gor Beglaryan May 2014 Copyright Copyright (c) 2014, Gor Beglaryan Permission to use, copy, modify, and/or distribute the software developed for this project for any purpose with or without fee is hereby granted. THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. Copyright by Gor Beglaryan ii Signature Page The graduate project of Gor Beglaryan is approved: __________________________________________ __________________ Prof. James A Flynn Date __________________________________________ __________________ Dr. Deborah K Van Alphen Date __________________________________________ __________________ Dr. Sharlene Katz, Chair Date California State University, Northridge iii Contents Copyright .......................................................................................................................................... ii Signature Page ............................................................................................................................... -
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. -
Improved Neural Network Based General-Purpose Lossless Compression Mohit Goyal, Kedar Tatwawadi, Shubham Chandak, Idoia Ochoa
JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 1 DZip: improved neural network based general-purpose lossless compression Mohit Goyal, Kedar Tatwawadi, Shubham Chandak, Idoia Ochoa Abstract—We consider lossless compression based on statistical [4], [5] and generative modeling [6]). Neural network based data modeling followed by prediction-based encoding, where an models can typically learn highly complex patterns in the data accurate statistical model for the input data leads to substantial much better than traditional finite context and Markov models, improvements in compression. We propose DZip, a general- purpose compressor for sequential data that exploits the well- leading to significantly lower prediction error (measured as known modeling capabilities of neural networks (NNs) for pre- log-loss or perplexity [4]). This has led to the development of diction, followed by arithmetic coding. DZip uses a novel hybrid several compressors using neural networks as predictors [7]– architecture based on adaptive and semi-adaptive training. Unlike [9], including the recently proposed LSTM-Compress [10], most NN based compressors, DZip does not require additional NNCP [11] and DecMac [12]. Most of the previous works, training data and is not restricted to specific data types. The proposed compressor outperforms general-purpose compressors however, have been tailored for compression of certain data such as Gzip (29% size reduction on average) and 7zip (12% size types (e.g., text [12] [13] or images [14], [15]), where the reduction on average) on a variety of real datasets, achieves near- prediction model is trained in a supervised framework on optimal compression on synthetic datasets, and performs close to separate training data or the model architecture is tuned for specialized compressors for large sequence lengths, without any the specific data type. -
DLI Implementation and Reference Guide
Implementation and Reference Guide Datalogics Interface Datalogics® Datalogics DATALOGICS INTERFACE Implementation and Reference Guide This guide is part of the Adobe® PDF Library v6.1.1Plus suite; 02/15/05. Copyright 1999-2005 Datalogics Incorporated. All Rights Reserved. Use of Datalogics software is subject to the applicable license agreement. DL Interface is a trademark of Datalogics Incorporated. Other products mentioned herein as Datalogics prod- ucts are also trademarks or registered trademarks of Datalogics, Incorporated. Adobe, Adobe PDF Library, Portable Document Format (PDF), PostScript, Acrobat, Distiller, Exchange and Reader are trademarks of Adobe Systems Incorporated. HP and HP-UX are registered trademarks of Hewlett Packard Corporation. IBM, AIX, AS/400, OS/400, MVS, and OS/390 are registered trademarks of International Business Machines. Java, J2EE, J2SE, J2ME, all Java-based marks, Sun and Solaris are trademarks or registered trademarks of Sun Microsystems, Inc. in the United States and other countries. Linux is a registered trademark of Linus Torvalds. Microsoft, Windows and Windows NT are trademarks or registered trademarks of Microsoft Corporation. SAS/C is a registered trademark of SAS Institute Inc. UNIX is a registered trademark of The Open Group. VeriSign® is a registered trademark of VeriSign, Inc. in the United States and/or other countries. All other trademarks and registered trademarks are the property of their respective owners. For additional information, contact: Datalogics, Incorporated 101 North Wacker -
Modification of Adaptive Huffman Coding for Use in Encoding Large Alphabets
ITM Web of Conferences 15, 01004 (2017) DOI: 10.1051/itmconf/20171501004 CMES’17 Modification of Adaptive Huffman Coding for use in encoding large alphabets Mikhail Tokovarov1,* 1Lublin University of Technology, Electrical Engineering and Computer Science Faculty, Institute of Computer Science, Nadbystrzycka 36B, 20-618 Lublin, Poland Abstract. The paper presents the modification of Adaptive Huffman Coding method – lossless data compression technique used in data transmission. The modification was related to the process of adding a new character to the coding tree, namely, the author proposes to introduce two special nodes instead of single NYT (not yet transmitted) node as in the classic method. One of the nodes is responsible for indicating the place in the tree a new node is attached to. The other node is used for sending the signal indicating the appearance of a character which is not presented in the tree. The modified method was compared with existing methods of coding in terms of overall data compression ratio and performance. The proposed method may be used for large alphabets i.e. for encoding the whole words instead of separate characters, when new elements are added to the tree comparatively frequently. Huffman coding is frequently chosen for implementing open source projects [3]. The present paper contains the 1 Introduction description of the modification that may help to improve Efficiency and speed – the two issues that the current the algorithm of adaptive Huffman coding in terms of world of technology is centred at. Information data savings. technology (IT) is no exception in this matter. Such an area of IT as social media has become extremely popular 2 Study of related works and widely used, so that high transmission speed has gained a great importance. -
Greedy Algorithm Implementation in Huffman Coding Theory
iJournals: International Journal of Software & Hardware Research in Engineering (IJSHRE) ISSN-2347-4890 Volume 8 Issue 9 September 2020 Greedy Algorithm Implementation in Huffman Coding Theory Author: Sunmin Lee Affiliation: Seoul International School E-mail: [email protected] <DOI:10.26821/IJSHRE.8.9.2020.8905 > ABSTRACT In the late 1900s and early 2000s, creating the code All aspects of modern society depend heavily on data itself was a major challenge. However, now that the collection and transmission. As society grows more basic platform has been established, efficiency that can dependent on data, the ability to store and transmit it be achieved through data compression has become the efficiently has become more important than ever most valuable quality current technology deeply before. The Huffman coding theory has been one of desires to attain. Data compression, which is used to the best coding methods for data compression without efficiently store, transmit and process big data such as loss of information. It relies heavily on a technique satellite imagery, medical data, wireless telephony and called a greedy algorithm, a process that “greedily” database design, is a method of encoding any tries to find an optimal solution global solution by information (image, text, video etc.) into a format that solving for each optimal local choice for each step of a consumes fewer bits than the original data. [8] Data problem. Although there is a disadvantage that it fails compression can be of either of the two types i.e. lossy to consider the problem as a whole, it is definitely or lossless compressions. -
Information Theory Revision (Source)
ELEC3203 Digital Coding and Transmission – Overview & Information Theory S Chen Information Theory Revision (Source) {S(k)} {b i } • Digital source is defined by digital source source coding 1. Symbol set: S = {mi, 1 ≤ i ≤ q} symbols/s bits/s 2. Probability of occurring of mi: pi, 1 ≤ i ≤ q 3. Symbol rate: Rs [symbols/s] 4. Interdependency of {S(k)} • Information content of alphabet mi: I(mi) = − log2(pi) [bits] • Entropy: quantifies average information conveyed per symbol q – Memoryless sources: H = − pi · log2(pi) [bits/symbol] i=1 – 1st-order memory (1st-order Markov)P sources with transition probabilities pij q q q H = piHi = − pi pij · log2(pij) [bits/symbol] Xi=1 Xi=1 Xj=1 • Information rate: tells you how many bits/s information the source really needs to send out – Information rate R = Rs · H [bits/s] • Efficient source coding: get rate Rb as close as possible to information rate R – Memoryless source: apply entropy coding, such as Shannon-Fano and Huffman, and RLC if source is binary with most zeros – Generic sources with memory: remove redundancy first, then apply entropy coding to “residauls” 86 ELEC3203 Digital Coding and Transmission – Overview & Information Theory S Chen Practical Source Coding • Practical source coding is guided by information theory, with practical constraints, such as performance and processing complexity/delay trade off • When you come to practical source coding part, you can smile – as you should know everything • As we will learn, data rate is directly linked to required bandwidth, source coding is to encode source with a data rate as small as possible, i.e.