Source Encoding and Compression
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Large Alphabet Source Coding Using Independent Component Analysis Amichai Painsky, Member, IEEE, Saharon Rosset and Meir Feder, Fellow, IEEE
IEEE TRANSACTIONS ON INFORMATION THEORY 1 Large Alphabet Source Coding using Independent Component Analysis Amichai Painsky, Member, IEEE, Saharon Rosset and Meir Feder, Fellow, IEEE Abstract Large alphabet source coding is a basic and well–studied problem in data compression. It has many applications such as compression of natural language text, speech and images. The classic perception of most commonly used methods is that a source is best described over an alphabet which is at least as large as the observed alphabet. In this work we challenge this approach and introduce a conceptual framework in which a large alphabet source is decomposed into “as statistically independent as possible” components. This decomposition allows us to apply entropy encoding to each component separately, while benefiting from their reduced alphabet size. We show that in many cases, such decomposition results in a sum of marginal entropies which is only slightly greater than the entropy of the source. Our suggested algorithm, based on a generalization of the Binary Independent Component Analysis, is applicable for a variety of large alphabet source coding setups. This includes the classical lossless compression, universal compression and high-dimensional vector quantization. In each of these setups, our suggested approach outperforms most commonly used methods. Moreover, our proposed framework is significantly easier to implement in most of these cases. I. INTRODUCTION SSUME a source over an alphabet size m, from which a sequence of n independent samples are drawn. The classical A source coding problem is concerned with finding a sample-to-codeword mapping, such that the average codeword length is minimal, and the samples may be uniquely decodable. -
Design and Implementation of a Decompression Engine for a Huffman-Based Compressed Data Cache Master’S Thesis in Embedded Electronic System Design
Chapter 1 Introduction Design and implementation of a decompression engine for a Huffman-based compressed data cache Master’s Thesis in Embedded Electronic System Design LI KANG Department of Computer Science and Engineering CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden, 2014 The Author grants to Chalmers University of Technology and University of Gothenburg the non-exclusive right to publish the Work electronically and in a non-commercial purpose make it accessible on the Internet. The Author warrants that he/she is the author to the Work, and warrants that the Work does not contain text, pictures or other material that violates copyright law. The Author shall, when transferring the rights of the Work to a third party (for example a publisher or a company), acknowledge the third party about this agreement. If the Author has signed a copyright agreement with a third party regarding the Work, the Author warrants hereby that he/she has obtained any necessary permission from this third party to let Chalmers University of Technology and University of Gothenburg store the Work electronically and make it accessible on the Internet. Design and implementation of a decompression engine for a Huffman-based compressed data cache Li Kang © Li Kang January 2014. Supervisor & Examiner: Angelos Arelakis, Per Stenström Chalmers University of Technology Department of Computer Science and Engineering SE-412 96 Göteborg Sweden Telephone + 46 (0)31-772 1000 [Cover: Pipelined Huffman-based decompression engine, page 8. Source: A. Arelakis and P. Stenström, “A Case for a Value-Aware Cache”, IEEE Computer Architecture Letters, September 2012.] Department of Computer Science and Engineering Göteborg, Sweden January 2014 2 Abstract This master thesis studies the implementation of a decompression engine for Huffman based compressed data cache. -
Source Coding: Part I of Fundamentals of Source and Video Coding
Foundations and Trends R in sample Vol. 1, No 1 (2011) 1–217 c 2011 Thomas Wiegand and Heiko Schwarz DOI: xxxxxx Source Coding: Part I of Fundamentals of Source and Video Coding Thomas Wiegand1 and Heiko Schwarz2 1 Berlin Institute of Technology and Fraunhofer Institute for Telecommunica- tions — Heinrich Hertz Institute, Germany, [email protected] 2 Fraunhofer Institute for Telecommunications — Heinrich Hertz Institute, Germany, [email protected] Abstract Digital media technologies have become an integral part of the way we create, communicate, and consume information. At the core of these technologies are source coding methods that are described in this text. Based on the fundamentals of information and rate distortion theory, the most relevant techniques used in source coding algorithms are de- scribed: entropy coding, quantization as well as predictive and trans- form coding. The emphasis is put onto algorithms that are also used in video coding, which will be described in the other text of this two-part monograph. To our families Contents 1 Introduction 1 1.1 The Communication Problem 3 1.2 Scope and Overview of the Text 4 1.3 The Source Coding Principle 5 2 Random Processes 7 2.1 Probability 8 2.2 Random Variables 9 2.2.1 Continuous Random Variables 10 2.2.2 Discrete Random Variables 11 2.2.3 Expectation 13 2.3 Random Processes 14 2.3.1 Markov Processes 16 2.3.2 Gaussian Processes 18 2.3.3 Gauss-Markov Processes 18 2.4 Summary of Random Processes 19 i ii Contents 3 Lossless Source Coding 20 3.1 Classification -
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. -
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. -
A Survey on Different Compression Techniques Algorithm for Data Compression Ihardik Jani, Iijeegar Trivedi IC
International Journal of Advanced Research in ISSN : 2347 - 8446 (Online) Computer Science & Technology (IJARCST 2014) Vol. 2, Issue 3 (July - Sept. 2014) ISSN : 2347 - 9817 (Print) A Survey on Different Compression Techniques Algorithm for Data Compression IHardik Jani, IIJeegar Trivedi IC. U. Shah University, India IIS. P. University, India Abstract Compression is useful because it helps us to reduce the resources usage, such as data storage space or transmission capacity. Data Compression is the technique of representing information in a compacted form. The actual aim of data compression is to be reduced redundancy in stored or communicated data, as well as increasing effectively data density. The data compression has important tool for the areas of file storage and distributed systems. To desirable Storage space on disks is expensively so a file which occupies less disk space is “cheapest” than an uncompressed files. The main purpose of data compression is asymptotically optimum data storage for all resources. The field data compression algorithm can be divided into different ways: lossless data compression and optimum lossy data compression as well as storage areas. Basically there are so many Compression methods available, which have a long list. In this paper, reviews of different basic lossless data and lossy compression algorithms are considered. On the basis of these techniques researcher have tried to purpose a bit reduction algorithm used for compression of data which is based on number theory system and file differential technique. The statistical coding techniques the algorithms such as Shannon-Fano Coding, Huffman coding, Adaptive Huffman coding, Run Length Encoding and Arithmetic coding are considered. -
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. -
16.1 Digital “Modes”
Contents 16.1 Digital “Modes” 16.5 Networking Modes 16.1.1 Symbols, Baud, Bits and Bandwidth 16.5.1 OSI Networking Model 16.1.2 Error Detection and Correction 16.5.2 Connected and Connectionless 16.1.3 Data Representations Protocols 16.1.4 Compression Techniques 16.5.3 The Terminal Node Controller (TNC) 16.1.5 Compression vs. Encryption 16.5.4 PACTOR-I 16.2 Unstructured Digital Modes 16.5.5 PACTOR-II 16.2.1 Radioteletype (RTTY) 16.5.6 PACTOR-III 16.2.2 PSK31 16.5.7 G-TOR 16.2.3 MFSK16 16.5.8 CLOVER-II 16.2.4 DominoEX 16.5.9 CLOVER-2000 16.2.5 THROB 16.5.10 WINMOR 16.2.6 MT63 16.5.11 Packet Radio 16.2.7 Olivia 16.5.12 APRS 16.3 Fuzzy Modes 16.5.13 Winlink 2000 16.3.1 Facsimile (fax) 16.5.14 D-STAR 16.3.2 Slow-Scan TV (SSTV) 16.5.15 P25 16.3.3 Hellschreiber, Feld-Hell or Hell 16.6 Digital Mode Table 16.4 Structured Digital Modes 16.7 Glossary 16.4.1 FSK441 16.8 References and Bibliography 16.4.2 JT6M 16.4.3 JT65 16.4.4 WSPR 16.4.5 HF Digital Voice 16.4.6 ALE Chapter 16 — CD-ROM Content Supplemental Files • Table of digital mode characteristics (section 16.6) • ASCII and ITA2 code tables • Varicode tables for PSK31, MFSK16 and DominoEX • Tips for using FreeDV HF digital voice software by Mel Whitten, KØPFX Chapter 16 Digital Modes There is a broad array of digital modes to service various needs with more coming. -
On the Coding Gain of Dynamic Huffman Coding Applied to a Wavelet-Based Perceptual Audio Coder
ON THE CODING GAIN OF DYNAMIC HUFFMAN CODING APPLIED TO A WAVELET-BASED PERCEPTUAL AUDIO CODER N. Ruiz Reyes1, M. Rosa Zurera2, F. López Ferreras2, P. Jarabo Amores2, and P. Vera Candeas1 1Departamento de Electrónica, Universidad de Jaén, Escuela Universitaria Politénica, 23700 Linares, Jaén, SPAIN, e-mail: [email protected] 2Dpto. de Teoría de la Señal y Comunicaciones, Universidad de Alcalá, Escuela Politécnica 28871 Alcalá de Henares, Madrid, SPAIN, e-mail: [email protected] ABSTRACT The last one, the ISO/MPEG-4 standard, is composed of several speech and audio coders supporting bit rates This paper evaluates the coding gain of using a dynamic from 2 to 64 kbps per channel. ISO/MPEG-4 includes Huffman entropy coder in an audio coder that uses a the already proposed AAC standard, which provides high wavelet-packet decomposition that is close to the sub- quality audio coding at bit rates of 64 kbps per channel. band decomposition made by the human ear. The sub- Parallel to the definition of the ISO/MPEG standards, band audio signals are modeled as samples of a station- several audio coding algorithms have been proposed that ary random process with laplacian probability density use the wavelet transform as the tool to decompose the function because experimental results indicate that the audio signal. The most promising results correspond to highest coding efficiency is obtained in that case. We adapted wavelet-based audio coders. Probably, the most have also studied how the entropy coding gain varies cited is the one designed by Sinha and Tewfik [2], a high with the band index. -
Revisiting Huffman Coding: Toward Extreme Performance on Modern GPU Architectures
Revisiting Huffman Coding: Toward Extreme Performance on Modern GPU Architectures Jiannan Tian?, Cody Riveray, Sheng Diz, Jieyang Chenx, Xin Liangx, Dingwen Tao?, and Franck Cappelloz{ ?School of Electrical Engineering and Computer Science, Washington State University, WA, USA yDepartment of Computer Science, The University of Alabama, AL, USA zMathematics and Computer Science Division, Argonne National Laboratory, IL, USA xOak Ridge National Laboratory, TN, USA {University of Illinois at Urbana-Champaign, IL, USA Abstract—Today’s high-performance computing (HPC) appli- much more slowly than computing power, causing intra-/inter- cations are producing vast volumes of data, which are challenging node communication cost and I/O bottlenecks to become a to store and transfer efficiently during the execution, such that more serious issue in fast stream processing [6]. Compressing data compression is becoming a critical technique to mitigate the storage burden and data movement cost. Huffman coding is the raw simulation data at runtime and decompressing them arguably the most efficient Entropy coding algorithm in informa- before post-analysis can significantly reduce communication tion theory, such that it could be found as a fundamental step and I/O overheads and hence improving working efficiency. in many modern compression algorithms such as DEFLATE. On Huffman coding is a widely-used variable-length encoding the other hand, today’s HPC applications are more and more method that has been around for over 60 years [17]. It is relying on the accelerators such as GPU on supercomputers, while Huffman encoding suffers from low throughput on GPUs, arguably the most cost-effective Entropy encoding algorithm resulting in a significant bottleneck in the entire data processing.