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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 -
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. -
Image Compression Using Discrete Cosine Transform Method
Qusay Kanaan Kadhim, International Journal of Computer Science and Mobile Computing, Vol.5 Issue.9, September- 2016, pg. 186-192 Available Online at www.ijcsmc.com International Journal of Computer Science and Mobile Computing A Monthly Journal of Computer Science and Information Technology ISSN 2320–088X IMPACT FACTOR: 5.258 IJCSMC, Vol. 5, Issue. 9, September 2016, pg.186 – 192 Image Compression Using Discrete Cosine Transform Method Qusay Kanaan Kadhim Al-Yarmook University College / Computer Science Department, Iraq [email protected] ABSTRACT: The processing of digital images took a wide importance in the knowledge field in the last decades ago due to the rapid development in the communication techniques and the need to find and develop methods assist in enhancing and exploiting the image information. The field of digital images compression becomes an important field of digital images processing fields due to the need to exploit the available storage space as much as possible and reduce the time required to transmit the image. Baseline JPEG Standard technique is used in compression of images with 8-bit color depth. Basically, this scheme consists of seven operations which are the sampling, the partitioning, the transform, the quantization, the entropy coding and Huffman coding. First, the sampling process is used to reduce the size of the image and the number bits required to represent it. Next, the partitioning process is applied to the image to get (8×8) image block. Then, the discrete cosine transform is used to transform the image block data from spatial domain to frequency domain to make the data easy to process. -
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. -
Soft Compression for Lossless Image Coding
1 Soft Compression for Lossless Image Coding Gangtao Xin, and Pingyi Fan, Senior Member, IEEE Abstract—Soft compression is a lossless image compression method, which is committed to eliminating coding redundancy and spatial redundancy at the same time by adopting locations and shapes of codebook to encode an image from the perspective of information theory and statistical distribution. In this paper, we propose a new concept, compressible indicator function with regard to image, which gives a threshold about the average number of bits required to represent a location and can be used for revealing the performance of soft compression. We investigate and analyze soft compression for binary image, gray image and multi-component image by using specific algorithms and compressible indicator value. It is expected that the bandwidth and storage space needed when transmitting and storing the same kind of images can be greatly reduced by applying soft compression. Index Terms—Lossless image compression, information theory, statistical distributions, compressible indicator function, image set compression. F 1 INTRODUCTION HE purpose of image compression is to reduce the where H(X1;X2; :::; Xn) is the joint entropy of the symbol T number of bits required to represent an image as much series fXi; i = 1; 2; :::; ng. as possible under the condition that the fidelity of the It’s impossible to reach the entropy rate and everything reconstructed image to the original image is higher than a we can do is to make great efforts to get close to it. Soft com- required value. Image compression often includes two pro- pression [1] was recently proposed, which uses locations cesses, encoding and decoding. -
Comparison of Entropy and Dictionary Based Text Compression in English, German, French, Italian, Czech, Hungarian, Finnish, and Croatian
mathematics Article Comparison of Entropy and Dictionary Based Text Compression in English, German, French, Italian, Czech, Hungarian, Finnish, and Croatian Matea Ignatoski 1 , Jonatan Lerga 1,2,* , Ljubiša Stankovi´c 3 and Miloš Dakovi´c 3 1 Department of Computer Engineering, Faculty of Engineering, University of Rijeka, Vukovarska 58, HR-51000 Rijeka, Croatia; [email protected] 2 Center for Artificial Intelligence and Cybersecurity, University of Rijeka, R. Matejcic 2, HR-51000 Rijeka, Croatia 3 Faculty of Electrical Engineering, University of Montenegro, Džordža Vašingtona bb, 81000 Podgorica, Montenegro; [email protected] (L.S.); [email protected] (M.D.) * Correspondence: [email protected]; Tel.: +385-51-651-583 Received: 3 June 2020; Accepted: 17 June 2020; Published: 1 July 2020 Abstract: The rapid growth in the amount of data in the digital world leads to the need for data compression, and so forth, reducing the number of bits needed to represent a text file, an image, audio, or video content. Compressing data saves storage capacity and speeds up data transmission. In this paper, we focus on the text compression and provide a comparison of algorithms (in particular, entropy-based arithmetic and dictionary-based Lempel–Ziv–Welch (LZW) methods) for text compression in different languages (Croatian, Finnish, Hungarian, Czech, Italian, French, German, and English). The main goal is to answer a question: ”How does the language of a text affect the compression ratio?” The results indicated that the compression ratio is affected by the size of the language alphabet, and size or type of the text. For example, The European Green Deal was compressed by 75.79%, 76.17%, 77.33%, 76.84%, 73.25%, 74.63%, 75.14%, and 74.51% using the LZW algorithm, and by 72.54%, 71.47%, 72.87%, 73.43%, 69.62%, 69.94%, 72.42% and 72% using the arithmetic algorithm for the English, German, French, Italian, Czech, Hungarian, Finnish, and Croatian versions, respectively. -
Generalized Golomb Codes and Adaptive Coding of Wavelet-Transformed Image Subbands
IPN Progress Report 42-154 August 15, 2003 Generalized Golomb Codes and Adaptive Coding of Wavelet-Transformed Image Subbands A. Kiely1 and M. Klimesh1 We describe a class of prefix-free codes for the nonnegative integers. We apply a family of codes in this class to the problem of runlength coding, specifically as part of an adaptive algorithm for compressing quantized subbands of wavelet- transformed images. On test images, our adaptive coding algorithm is shown to give compression effectiveness comparable to the best performance achievable by an alternate algorithm that has been previously implemented. I. Generalized Golomb Codes A. Introduction Suppose we wish to use a variable-length binary code to encode integers that can take on any non- negative value. This problem arises, for example, in runlength coding—encoding the lengths of runs of a dominant output symbol from a discrete source. Encoding cannot be accomplished by simply looking up codewords from a table because the table would be infinite, and Huffman’s algorithm could not be used to construct the code anyway. Thus, one would like to use a simply described code that can be easily encoded and decoded. Although in practice there is generally a limit to the size of the integers that need to be encoded, a simple code for the nonnegative integers is often still the best choice. We now describe a class of variable-length binary codes for the nonnegative integers that contains several useful families of codes. Each code in this class is completely specified by an index function f from the nonnegative integers onto the nonnegative integers. -
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. -
Data Compression
Data Compression Data Compression Compression reduces the size of a file: ! To save space when storing it. ! To save time when transmitting it. ! Most files have lots of redundancy. Who needs compression? ! Moore's law: # transistors on a chip doubles every 18-24 months. ! Parkinson's law: data expands to fill space available. ! Text, images, sound, video, . All of the books in the world contain no more information than is Reference: Chapter 22, Algorithms in C, 2nd Edition, Robert Sedgewick. broadcast as video in a single large American city in a single year. Reference: Introduction to Data Compression, Guy Blelloch. Not all bits have equal value. -Carl Sagan Basic concepts ancient (1950s), best technology recently developed. Robert Sedgewick and Kevin Wayne • Copyright © 2005 • http://www.Princeton.EDU/~cos226 2 Applications of Data Compression Encoding and Decoding hopefully uses fewer bits Generic file compression. Message. Binary data M we want to compress. ! Files: GZIP, BZIP, BOA. Encode. Generate a "compressed" representation C(M). ! Archivers: PKZIP. Decode. Reconstruct original message or some approximation M'. ! File systems: NTFS. Multimedia. M Encoder C(M) Decoder M' ! Images: GIF, JPEG. ! Sound: MP3. ! Video: MPEG, DivX™, HDTV. Compression ratio. Bits in C(M) / bits in M. Communication. ! ITU-T T4 Group 3 Fax. Lossless. M = M', 50-75% or lower. ! V.42bis modem. Ex. Natural language, source code, executables. Databases. Google. Lossy. M ! M', 10% or lower. Ex. Images, sound, video. 3 4 Ancient Ideas Run-Length Encoding Ancient ideas. Natural encoding. (19 " 51) + 6 = 975 bits. ! Braille. needed to encode number of characters per line ! Morse code. -
New Approaches to Fine-Grain Scalable Audio Coding
New Approaches to Fine-Grain Scalable Audio Coding Mahmood Movassagh Department of Electrical & Computer Engineering McGill University Montreal, Canada December 2015 Research Thesis submitted to McGill University in partial fulfillment of the requirements for the degree of PhD. c 2015 Mahmood Movassagh In memory of my mother whom I lost in the last year of my PhD studies To my father who has been the greatest support for my studies in my life Abstract Bit-rate scalability has been a useful feature in the multimedia communications. Without the need to re-encode the original signal, it allows for improving/decreasing the quality of a signal as more/less of a total bit stream becomes available. Using scalable coding, there is no need to store multiple versions of a signal encoded at different bit-rates. Scalable coding can also be used to provide users with different quality streaming when they have different constraints or when there is a varying channel; i.e., the receivers with lower channel capacities will be able to receive signals at lower bit-rates. It is especially useful in the client- server applications where the network nodes are able to drop some enhancement layer bits to satisfy link capacity constraints. In this dissertation, we provide three contributions to practical scalable audio coding systems. Our first contribution is the scalable audio coding using watermarking. The proposed scheme uses watermarking to embed some of the information of each layer into the previous layer. This approach leads to a saving in bitrate, so that it outperforms (in terms of rate-distortion) the common scalable audio coding based on the reconstruction error quantization (REQ) as used in MPEG-4 audio. -
Critical Assessment of Advanced Coding Standards for Lossless Audio Compression
TONNY HIDAYAT et al: A CRITICAL ASSESSMENT OF ADVANCED CODING STANDARDS FOR LOSSLESS .. A Critical Assessment of Advanced Coding Standards for Lossless Audio Compression Tonny Hidayat Mohd Hafiz Zakaria, Ahmad Naim Che Pee Department of Information Technology Faculty of Information and Communication Technology Universitas Amikom Yogyakarta Universiti Teknikal Malaysia Melaka Yogyakarta, Indonesia Melaka, Malaysia [email protected] [email protected], [email protected] Abstract - Image data, text, video, and audio data all require compression for storage issues and real-time access via computer networks. Audio data cannot use compression technique for generic data. The use of algorithms leads to poor sound quality, small compression ratios and algorithms are not designed for real-time access. Lossless audio compression has achieved observation as a research topic and business field of the importance of the need to store data with excellent condition and larger storage charges. This article will discuss and analyze the various lossless and standardized audio coding algorithms that concern about LPC definitely due to its reputation and resistance to compression that is audio. However, another expectation plans are likewise broke down for relative materials. Comprehension of LPC improvements, for example, LSP deterioration procedures is additionally examined in this paper. Keywords - component; Audio; Lossless; Compression; coding. I. INTRODUCTION Compression is to shrink / compress the size. Data compression is a technique to minimize the data so that files can be obtained with a size smaller than the original file size. Compression is needed to minimize the data storage (because the data size is smaller than the original), accelerate information transmission, and limit bandwidth prerequisites.