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Applications of (a, b)-continued fraction transformations

ERGODIC THEORY AND DYNAMICAL SYSTEMS 2012年第02期32卷 755-U466页

作者： Katok, Svetlana Ugarcovici, Ilie Penn State Univ Dept Math University Pk PA 16802 USA DePaul Univ Dept Math Sci Chicago IL 60614 USA

We describe a general method of arithmetic coding of geodesics on the modular surface based on the study of one-dimensional Gauss-like maps associated to a two-parameter family of continued fractions introduced in [Katok and Ugarcovici. Structure of attractors for (a, b)-continued fraction transformations. J. Modern Dynamics 4 (2010), 637-691]. The finite rectangular structure of the attractors of the natural extension maps and the corresponding 'reduction theory' play an essential role. In special cases, when an (a, b)-expansion admits a so-called 'dual', the coding sequences are obtained by juxtaposition of the boundary expansions of the fixed points, and the set of coding sequences is a countable sofic shift. We also prove that the natural extension maps are Bernoulli shifts and compute the density of the absolutely continuous invariant measure and the measure-theoretic entropy of the one-dimensional map.

关键词： Geodesic Attractor arithmetic coding maps

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On a hybrid lossless compression technique for three-dimensional medical images

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JOURNAL OF APPLIED CLINICAL MEDICAL PHYSICS 2021年第8期22卷 191-203页

作者： Subramanian, Boopathiraja Palanisamy, Kalavathi Prasath, V. B. Surya Gandhigram Rural Inst Dept Comp Sci & Applicat Gandhigram Tamil Nadu India Cincinnati Childrens Hosp Med Ctr Div Biomed Informat Cincinnati OH 45229 USA Univ Cincinnati Dept Pediat Cincinnati OH 45221 USA Univ Cincinnati Coll Med Dept Biomed Informat Cincinnati OH 45221 USA Univ Cincinnati Dept Elect Engn & Comp Sci Cincinnati OH 45221 USA

In the last two decades, incredible progress in various medical imaging modalities and sensing techniques have been made, leading to the proliferation of three-dimensional (3D) imagery. Byproduct of such great progress is the production of huge volume of medical images and this big data place a burden on automatic image processing methods for diagnostic assistance processes. Moreover, large amount of medical imaging data needs to be transmitted with no loss of information for the purpose of telemedicine, remote diagnosis etc. In this work, we consider a hybrid lossless compression technique with object-based features for three-dimensional (3D) medical images. Our approach utilizes two phases as follows: first we determine the volume of interest (VOI) for a given 3D medical imagery using selective bounding volume (SBV) method, and second the obtained VOI is encoded using a hybrid lossless algorithm using Lembel-Ziv-Welch coding (LZW) followed by arithmetic coding (L to A). Experimental results show that our proposed 3D medical image compression method is comparable with other existing standard lossless encoding methods such as Huffman coding, Run Length coding, LZW, and arithmetic coding and obtains superior results overall.

关键词： arithmetic coding lossless compression object features radiological images volume of interest

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arithmetic N-gram: an efficient data compression technique

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DISCOVER COMPUTING 2024年第1期27卷 1-1页

作者： Hassan, Ali Javed, Sadaf Hussain, Sajjad Ahmad, Rizwan Qazi, Shams Natl Univ Sci & Technol NUST Sch Elect Engn & Comp Sci SEECS Islamabad 44000 Pakistan

Due to the increase in the growth of data in this era of the digital world and limited resources, there is a need for more efficient data compression techniques for storing and transmitting data. Data compression can significantly reduce the amount of storage space and transmission time to store and transmit given data. More specifically, text compression has got more attention for effectively managing and processing data due to the increased use of the internet, digital devices, data transfer, etc. Over the years, various algorithms have been used for text compression such as Huffman coding, Lempel-Ziv-Welch (LZW) coding, arithmetic coding, etc. However, these methods have a limited compression ratio specifically for data storage applications where a considerable amount of data must be compressed to use storage resources efficiently. They consider individual characters to compress data. It can be more advantageous to consider words or sequences of words rather than individual characters to get a better compression ratio. Compressing individual characters results in a sizeable compressed representation due to their less repetition and structure in the data. In this paper, we proposed the ArthNgram model, in which the N-gram language model coupled with arithmetic coding is used to compress data more efficiently for data storage applications. The performance of the proposed model is evaluated based on compression ratio and compression speed. Results show that the proposed model performs better than traditional techniques.

关键词： Data compression Huffman LZW N-gram arithmetic coding Compression ratio Large language models

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Multichannel EEG Compression: Wavelet-Based Image and Volumetric coding Approach

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IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS 2013年第1期17卷 113-120页

作者： Srinivasan, K. Dauwels, Justin Reddy, M. Ramasubba IIT Madras Dept Appl Mech Biomed Engn Grp Madras 600036 Tamil Nadu India Nanyang Technol Univ Sch Elect Elect Engn Singapore 639798 Singapore

In this paper, lossless and near-lossless compression algorithms for multichannel electroencephalogram (EEG) signals are presented based on image and volumetric coding. Multichannel EEG signals have significant correlation among spatially adjacent channels;moreover, EEG signals are also correlated across time. Suitable representations are proposed to utilize those correlations effectively. In particular, multichannel EEG is represented either in the form of image (matrix) or volumetric data (tensor), next a wavelet transform is applied to those EEG representations. The compression algorithms are designed following the principle of "lossy plus residual coding," consisting of a wavelet-based lossy coding layer followed by arithmetic coding on the residual. Such approach guarantees a specifiable maximum error between original and reconstructed signals. The compression algorithms are applied to three different EEG datasets, each with different sampling rate and resolution. The proposed multichannel compression algorithms achieve attractive compression ratios compared to algorithms that compress individual channels separately.

关键词： arithmetic coding compression electroencephalogram (EEG) multichannel EEG set partitioning coding

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Compression of Short Text on Embedded Systems

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JOURNAL OF COMPUTERS 2006年第6期1卷 1-10页

作者： Rein, Stephan Guhmann, Clemens Fitzek, Frank Tech Univ Berlin Dept Elect Measurement & Diagnost Technol Berlin Germany Aalborg Univ Dept Telecommun Technol Aalborg Denmark

The paper details a scheme for lossless compression of short data series larger than 50 Bytes. The method uses arithmetic coding and context modeling with a low-complexity data model. A data model that takes 32 kBytes of RAM already cuts the data size in half. The compression scheme just takes a few pages of source code, is scalable in memory size, and may be useful in sensor or cellular networks to spare bandwidth. As we demonstrate the method allows for battery savings when applied to mobile phones.

关键词： arithmetic coding context modeling prediction by partial matching (PPM) short message compression embedded system mobile phone sensor network

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A rapid probability estimator and binary arithmetic coder

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IEEE TRANSACTIONS ON INFORMATION THEORY 2001年第4期47卷 1533-1537页

作者： Withers, WD USN Acad Dept Math Annapolis MD 21402 USA Pegasus Imaging Corp Imagetech Tampa FL 33607 USA

We present a new integrated algorithm fur binary arithmetic coding and probability estimation, competitive in speed and compression performance with state-of-the-art algorithms such as the QM-coder and Z-coder. The chief innovation is representing the bracketing interval width both directly and by a logarithmic approximation. Performance is evaluated by experiments using bilevel-image data sets. An open-source software version is available.

关键词： algorithms arithmetic coding data compression entropy coding

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An innovative chain coding mechanism for information processing and compression using a virtual bat-bug agent-based modeling simulation

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2022年第0期113卷

作者： Dhou, Khaldoon Cruzen, Christopher Texas A&M Univ Cent Texas Killeen TX 76549 USA Univ Missouri St Louis MO 63121 USA

The continuous changes in the size of data create new challenges to design new techniques to reduce its size and encode it in a way that changes its original representation. In this article, we develop a bat-bug agent-based modeling simulation for chain coding and employ it in compressing bi-level image information. The system consists of agents that are classified into static and dynamic depending on their movements. Bugs are considered static agents, and they are distributed over the virtual environment according to the allocation of pixels in the original image. On the other hand, bats are dynamic agent, and their role is to move around to consume bugs while the algorithm tracks their movements. Bats are designed in a way to move within certain boundaries to avoid crashing into each other. Bats employ specific movements that allow them to move in relative directions. Therefore, the frequency of their movements can follow a certain pattern that can help in further size reduction. In other words, the integration of relative movements into our design proved to be advantageous because there is an observable pattern of repeated movements, which allows getting higher compression results. Finally, arithmetic coding is applied to the final strings that represent the movements of bats while searching for bugs to eat. To assess the performance of the algorithm, we compared the findings against standardized benchmarks used in the image processing community: G3, G4, JBIG1, and JBIG2. The outcomes show that we could outperform all these benchmarks using all the images we used for testing. Additionally, we conducted a series of paired samples t-tests, and they revealed that the mean differences between our results and those obtained from other benchmarks are statistically significant.

关键词： Agent-based modeling Chain code Bi-level image Compression Bats Simulation Virtual environment arithmetic coding JBIG

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A Joint Source/Channel Approach to Strengthen Embedded Programmable Devices against Flash Memory Errors

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IEEE EMBEDDED SYSTEMS LETTERS 2014年第4期6卷 77-80页

作者： Martina, Maurizio Condo, Carlo Masera, Guido Zamboni, Maurizio Politecn Torino Elec & Telecommun Dept I-10129 Turin Italy

Reconfigurable embedded systems can take advantage of programmable devices, such as microprocessors and field-programmable gate arrays (FPGAs), to achieve high performance and flexibility. Support to flexibility often comes at the expense of large amounts of nonvolatile memories. Unfortunately, nonvolatile memories, such as multilevel-cell (MLC) NAND flash, exhibit a high raw bit error rate that is mitigated by employing different techniques, including error correcting codes. Recent results show that low-density-parity-check (LDPC) codes are good candidates to improve the reliability of MLC NAND flash memories especially when page size increases. This letter proposes to use a joint source/ channel approach, based on a modified arithmetic code and LDPC codes, to achieve both data compression and improved system reliability. The proposed technique is then applied to the configuration data of FPGAs and experimental results show the superior performance of the proposed system with respect to state of the art. Indeed, the proposed system can achieve bit-error-rates as low as about for cell-to-cell coupling strength factors well higher than 1.0.

关键词： arithmetic coding flash memories field-programmable gate arrays (FPGAs) low-density-parity-check (LDPC) coding

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High-fidelity coding for super high-definition images

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ELECTRONICS AND COMMUNICATIONS IN JAPAN PART I-COMMUNICATIONS 1997年第3期80卷 47-57页

作者： Kuroki, Y Ohta, T Faculty of Engineering Kyushu Institute of Technology Kitakyushu 804 Japan Kyushu Institute of Technology Japan Kyushu University Japan Television Society of Japan Info. Processing Society of Japan Japan IEEE

The super high-definition images (SHDI) expected to be prominent in the systems of the 21st century consist of approximately 4000 scan lines and have extremely high fidelity. This paper describes a coding scheme for still SHDI. Predictive coding is thought to be a coding technique capable of not spoiling the quality of SHDI images. Thus, an extrapolative/interpolative prediction scheme that has been proposed [1] for high-efficiency coding of HDTV is used for intraframe coding of SHDI. The extrapolative prediction error is coded with a first-order Huffman code. Comparatively, the prediction efficiency of interpolative prediction is superior to that of extrapolative prediction [2]. Furthermore, since the pixel correlations of the images used in this paper are extremely high [9], the probability of the 0 representative level of the quantizer is high. Thus, in this paper, the prediction error is converted to binary levels when interpolative prediction is used and it is proposed that a coding method based on a type of arithmetic code, the QM-Coder [4], which is used in JPEG, be used to code the resulting binary information. When binary information is coded, the resulting conditional entropy of the reference pixels is shown to be rather constant;and, thus, the number of states can be reduced without an increase in the rate. Image coding simulation results show that the coding performance is improved with this method where extrapolative/interpolative prediction is used by 0.350 similar to 0.458 bits/pel when compared with the case that uses a first-order Huffman code. Accordingly, high-fidelity images whose signal-to-noise ratio (SNR) is greater than 50 dB with rates less than at 1.653 bits/pel are obtained.

关键词： super high-definition images arithmetic coding QM-Coder extrapolative, interpolative prediction quantization

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Joint Source-Channel Decoding Scheme for Image Transmission over Wireless Channel

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Wuhan University Journal of Natural Sciences 2002年第3期7卷 307-312页

作者： Xiao Dong-liang Sun Hong Wuhan University School of Electronic Information Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***)

We improve the iterative decoding algorithm by utilizing the “leaked” residual redundancy at the output of the source encoder without changing the encoder structure for the noisy channel. The experimental results show that using the residual redundancy of the compressed source in channel decoding is an effective method to improve the error correction performance.

关键词： turbo code joint source-channel decoding residual redundancy arithmetic coding

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