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Prefix Encoding by Means of the (2,3)-Representation of Numbers

IEEE TRANSACTIONS ON INFORMATION THEORY 2013年第4期59卷 2359-2374页

作者： Anisimov, Anatoly V. Taras Shevchenko Natl Univ Kyiv Dept Math Informat UA-03022 Kiev Ukraine

A new family of universal self-synchronizable variable-length codes is introduced. This family is not a generalization or improvement of the existing prefix codes, but is based on a new method of integer representation in a mixed base using the radix-2 and the auxiliary radix-3. Upper length bounds for such codes are obtained. The asymptotic estimates for the (2, 3)-encoding including the pointwise redundancy are also given. In particular, this implies that the average length of a (2, 3)-codeword is shorter than that of fibonacci code. Elias gamma and delta codes are adopted for the (2, 3)-variant with asymptotically shorter codewords as against the original case. Improvement of gamma and delta encoding for all numbers is also presented. One of (2, 3)-codes with high density is highlighted as a possible candidate for practical use in data compression. The (2, 3)-codes are very simple to construct and they have evident features of strong robustness.

关键词： Data compression Elias codes fibonacci code prefix code robustness

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Extended Golomb code for Integer representation

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IEEE TRANSACTIONS ON MULTIMEDIA 2007年第2期9卷 239-246页

作者： Somasundaram, K. Domnic, S. Gandhigram Rural Inst Dept Comp Sci & Appl Gandhigram 624302 India

In this paper, we have proposed two methods to represent nonnegative integers based on the principle used in Golomb code (GC). In both methods, the given integer is successively divided with a divisor, the quotient and the remainders are then used to represent the integer. One of our methods is best suited for representing short integers and gives bit length comparable to that of Elias root code which is best for representing short-range integers. Another of our methods is best suited for representing both short and long integers and gives a bit length comparable to that of fibonacci code which is best for representing long integers. Application of our methods as a final stage encoder of the Burrows-Wheeler Transform Compressor shows that our codes give a better compression rate than the Elias, fibonacci, Punctured, and GC codes.

关键词： Burrows-Wheeler compression Eilas root code fibonacci code Golomb code Huffman code integer coding Punctured Elias code

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Enhanced Context Sensitive Flash codes^†

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COMPUTER JOURNAL 2022年第5期65卷 1200-1210页

作者： Baruch, Gilad Klein, Shmuel T. Shapira, Dana Bar Ilan Univ Dept Comp Sci IL-52900 Ramat Gan Israel Ariel Univ Dept Comp Sci IL-40700 Ariel Israel

A major property of flash memory is that a 0-bit can be changed into a 1-bit, but the symmetric task of switching from a 1-bit to a zero may only be performed in blocks and is therefore often prohibited. This led to the development of rewriting codes using the same storage space more than once, subject to the constraint that 0-bits can be changed into 1-bits, but not vice versa. Context sensitive rewriting codes extend this idea by also incorporating information gathered from surrounding bits. Several new context sensitive rewriting codes are presented and analyzed, some of which are better than the state of the art for sparse input. Empirical simulations show a good match with the theoretical results.

关键词： data compression WOM codes flash memory fibonacci code

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Compressed matching for feature vectors

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THEORETICAL COMPUTER SCIENCE 2016年 638卷 52-62页

作者： Klein, Shmuel T. Shapira, Dana Bar Ilan Univ Dept Comp Sci IL-52900 Ramat Gan Israel Ariel Univ Dept Comp Sci IL-40700 Ariel Israel

The problem of compressing a large collection of feature vectors is investigated, so that object identification can be processed on the compressed form of the features. The idea is to perform matching of a query image against an image database, using directly the compressed form of the descriptor vectors, without decompression. Specifically, we concentrate on the Scale Invariant Feature Transform (SIFT), a known object detection method, as well as on Dense SIFT and PHOW features, that contain, for each image, about 300 times as many vectors as the original SIFT. Given two feature vectors, we suggest achieving our goal by compressing them using a lossless encoding by means of a fibonacci code, for which the pairwise matching can be done directly on the compressed files. In our experiments, this approach improves the processing time and incurs only a small loss in compression efficiency relative to standard compressors requiring a decoding phase. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Data compression Feature vectors SIFT fibonacci code

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Variable length integer codes based on radix number system conversion

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ELECTRONICS LETTERS 2016年第16期52卷 1385-1386页

作者： Joseph, Nelson Raja Planichamy, Jaganathan Sandanam, Domnic Bharathiyar Univ R&D Ctr Coimbatore Tamil Nadu India PSNA Coll Engn & Technol Dindigul India Natl Inst Technol Tiruchirappalli India

A new coding scheme called radix conversion variable length code (RCVLC) is proposed to represent non-negative integers from small values to very large values. RCVLC obtains lowest code length to represent mid-range and large-range integers than fibonacci code, Elias codes and other existing schemes. This RCVLC is applied as an entropy coder of the Burrows Wheeler Transform data compressor to compress Calgary corpus which contains both binary and text files. It is observed from the experimental results that the new RCVLC obtains better compression than the existing coding schemes on an average.

关键词： data compression digital arithmetic entropy codes variable length codes Burrows-Wheeler transform data compressor Calgary corpus compression Elias codes fibonacci code RCVLC entropy coder nonnegative integers radix conversion variable length code radix number system conversion text files variable length integer codes

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Variable-Length Prefix codes With Multiple Delimiters

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IEEE TRANSACTIONS ON INFORMATION THEORY 2017年第5期63卷 2885-2895页

作者： Anisimov, Anatoly V. Zavadskyi, Igor O. Taras Shevchenko Natl Univ Kyiv Dept Math Informat Kiev Ukraine

Let m(1), m(2),..., m(t) be a fixed set of natural integers given in ascending order. A multi-delimiter code Dm(1),..., m(t) consists of t words of the form 1(mi)0 and all other binary words with suffixes having one of the forms 01(mi)0 that cannot occur in other places of a word, i = 1,..., t. Completeness, universality, and density characteristics of multi-delimitercodes are proved. Encoding of integers by multi-delimitercodes is considered in detail. For these codes, fast byte aligned decoding algorithms are also discussed. The comparison of compression rate and decoding speed of fibonacci codes, (s, c)-dense codes and different multi-delimiter codes is presented. By many useful properties, multi-delimiter codes are superior to fibonacci codes.

关键词： Prefix code fibonacci code pattern code data compression robustness completeness universality density multi-delimiter

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A Family of Data Compression codes with Multiple Delimiters 20

A Family of Data Compression Codes with Multiple Delimiters

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Prague Stringology Conference (PSC)

作者： Zavadskyi, Igor O. Anisimov, Anatoly V. Taras Shevchenko Natl Univ Kyiv 2d Glushkova ave Kiev Ukraine

ISBN: (纸本)9788001059968

A new family of perspective variable length self-synchronazable binary codes with multiple pattern delimiters is introduced. Each delimiter consists of a run of consecutive ones surrounded by zero brackets. These codes are complete and universal. A simple bijective correspondence between natural numbers and any multi-delimiter code set is established. A fast byte aligned decoding algorithm is constructed. Comparisons of text compression rate and decoding speed for different multi-delimiter codes, the fibonacci code Fib3 and (s, c)-dense codes are also presented.

关键词： prefix code fibonacci code data compression robustness completeness universality density multi-delimiter

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Studies on Gopala-Hemachandra codes and their Applications.

Studies on Gopala-Hemachandra Codes and their Applications.

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作者： Childers, Logan Gray East Carolina University

学位级别：硕士

Gopala-Hemachandra codes are a variation of the fibonacci universal code and have applications 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 GH_{a}(n) always exists for any 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.

关键词： Data Compression Zeckendorf Representation fibonacci code Gopala-Hemachandra codes Stream Ciphers Cryptanalysis

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Guided blocks WOM codes

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INFORMATION PROCESSING LETTERS 2023年 179卷

作者： Baruch, Gilad Klein, Shmuel T. Shapira, Dana Bar Ilan Univ Dept Comp Sci IL-52900 Ramat Gan Israel Ariel Univ Dept Comp Sci IL-40700 Ariel Israel

A new rewriting code is proposed, that is, the code is suitable for Write Once Memory (woM) devices, for example flash memory, in which the new data may overwrite the old one under the constraint of never changing a 1-bit into a 0-bit. A greedy heuristic is introduced and its compression performance is analyzed. Experimental results show that its efficiency for certain distributions of binary input data may outperform that of state-of-the-art woM codes. Moreover, the technique can be applied to transform any rewriting code for i writing rounds, for any i >= 1, into an enhanced rewriting code for i+1 rounds. (C) 2022 Elsevier B.V. All rights reserved.

关键词： Write Once Memory Information content fibonacci code Rewriting codes Design of algorithms

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