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Equivalences among Some Information Measures for Individual Sequences and Their Applications for fixed-length coding Problems

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2024年第3期E107A卷 393-403页

作者： Uyematsu, Tomohiko Matsuta, Tetsunao Tokyo Inst Technol Dept Informat & Commun Engn Tokyo 1528550 Japan Saitama Univ Grad Sch Sci & Engn Saitama 3388570 Japan

This paper proposes three new information measures for individual sequences and clarifies their properties. Our new information measures are called as the non -overlapping max -entropy, the overlapping smooth max -entropy, and the non -overlapping smooth max -entropy, respectively. These measures are related to the fixed -length coding of individual sequences. We investigate these measures, and show the following three properties: (1) The non -overlapping max -entropy coincides with the topological entropy. (2) The overlapping smooth max -entropy and the nonoverlapping smooth max -entropy coincide with the Ziv-entropy. (3) When an individual sequence is drawn from an ergodic source, the overlapping smooth max -entropy and the non -overlapping smooth max -entropy coincide with the entropy rate of the source. Further, we apply these information measures to the fixed -length coding of individual sequences, and propose some new universal coding schemes which are asymptotically optimum.

关键词： fixed-length coding individual sequence information measure topological entropy universal coding Ziv-entropy

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Relationship Between Source Resolvability with Normalized f-Divergence and fixed-length coding

Relationship Between Source Resolvability with Normalized <i...

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IEEE Information Theory Workshop (ITW)

作者： Nomura, Ryo Waseda Univ Ctr Data Sci Tokyo Japan

ISBN: (纸本)9781728159621

This paper deals with the relationship between the source resolvability problem (or resolvability problem for short) and the fixed-length source coding problem. In the literature, optimum achievable rates in the resolvability problem (optimum resolvability rate) with respect to the variational distance as well as the Kullback-Leibler (KL) divergence, have already been analyzed. The relationship between the optimum resolvability rate and the optimum rate of the fixed-length source coding has also been clarified in each cases. In particular, it has been reported that the optimum source resolvability rate with respect to the normalized KL divergence has a close relationship with the optimum fixed-length source coding rate with the correct decoding exponent. Recently, the optimum resolvability rate with respect to a class of f-divergences has been analyzed. This result can be considered as a generalization of the optimum resolvability rate with respect to the unnormalized KL divergence. However, unnormalized f-divergences has not been considered yet in the resolvability problem. Hence, in this paper, we consider the resolvability problem with respect to a class of unnormalized f-divergences. In particular, we derive the relationship between the optimum resolvability rate with a class of normalized f-divergences and the optimum rate of the fixed-length source coding.

关键词： f-divergence fixed-length coding General source Random number generation Source resolvability

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coding Theorems on the Worst-Case Redundancy of fixed-length coding for a General Source

Coding Theorems on the Worst-Case Redundancy of Fixed-Length...

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IEEE International Symposium on Information Theory (ISIT)

作者： Koga, Hiroki Arimura, Mitsuharu Iwata, Ken-ichi Univ Tsukuba Grad Sch Syst & Informat Engn 1-1-1 Tennoudai Tsukuba Ibaraki 3058571 Japan Shonan Inst Technol Dept Appl Comp Sci Kanagawa 2518511 Japan Univ Fukui Grad Sch Engn Fukui 9108507 Japan

ISBN: (纸本)9781457705953

We consider a situation where n-tuples generated from a general source are encoded by a fixed-length code and discuss coding theorems on the worst-case redundancy, where the worst-case redundancy is defined as the maximum of the difference between the rate and the ideal codeword length per symbol with respect to all the correctly decodable n-tuples. We treat the four cases where the decoding error probability epsilon(n) is required to satisfy (a) lim(n ->infinity) epsilon(n) = 0, (b) lim inf(n ->infinity) epsilon(n) = 0, (c) lim sup(n ->infinity) epsilon(n) <= epsilon, and (d) lim inf(n ->infinity) epsilon(n) <= epsilon, respectively, where epsilon is an element of [0;1) is an arbitrary constant. We give general formulas of the optimum worst-case redundancy that are closely related to the width of the entropy-spectrum of a source.

关键词： Channel coding Decoding Error probability Manganese Redundancy Source coding arbitrary constant coding theorem decodable n-tuple decoding decoding error probability entropy codes entropy-spectrum source error statistics fixed-length coding general source coding ideal codeword length per symbol optimum worst-case redundancy source coding

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Relationship Between Intrinsic Randomness with f-Divergence and fixed-length Source coding

Relationship Between Intrinsic Randomness with f-Divergence ...

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IEEE International Symposium on Information Theory (ISIT)

作者： Nomura, Ryo Waseda Univ Ctr Data Sci Tokyo Japan

ISBN: (纸本)9781665421607;9781665421591

This paper deals with the relationship between the intrinsic randomness (IR) problem and the fixed-length source coding problem. The IR problem is one of random number generation problems and optimum achievable rates (optimum IR rate) with respect to several approximation measures such as the variational distance, the Kullback-Leibler (KL) divergence and f-divergences, have been investigated. In particular, it has been shown that the optimum IR rate with respect to the variational distance has a close relationship with the supremum of the unachievable rate in the source coding problem. Inspired by this result, in this paper, we consider the optimum IR rate with respect to a subclass of f-divergences and try to show a relationship with the unachievable rate in the source coding problem. The subclass of f-divergences considered in this paper includes several well-known measures, such as the variational distance, the KL divergence, the Hellinger distance. We also consider a class of normalized f-divergences, which includes the normalized KL divergence.

关键词： f-divergence fixed-length coding General source Intrinsic randomness Random number generation

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Test data compression scheme based on variable-to-fixed-plus-variable-length coding

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JOURNAL OF SYSTEMS ARCHITECTURE 2007年第11期53卷 877-887页

作者： Zhan, Wenfa Liang, Huaguo Shi, Feng Huang, Zhengfeng Hefei Univ Technol Sch Comp & Informat Hefei Anhui Peoples R China

A test data compression scheme based on Variable-to-fixed-Plus-Variable-length (VTFPVL) coding is presented, by using which the test data can be compressed efficiently. In this scheme, code words are divided into fixed-length head section and variable-length tail section. In order to attain further compression, the highest bit of the tail is omitted from the code words, because all of the highest bits in the tail section of the code words are the same as 1. A special shift counter is also used, which further eases the control circuit. Experimental results of the MinTest fault sets which are part of ISCAS-89 benchmark circuits show that the proposed scheme is obviously better than traditional coding methods in the compression ratio and the implementation of decompression, such as Golomb, FDR, VIHC, v9C coding. (c) 2007 Elsevier B.V. All rights reserved.

关键词： test data compression coding fixed-length coding variable-length coding

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Parametric Forms of the Achievable Rate Region for Source coding with a Helper

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2012年第12期E95A卷 2493-2497页

作者： Matsuta, Tetsunao Uyematsu, Tomohiko Matsumoto, Ryutaroh Tokyo Inst Technol Dept Commun & Integrated Syst Tokyo 1528550 Japan

Source coding with a helper is one of the most fundamental fixed-length source coding problem for correlated sources. For this source coding, Wyner and Ahlswede-Korner showed the achievable rate region which is the set of rate pairs of encoders such that the probability of error can be made arbitrarily small for sufficiently large block length. However, their expression of the achievable rate region consists of the sum of indefinitely many sets. Thus, their expression is not useful for computing the achievable rate region. This paper deals with correlated sources whose conditional distribution is related by a binary-input output-symmetric channel, and gives a parametric form of the achievable rate region in order to compute the region easily.

关键词： achievable rate region correlated sources data compression fixed-length coding source coding with a helper

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New results on optimistic source coding

New results on optimistic source coding

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26th Symposium on Information Theory and Its Applications (SITA2003)

作者： Sato, N Koga, H Univ Tsukuba Masters Program Sci & Engn Tsukuba Ibaraki 3058573 Japan Univ Tsukuba Grad Sch Syst & Informat Engn Tsukuba Ibaraki 3058573 Japan

Optimistic coding is a coding in which we require the existence of reliable codes for infinitely many block length. In this letter we consider the optimistic source coding theorems for a general source Z from the information-spectrum approach. We first formulate the problem to be considered clearly. We obtain the optimistic infimum achievable source coding rate T-epsilon(Z) for the case where decoding error probability epsilon(n) is asymptotically less than or equal to an arbitrarily given epsilonis an element of [0, 1). In fact, T-epsilon(Z) turns out to be expressed in a form similar to the ordinary infimum achievable source coding rate. A new expression for T-epsilon(Z) is also given. In addition. we investigate the case where epsilon(n) = 0 for infinitely many n and obtain the infimum achievable coding rate.

关键词： source coding fixed-length coding general source information-spectrum optimistic coding

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On Wyner-Ziv Problem for general sources with average distortion criterion

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2007年第8期8卷 1263-1270页

作者： YANG Sheng-tian ZHAO Min-jian QIU Pei-liang Department of Information Science and Electronic Engineering Zhejiang University Hangzhou 310027 China

The Wyner-Ziv Problem for general sources with average distortion under fixed-length coding is investigated in this paper. To solve the problem,an enhanced covering lemma for a Markov chain is first established. Then based on the lemma,a general formula for the rate-distortion function of the problem is derived,where the distortion is only assumed uniformly bounded and may be nonadditive. Finally,it is further pointed out that such methods can be used to establish more general results on multiterminal source coding problems.

关键词： Rate-distortion with side information Information spectrum fixed-length coding Average distortion criterion

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LZW-CIE: a high-capacity linguistic steganography based on LZW char index encoding

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NEURAL COMPUTING & APPLICATIONS 2022年第21期34卷 19117-19145页

作者： Varol Arisoy, Merve Burdur Mehmet Akif Ersoy Univ Fac Technol Informat Syst Engn TR-15300 Burdur Turkey

With the effect of digitalization, the transfer of all text documents over the Internet rather than human transmission has increased, and this situation has revealed the idea that text documents can be used as a carrier that can safely store information. Realizing that methods such as word-line shifting, usage of spaces, replacement of the word with its synonym are fragile against steganalysis, led to new searches and it was determined that deep learning models were more resistant to detecting the presence of hidden words. In this study, the text generation based on the information that is wanted to be hidden without a carrier text, both at word and character level, was performed. Arithmetic coding, perfect tree and Huffman coding methods were used as secret information embedding methods in text generation based on word level. In this part of the study, bidirectional LSTM architecture with attention mechanism was created as language model. In text generation based on character level, a new secret information embedding algorithm is created by combining the LZW compression algorithm with the Char Index (LZW-Char Index Encoding) method. The character-level model is created as a result of using the encoder-decoder architecture together with bidirectional LSTM and Bahdanau attention. The proposed method was evaluated from the perspectives of information embedding efficiency, information imperceptibility and hidden information capacity. As a result of the experiments, it was determined that the method exceeded the state-of-the-art performance and was more resistant to steganalysis.

关键词： Linguistic steganography LZW-CIE encoding Arithmetic coding Huffman coding fixed-length coding Automatic text generation

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Uniform threshold TCQ with block classification for image transmission over noisy channels

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY 2001年第1期11卷 105-110页

作者： Cai, JF Chen, CW Univ Missouri Dept Elect Engn Columbia MO 65211 USA

A combined source-channel coding scheme without explicit error protection is proposed to transmit images over noisy channels. Major components of the proposed coding scheme include 2-D DCT with block classification, fixed-length uniform threshold trellis coded quantization, optimal bit-allocation algorithm, and noise reduction filters. The integration of these components allows us to organize the compressed bitstream in such a way that it is less sensitive to channel noise, and hence achieves data compression and error resilience at the same time. This paper reports our recent study by incorporating the block classification into the integrated scheme. Experimental results show that, in the case of noise-free channels and at the bit rate of 0.5 bpp, an improvement of 2.33 dB can be achieved with the classification, In the case of noisy channels, the gain decreases as the bit error rate increases. However, we can still achieve an average improvement of 0.46 dB, even for highly noisy channels with BER = 0.1, Our proposed system uses no error protection, no synchronization codewords and no entropy coding. However, it shows decent compression ratio and graceful degradation with respect to increasing channel errors.

关键词： bit allocation block classification fixed-length coding image transmission uniform threshold TCQ

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