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 -ent...
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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 -lengthcoding 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 -lengthcoding of individual sequences, and propose some new universal coding schemes which are asymptotically optimum.
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 resol...
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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.
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 ...
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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.
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 carri...
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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.
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 max...
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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.
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 se...
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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.
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 fixe...
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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.
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 ...
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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.
作者：
Sato, NKoga, HUniv 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 info...
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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.
Wyner and Ziv considered the rate-distortion function for source coding with side information at the decoder (we call the Wyner-Ziv problem). In this paper we show an information-spectrum approach to the Wyner-Ziv pro...
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Wyner and Ziv considered the rate-distortion function for source coding with side information at the decoder (we call the Wyner-Ziv problem). In this paper we show an information-spectrum approach to the Wyner-Ziv problem for general class of nonstationary and/or nonergodic sources with side information at the decoder, where the distortion measure is arbitrary and may be nonadditive. We show that a general formula for the rate-distortion function of the Wyner-Ziv problem for general sources with the maximum distortion criterion under fixed-length coding by using the information spectrum approach.
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