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| Title | On Precise Achievable Conditions in Resolvability Problem Based on the Asymptotic Normality (in Japanese) |
|---|---|
| Authors | Ryo NOMURA 、Toshiyasu MATSUSHIMA |
| Released Year | 2009 |
| Format | Journal |
| Category | Source coding |
| Jounal Name | Far East Journal of Electronics and Communications |
| Jounal Page | vol.3, no.3, pp.85-99 |
| Published Year | 2009 |
| Published Month | 8 |
| Abstract （English） |
Random number generation problem is one of the main topics in information theory. The resolvability problem is a kind of random number generation problems and formulated as follows. Given an arbitrary discrete random variables (called a source or a target random number), we generate it by using a discrete uniform random number whose size is as small as possible under the condition that the distance between the probability distribution of the source and the probability distribution of random variables to be generated is small. One of main problems in this setting is to construct the efficient algorithm and the other is to show the achievable condition. The achievable condition for the source guarantees following. That is, there exists an algorithm under the condition that the distance between the probability distribution of the source and the probability distribution of random variables to be generated is small. Steinberg et al.\ and Han et al.\ showed the achievable condition for an arbitrary given general sources by using information spectrum methods. The class of general sources is quite large, so their result is very important. However their result is not so precise, since the general source has no assumption for the source such as the consistency condition. On the other hand it is important to show the achievable condition more precisely by using the assumption for the source. In this paper we show the achievable condition more precisely by using the asymptotic normality. |
| Note （English） |
3 |
| Manuscript | |
| Presentation |
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- Almost Sure and Mean Convergence of Extended Stochastic Complexity
- A Source Model with Probability Distribution over Word Set and Recurrence Time Theorem
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- An Analysis of Slepian-Wolf Coding Problem Based on the Asymptotic Normality
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- A Study on the Degrees of Freedom in an Experimental Design Model Based on an Orthonormal System
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- Asymptotic property of universal lossless coding for independent piecewise identically distributed sources
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- Estimation of the Effects in the Experimental Design using Fourier Transforms
- A Note on a Sampling Theorem for Functions over $GF(q)^n$ Domain
