2003 Fiscal Year Final Research Report Summary
Research on Stochastic Processes and Information Theory
| Project/Area Number |
14540111
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Nagoya University |
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Principal Investigator |
IHARA Shunsuke Nagoya University, Graduate School of Information Science, Professor, 情報科学研究科, 教授 (00023200)
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| Co-Investigator(Kenkyū-buntansha) |
SATO Junya Nagoya University, Graduate School of Information Science, Associate Professor, 情報科学研究科, 助教授 (20235352)
MATSUBARA Yo Nagoya University, Graduate School of Information Science, Associate Professor, 情報科学研究科, 助教授 (30242788)
MATSUMOTO Hiroyuki Nagoya University, Graduate School of Information Science, Professor, 情報科学研究科, 教授 (00190538)
TSUKIJI Tatsuie Tokyo Electrical University, School of Eng. and Sci., Associate Professor, 理工学部, 助教授 (70291961)
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| Project Period (FY) |
2002 – 2003
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| Keywords | Gaussian channel / Source coding / Channel coding / Waiting time for string matching / Large deviation theorem |
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| Research Abstract |
We have studied on stochastic processes and information theory and obtained the following results.
[1]Error probability for Gaussian channels with feedback.
For the white Gaussian channel with feedback, it is known that the error probability decreases to zero more rapidly than the exponential of any order. Note that the precise proof of this fact is not familiar. We have given a new proof for this fact, not only for the discrete-time case but also for the continuous-time white Gaussian channel with feedback.
[2]Error exponents for the source coding with distortion.
For the lossy source coding, if the coding rate is greater than the rate distortion function, Marton (1974) proved that, for the stationary memoryless source with finite alphabet, the optimum error probability, namely the minimum probability of distortion exceeding a prescribed level, decreases to zero exponentially fast and gave a formula for the error exponent. We extended the Marton's results to the stationary memoryless sources with general alphabet and, proved that the Marton's formula remains true even if the alphabet is not finite.
[3]Asymptotic behavior of probability of string matching.
Applying a large deviation theorem to Gaussian stationary processes, we obtained formulas of the asymptotic behavior of probability of string matching and of the waiting time for string matching.
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Research Products
(12 results)
