| Project/Area Number |
09640258
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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 U., Inform. & Sci., Prof., 情報文化学部, 教授 (00023200)
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| Co-Investigator(Kenkyū-buntansha) |
ITO Masayuki Nagoya U., Inform. & Sci., Prof., 情報文化学部, 教授 (60022638)
MATSUMOTO Hiroyuki Nagoya U., Inform. & Sci., Assoc. Prof., 情報文化学部, 助教授 (00190538)
OZAWA Masanao Nagoya U., Inform. & Sci., Prof., 情報文化学部, 教授 (40126313)
TSUKIJI Tastue Nagoya U., Inform. & Sci., Res. Assoc., 情報文化学部, 助手 (70291961)
MATSUBARA Yo Nagoya U., Inform. & Sci., Assoc. Prof., 情報文化学部, 助教授 (30242788)
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| Project Period (FY) |
1997 – 1999
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| Keywords | Gaussian channel / mutual information / large deviation theorem / data compression / coding theorem / entropy |
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| Research Abstract |
We have studied theory of stochastic process and their application to information theory. We have obtained some results on the information transmission over Gaussian channels, and on large deviation theorems and their applications to information theory.
The Gaussian channel is one of the most important communication channels and has been studied by many researches. Particularly, it is fundamental to calculate the mutual information transmitted over the Gaussian channel. Using the canonical representation of stochastic processes, we have succeeded to derive a general formula to calculate the mutual information transmitted over the continuous-time Gaussian channel with feedback, without any special assumptions on the noise. Using this formula, we have proved some basic properties on the capacities of Gaussian channels and on the channel coding theorms.
In the development of information theory, various limit theorems have been played important roles. We may say that most of these limit theorems have been obtained by using law of large numbers. We have applied large deviation theorems, in stead of law of large numbers, to refine some of these limit theorems. We have studied the asymptotic behavior of the probability of string matching and the waiting time of the string matching. Then the results obtained here is used to evaluate the error probability in the source coding. On the other hand, applying large deviation theorems, we have determined the asymptotic behavior of error probabilities in a problem of hypotheses testing.
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