On a Relation of the Reliability Function and the Asymptotic Distance Ratio in Shannon's Channel Coding Theorem
| Project/Area Number |
12650398
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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 |
情報通信工学
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| Research Institution | Hosei University |
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Principal Investigator |
NISHIJIMA Toshihisa Hosei University, Faculty of Computer and Information Sciences, Professor, 情報科学部, 教授 (70211456)
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| Project Period (FY) |
2000 – 2002
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| Project Status |
Completed (Fiscal Year 2002)
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| Budget Amount *help |
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 2002: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2001: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2000: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Keywords | Probability of Undetected Error / Average Probability of Undetected Error / Varshamov-Gilbert Bound / Expurgated Bound / Concatenated Codes / Iterated Codes / Generalized Reed-Solomon Codes / Binary Weight Distribution / 繰り返し符号 |
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| Research Abstract |
There are three main points of our research results as follows.
1. We get an upper bound on the average probability of undetected error for the ensemble of binary expansions of generalized Reed-Solomon codes. From this bound, we simultaneously show that the asymptotic distance ration for the ensemble of these codes meets the Varshamov-Gilbert bound and this ensemble satisfies the expurgated bound.
2. Iterated codes given by P. Elias are well known as a class of the codes satisfying the channel-coding theorem. By utilizing the way for deriving an upper bound on the average probability of undetected error for the ensemble of all binary systematic linear block codes, we can easily get that for the ensemble of all iterated codes. It is shown that the average capability for the ensemble of all iterated codes is poorer than that for all binary systematic linear block codes.
3. Concatenated codes given by G. D. Forney, Jr. are very important codes from practical and theoretical viewpoint. By utilizing a characteristic structure of the concatenated code, an approximately good computation method of the probability of undetected error without knowing binary weight distribution of the concatenated code is proposed. Since the computational complexity of the method is at the most O(n) where n is a code length of a outer code of the concatenated code, it is an efficient method when investigating the capability of error detection for the concatenated code from practical and theoretical viewpoint. By comparing exact values with approximate values in some examples of the codes, which are small enough for the weight distribution to be found by computer search, we show the efficiency of the approximate values by the proposed method.
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Report
(4 results)
Research Products
(3 results)
