| Presentation | 2013-01-21 The second order asymptotic rates in fixed-length source coding and resolvability problem in terms of smooth Renyi entropy Susumu TAGASHIRA, Tomohiko UYEMATSU, |
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| Abstract(in English) | Fixed-length source coding problem is to convert source output sequences to fixed-length codewords. In stationary memoryless sources, when the coding rate is greater than the entropy of the source, there exists a code whose error probability vanishes as the length of the sequence increases. Contrarily, when the coding rate is less than the entropy, the error probability of any code converges to 1 as the length of sequence increases. However, when the coding rate is equal to the entropy, we need to examine the second order asymptotic rate in order to investigate the error probability. When the logarithm of the number of codewords is represented by nR + nb, the second order asymptotic rate is defined as the coefficient b, where n denotes the length of sequences and R denotes the coding rate. On the other hand, resolvability problem is to generate random numbers with a given probability distribution from uniform random numbers. The second order asymptotic rate in resolvability problem also has similar properties as those in fixed-length source coding problem. In this paper, we represent the second order asymptotic rates for a given error probability in terms of the smooth Renyi entropy of order zero, and we clarify the second order asymptotic rates without using the information-spectrum. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | fixed-length source coding / resolvability / smooth Renyi entropy / second order asymptotic rate |
| Paper # | IT2012-60 |
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| Committee | IT |
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| Conference Date | 2013/1/14(1days) |
| Place (in Japanese) | (See Japanese page) |
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| Registration To | Information Theory (IT) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | The second order asymptotic rates in fixed-length source coding and resolvability problem in terms of smooth Renyi entropy |
| Sub Title (in English) | |
| Keyword(1) | fixed-length source coding |
| Keyword(2) | resolvability |
| Keyword(3) | smooth Renyi entropy |
| Keyword(4) | second order asymptotic rate |
| 1st Author's Name | Susumu TAGASHIRA |
| 1st Author's Affiliation | Dept. of Communications and Integrated Systems, Tokyo Institute of Technology() |
| 2nd Author's Name | Tomohiko UYEMATSU |
| 2nd Author's Affiliation | Dept. of Communications and Integrated Systems, Tokyo Institute of Technology |
| Date | 2013-01-21 |
| Paper # | IT2012-60 |
| Volume (vol) | vol.112 |
| Number (no) | 382 |
| Page | pp.pp.- |
| #Pages | 6 |
| Date of Issue | |