2006 Fiscal Year Final Research Report Summary
A Novel Geometrical Approach to Two-Stage Multi-Dimensional Quantizer
| Project/Area Number |
16560325
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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 |
Communication/Network engineering
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| Research Institution | The University of Electro-Communications |
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Principal Investigator |
KAWABATA Tsutomu The University of Electro-Communications, Faculty of Electro-Communications, Professor (50152997)
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| Project Period (FY) |
2004 – 2006
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| Keywords | quantization / asymptotic vector quantization / two-stage quantization / geodesic compander / source coding / rate distortion theory / fractal geometry / data compressions |
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| Research Abstract |
The approach in the title "A Novel Geometrical Approach to Two-Stage Multi-Dimensional Quantizer," aims to provide a design theory, guided with a differential geometrical idea, of high resolution block quantizer. This purposes lossless codings for sources with from discrete to continuous alphabet, as applications of information theory. Thus we report our research activities, according to the following three categories.
First category is on the researches directly dealings with the two-stage multi-dimensional quantizer, which combine the first-stage and the second-stage quantizers. In the second-stage quantizer, we use a combination of compander and a lattice quantizer. For the latter, we have proposed a new concept of geodesic compander. Moreover the geodesic companders are arranged with a symmetric connection and minimizes the production rate of Burgers vector, on the second stage quantizer boundaries. We also have analysed the distortion performance for the defined method. In addition, we found a proof which justifies a fast quantization algorithm for the lattice An.
Second, we collected researches on developments of lossless source code and their applications. This activities will include geometrical and statistical applications for universal data compressions.
Third, we collect researches on information theory, whose topics range from channel capacity, rate-distortion theory, and network information, to stochastic processes applications.
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