2006 Fiscal Year Final Research Report Summary
A fundamental study of generalized compound-error-correcting-codes and their decoding algorithms
| Project/Area Number |
17560333
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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 |
KURIHARA Masazumi The University of Electro-Communications, Faculty of Electro-Communications, Associate Researcher, 電気通信学部, 助手 (90242346)
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| Project Period (FY) |
2005 – 2006
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| Keywords | Compound-errors / random-errors / burst-errors / compound-erasures / random-erasures / burst-erasures / compound-distance / decoding algorithm |
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| Research Abstract |
In this research we introduce a new concept of error which occurs in the communication channel. The error is called a compound error in this research, and the error consists of two types of errors which are random-errors and burst-errors. After that, we discuss a principle of decoding compound errors in the received space. Moreover, we discuss some compound-error-correcting-codes and their decoding algorithms. In particular, we extend the concept of compound error to erasures, that is, we consider two types of erasures, random-erasures and burst-erasures, as erasures. Then we introduce a new compound distance, which can not satisfy the true triangle inequation which is one of conditions for a mathematical distance, in the received space. But it can be proved that we can theoretically correct compound-erasures and compound-errors when we execute a bounded-distance decoding by using the new compound distance. From this key theorem, we can positively consider concrete decoding methods for compound-erasure and compound-error correcting codes. We show that iterated codes are able to be used as compound-erasure and compound-error correcting codes, where the iterated code is a generalized version of the well-known product code. After that, we propose the decoding algorithm for the iterated codes. The proposed decoding algorithm can correct compound-erasures and compound-errors up to theoretical bound which is the half of minimum compound distance of the iterated code. Moreover, for future works, we researched several network codes as applications of concepts of compound-erasures and compound-errors. Concretely, we proposed coding methods and their algorithms about robust network codes and secure network codes. And we estimated theoretical properties of their network codes.
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Research Products
(20 results)
