2005 Fiscal Year Final Research Report Summary
Studies on weight structure analysis and search of codes with good error performance
| Project/Area Number |
16560337
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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 | Osaka University |
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Principal Investigator |
FUJIWARA Toru Osaka University, Grad.Sch.Information Science and Technology, Professor, 情報科学研究科, 教授 (70190098)
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| Project Period (FY) |
2004 – 2005
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| Keywords | linear code / minimum weight / local weight distribution / trellis structure / invariant property / binary shift |
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| Research Abstract |
Development of efficient algorithms for computing the local weight distribution is done. Using invariant property with respect to symbol position permutation, we considered algorithms based on partitioning the set of cosets of subcode into equivalence classes for the local weight distribution. We also devised a method for using the invariance property in a coset. Furthermore, we reduced the computational complexity by using the trellis structure of the cosets.
For BCH codes and Reed-Muller codes, the extended codes are closed under wider class of permutations and the computational complexity of local weight distribution is smaller. We obtained several theoretical results on the relation between the local weight distributions of the extended code and original codes, and derived a method of computation. For Reed-Muller codes, several results on local weight distribution for the cosets of its Reed-Muller subcodes. Using these, we computed the local weight distributions of several codes of lengths 128 and 256 including the (256,93) third-order Reed-Muller code. We also improved Seguin lower bound on decoding error probability using local weight distribution.
For search of codes with good error performance, binary image of Reed-Solomon codes which are MDS codes are expected to have large minimum distances. Including this class of code, we have searched codes. Decoding complexity is also important. We devised bit position permutation considering trellis structure. By searching the binary image codes over GF(256) and GF(64), we found several good (64,40) codes suitable for concatenated coding.
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Research Products
(16 results)
