Local list decoding of homomorphisms
Name
136936209-MIT.pdf
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Full printable version
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1.8 MB
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93688c2a6f88917ea1ce9c6b76e1d362
Author(s)
Grigorescu, Elena, Ph. D. Massachusetts Institute of Technology
Advisor(s)
Madhu Sudan.
Date Issued
2006
Publisher
Massachusetts Institute of Technology
Abstract
We investigate the local-list decodability of codes whose codewords are group homomorphisms. The study of such codes was intiated by Goldreich and Levin with the seminal work on decoding the Hadamard code. Many of the recent abstractions of their initial algorithm focus on Locally Decodable Codes (LDC's) over finite fields. We derive our algorithmic approach from the list decoding of the Reed-Muller code over finite fields proposed by Sudan, Trevisan and Vadhan. Given an abelian group G and a fixed abelian group H, we give combinatorial bounds on the number of homomorphisms that have agreement 6 with an oracle-access function f : G --> H. Our bounds are polynomial in , where the degree of the polynomial depends on H. Also, depends on the distance parameter of the code, namely we consider to be slightly greater than 1-minimum distance. Furthermore, we give a local-list decoding algorithm for the homomorphisms that agree on a 3 fraction of the domain with a function f, the running time of which is poly(1/e, log G).
Description
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.
Includes bibliographical references (leaves 47-49).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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