Improved inapproximability of lattice and coding problems with preprocessing

Authors:
O. Regev
Affiliations:
Dept. of Comput. Sci., Tel-Aviv Univ., Ramat-Aviv, Israel
Venue:
IEEE Transactions on Information Theory
Year:
2006

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Abstract

We show that the closest vector problem with preprocessing (CVPP) is NP-hard to approximate to within √3-ε for any ε0. In addition, we show that the nearest codeword problem with preprocessing (NCPP) is NP-hard to approximate to within 3-ε. These results improve previous results of Feige and Micciancio. We also present the first inapproximability result for the relatively nearest codeword problem with preprocessing (RNCP). Finally, we describe an n-approximation algorithm to CVPP.