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List Decoding from Erasures: Bounds and Code Constructions

  • Venkatesan Guruswami
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2245)

Abstract

We consider the problem of list decoding from erasures. We establish lower and upper bounds on the rate of a (linear) code that can be list decoded with list size L when up to a fraction p of its symbols are adversarially erased. Our results show that in the limit of large L, the rate of such a code approaches the capacity (1 - p) of the erasure channel. Such nicely list decodable codes are then used as inner codes in a suitable concatenation scheme to give a uniformly constructive family of asymptotically goodbinary linear codes of rate Ω(ɛ2/ lg(1/ɛ)) that can be efficiently list decoded using lists of size O(1/ɛ) from up to a fraction (1-ɛ) of erasures. This improves previous results from [14] in this vein, which achieveda rate of Ω(ɛ3 lg(1/ɛ)).

Keywords

Error-correcting codes Linear codes Decoding algorithms List decoding Erasure channel 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Venkatesan Guruswami
    • 1
  1. 1.Computer Science DivisionUniversity of California at BerkeleyBerkeley

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