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International Conference on Foundations of Software Technology and Theoretical Computer Science

FSTTCS 2001: FST TCS 2001: Foundations of Software Technology and Theoretical Computer Science pp 195–206Cite as

List Decoding from Erasures: Bounds and Code Constructions

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Part of the book series: Lecture Notes in Computer Science ((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)).

Work done while the author was at the Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139.

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Author information

Authors and Affiliations

  1. Computer Science Division, University of California at Berkeley, 94720, Berkeley, CA

    Venkatesan Guruswami

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  1. Venkatesan Guruswami
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Automation, Indian Institute of Science, 560012, Bangalore, India

    Ramesh Hariharan  & V. Vinay  & 

  2. Chennai Mathematical Institute, 92 G.N. Chetty Road, 600 017, Chennai, India

    Madhavan Mukund

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Guruswami, V. (2001). List Decoding from Erasures: Bounds and Code Constructions. In: Hariharan, R., Vinay, V., Mukund, M. (eds) FST TCS 2001: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2001. Lecture Notes in Computer Science, vol 2245. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45294-X_17

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  • DOI: https://doi.org/10.1007/3-540-45294-X_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43002-5

  • Online ISBN: 978-3-540-45294-2

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