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The complexity of error-correcting codes

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Fundamentals of Computation Theory (FCT 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1279))

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Abstract

By concatenating linear-time codes with small, good codes, it is possible to construct in polynomial time a family of asymptotically good codes that approach the Shannon bound that can be encoded and decoded in linear time. Moreover, their probability of decoder error is exponentially small in the block length of the codes. In this survey, we will explain exactly what this statement means, how it is derived, and what problems in the complexity of error-correcting codes remain open. Along the way, we will survey some key developments in the complexity of error-correcting codes.

We should point out that, at the present time, almost every implementation of error-correcting codes uses special-purpose hardware. Moreover, coding schemes that are efficient in software can be inefficient in hardware, and vice versa.

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Authors and Affiliations

  1. Massachusetts Institute of Technology, USA

    Daniel A. Spielman

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  1. Daniel A. Spielman
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Bogdan S. Chlebus Ludwik Czaja

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© 1997 Springer-Verlag Berlin Heidelberg

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Spielman, D.A. (1997). The complexity of error-correcting codes. In: Chlebus, B.S., Czaja, L. (eds) Fundamentals of Computation Theory. FCT 1997. Lecture Notes in Computer Science, vol 1279. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036172

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  • DOI: https://doi.org/10.1007/BFb0036172

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63386-0

  • Online ISBN: 978-3-540-69529-5

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