Decoding of interleaved Reed Solomon codes over noisy data

  • Authors:

  • Daniel Bleichenbacher;Aggelos Kiayias;Moti Yung

  • Affiliations:

  • Bell Laboratories, Murray Hill, NJ;Department of Computer Science and Engineering, University of Connecticut, Storrs, CT;Department of Computer Science, Columbia University, New York, NY

  • Venue:
  • ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
  • Year:
  • 2003

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Abstract

We consider error-correction over the Non-Binary Symmetric Channel (NBSC) which is a natural probabilistic extension of the Binary Symmetric Channel (BSC). We propose a new decoding algorithm for interleaved Reed-Solomon Codes that attempts to correct all "interleaved" codewords simultaneously. In particular, interleaved encoding gives rise to multi-dimensional curves and more specifically to a variation of the Polynomial Reconstruction Problem, which we call Simultaneous Polynomial Reconstruction. We present and analyze a novel probabilistic algorithm that solves this problem. Our construction yields a decoding algorithm for interleaved RS-codes that allows efficient transmission arbitrarily close to the channel capacity in the NBSC model.