Decoding interleaved Reed-Solomon codes over noisy channels

Authors:
Daniel Bleichenbacher;Aggelos Kiayias;Moti Yung
Affiliations:
Bell Laboratories, Murray Hill, NJ, USA;Department of Computer Science and Engineering, University of Connecticut, Storrs, CT, USA;RSA Laboratories, Bedford, MA, USA and Department of Computer Science, Columbia University, New York, NY, USA
Venue:
Theoretical Computer Science
Year:
2007

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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.