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.
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Bleichenbacher, D., Kiayias, A., Yung, M. (2003). Decoding of Interleaved Reed Solomon Codes over Noisy Data. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_9
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DOI: https://doi.org/10.1007/3-540-45061-0_9
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