Decoding interleaved Reed–Solomon codes over noisy channels

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.