Decoding of Reed Solomon codes beyond the error-correction bound
Journal of Complexity
Reed-Solomon Codes and Their Applications
Reed-Solomon Codes and Their Applications
Towards a VLSI Architecture for Interpolation-Based Soft-Decision Reed-Solomon Decoders
Journal of VLSI Signal Processing Systems
Low-complexity soft decoding algorithms for reed-solomon codes
Low-complexity soft decoding algorithms for reed-solomon codes
IEEE Transactions on Information Theory
Efficient decoding of Reed-Solomon codes beyond half the minimum distance
IEEE Transactions on Information Theory
On algebraic soft-decision decoding algorithms for BCH codes
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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In this paper, we present an algebraic methodology for implementing low-complexity, Chase-type, decoding of Reed-Solomon (RS) codes of length n. In such, a set of 2η test-vectors that are equivalent on all except η ≪ n coordinate positions is first produced. The similarity of the test-vectors is utilized to reduce the complexity of interpolation, the process of constructing a set of polynomials that obey constraints imposed by each test-vector. By first considering the equivalent indices, a polynomial common to all test-vectors is constructed. The required set of polynomials is then produced by interpolating the final η dissimilar indices utilizing a binary-tree structure. In the second decoding step (factorization) a candidate message is extracted from each interpolation polynomial such that one may be chosen as the decoded message. Although an expression for the direct evaluation of each candidate message is provided, carrying out this computation for each polynomial is extremely complex. Thus, a novel, reduced-complexity, methodology is also given. Although suboptimal, simulation results affirm that the loss in performance incurred by this procedure is decreasing with increasing code length n, and negligible for long (n 100) codes. Significant coding gains are shown to be achievable over traditional hardin hard-out decoding procedures (e.g., Berlekamp-Massey) at an equivalent (and, in some cases, lower) computational complexity. Furthermore, these gains are shown to be similar to the recently proposed soft-in-hard-out algebraic techniques (e.g., Sudan, Kötter-Vardy) that bear significantly more complex implementations than the proposed algorithm.