Decoding Reed Solomon Codes beyond the Error-Correction Diameter

Decoding of Reed Solomon codes beyond the error-correction bound

Decoding interleaved Reed-Solomon codes beyond their joint error-correcting capability

A new probabilistic decoding algorithm for low-rate Interleaved Reed– Solomon (IRS) codes is presented. This approach increases the error correcting capability of IRS codes compared to other known approaches (e.g. joint decoding) with high probability. It is a generalization of well-known decoding approaches and its complexity is quadratic with the length of the code. Asymptotic parameters of t...

Unambiguous Decoding of Generalized Reed–Solomon Codes Beyond Half the Minimum Distance

The Schmidt–Sidorenko–Bossert scheme extends a low-rate Reed–Solomon code to an Interleaved Reed–Solomon code and achieves the decoding radius of Sudan’s original list decoding algorithm while the decoding result remains unambiguous. We adapt this result to the case of Generalized Reed– Solomon codes and calculate the parameters of the corresponding Interleaved Generalized Reed–Solomon code. Fu...

Collaborative Decoding of Interleaved Reed-Solomon Codes and Concatenated Code Designs

Interleaved Reed–Solomon codes are applied in numerous data processing, data transmission, and data storage systems. They are generated by interleaving several codewords of ordinary Reed–Solomon codes. Usually, these codewords are decoded independently by classical algebraic decoding methods. However, by collaborative algebraic decoding approaches, such interleaved schemes allow the correction ...

Simultaneous Partial Inverses and Decoding Interleaved Reed-Solomon Codes

This paper introduces the simultaneous partialinverse problem for polynomials and develops its application to decoding interleaved Reed-Solomon codes and subfield-evaluation codes beyond half the minimum distance. The simultaneous partial-inverse problem has a unique solution (up to a scale factor), which can be computed by an efficient new algorithm, for which we also offer some variations. De...