Stopping Redundancy Hierarchy Beyond the Minimum Distance

The Stopping Redundancy Hierarchy of Cyclic Codes

We extend the framework for studying the stopping redundancy of a linear block code by introducing and analyzing the stopping redundancy hierarchy. The stopping redundancy hierarchy of a code represents a measure of the trade-off between performance and complexity of iteratively decoding a code used over the binary erasure channel. It is defined as an ordered list of positive integers in which ...

Decoding Reed-Muller Codes beyond Half the Minimum Distance

The minimum barrier distance

In this paper we introduce a minimum barrier distance, MBD, defined for the (graphs of) real-valued bounded functions fA, whose domain D is a compact subsets of the Euclidean space R. The formulation of MBD is presented in the continuous setting, where D is a simply connected region in R, as well as in the case where D is a digital scene. The MBD is defined as the minimal value of the barrier s...

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...

Efficient decoding of Reed-Solomon codes beyond half the minimum distance

A list decoding algorithm is presented for [ ] Reed–Solomon (RS) codes over GF ( ), which is capable of correcting more than ( ) 2 errors. Based on a previous work of Sudan, an extended key equation (EKE) is derived for RS codes, which reduces to the classical key equation when the number of errors is limited to ( ) 2 . Generalizing Massey’s algorithm that finds the shortest recurrence that gen...