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

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...

Decoding Reed-Muller Codes beyond Half the Minimum Distance

Algebraic Soft-Decision Decoding of Reed-Solomon Codes Using Bit-level Soft Information

The performance of algebraic soft-decision decoding (ASD) of Reed-Solomon (RS) codes using bit-level soft information is investigated. Optimal multiplicity assignment strategies (MAS) of ASD with infinite cost are first studied over erasure channels and binary symmetric channels (BSC). The corresponding decoding radii are calculated in closed forms and tight bounds on the error probability are ...

Code Constructions based on Reed-Solomon Codes

Reed–Solomon codes are a well–studied code class which fulfill the Singleton bound with equality. However, their length is limited to the size q of the underlying field Fq. In this paper we present a code construction which yields codes with lengths of factors of the field size. Furthermore a decoding algorithm beyond half the minimum distance is given and analyzed.

An Alternative to Factorization: a Speedup for SUDAN’s Decoding Algorithm and its Generalization to Algebraic-Geometric Codes

We propose an improvement to Sudan's algorithm for decoding Reed-Solomon codes beyond half of their minimum distance, and its generalisation to algebraic-geometric codes. Both algorithms, in their original version, involve factorisation of polynomials. The main idea consists in replacing factorisation by an iterative root nding procedure of low complexity based on Newton approximation. In the c...