A parametric approach to list decoding of Reed-Solomon codes using interpolation

Abstract

In this paper we present a minimal list decoding algorithm for Reed-Solomon (RS) codes. Minimal list decoding for a code $C$ refers to list decoding with radius $L$, where $L$ is the minimum of the distances between the received word $\mathbf{r}$ and any codeword in $C$. We consider the problem of determining the value of $L$ as well as determining all the codewords at distance $L$. Our approach involves a parametrization of interpolating polynomials of a minimal Gröbner basis $G$. We present two efficient ways to compute $G$. We also show that so-called re-encoding can be used to further reduce the complexity. We then demonstrate how our parametric approach can be solved by a computationally feasible rational curve fitting solution from a recent paper by Wu. Besides, we present an algorithm to compute the minimum multiplicity as well as the optimal values of the parameters associated with this multiplicity which results in overall savings in both memory and computation.

Corrected Definition 2.3. Accepted for publication in IEEE Transactions on Information Theory

Cited by in corpus (7)

• On Rational-Interpolation Based List-Decoding and List-Decoding Binary Goppa Codes
• List Decoding Algorithms based on Groebner Bases for General One-Point AG Codes
• An iterative algorithm for parametrization of shortest length shift registers over finite rings
• List Decoding Algorithm based on Voting in Groebner Bases for General One-Point AG Codes
• List-Decoding Gabidulin Codes via Interpolation and the Euclidean Algorithm
• Gabidulin Decoding via Minimal Bases of Linearized Polynomial Modules
• Iterative List-Decoding of Gabidulin Codes via Gröbner Based Interpolation