Reduced List-Decoding of Reed--Solomon Codes Using Reliability Information

TL;DR

This paper introduces a reduced list-decoding method for Reed-Solomon codes that leverages reliability information to lower computational complexity while maintaining comparable error correction performance.

Contribution

It proposes a novel decoding approach that selectively uses received positions based on reliability, reducing interpolation complexity compared to existing list-decoding algorithms.

Findings

Lower complexity in decoding process.

Comparable error correction performance to Kötter-Vardy algorithm.

Adjustable parameters to minimize failure probability.

Abstract

We decode Reed-Solomon codes using soft information provided at the receiver. The Extended Euclidean Algorithm (EEA) is considered as an initial step to obtain an intermediate result. The final decoding result is obtained by interpolating the output of the EEA at the least reliable positions of the received word. We refer to this decoding method as reduced list-decoding, since not all received positions are used in the interpolation as in other list-decoding methods, such as the Guruswami-Sudan and Wu algorithms. Consequently the complexity of the interpolation step is reduced considerably. The probability of failure can be minimised by adjusting certain parameters, making it comparable with the K\"otter-Vardy algorithm but having a much lower complexity.