Efficient Interpolation-Based Decoding of Interleaved Subspace and Gabidulin Codes

TL;DR

This paper introduces an efficient decoding scheme for interleaved subspace and Gabidulin codes, enabling decoding beyond traditional limits through novel interpolation and root-finding algorithms.

Contribution

It presents a new interpolation-based decoding method that surpasses half the minimum subspace distance for interleaved codes, with efficient algorithms for polynomial interpolation and root-finding.

Findings

Decodes interleaved subspace codes beyond half the minimum distance

Provides efficient algorithms for interpolation and root-finding

Accelerates decoding of interleaved Gabidulin codes

Abstract

An interpolation-based decoding scheme for interleaved subspace codes is presented. The scheme can be used as a (not necessarily polynomial-time) list decoder as well as a probabilistic unique decoder. Both interpretations allow to decode interleaved subspace codes beyond half the minimum subspace distance. Further, an efficient interpolation procedure for the required linearized multivariate polynomials is presented and a computationally- and memory-efficient root-finding algorithm for the probabilistic unique decoder is proposed. These two efficient algorithms can also be applied for accelerating the decoding of interleaved Gabidulin codes.