Decoding of Interleaved Linearized Reed-Solomon Codes with Applications to Network Coding

TL;DR

This paper introduces a decoding method for interleaved linearized Reed-Solomon codes that enhances error correction in network coding, offering larger decoding regions and better code rates with practical decoding performance.

Contribution

It presents a new construction and list decoding algorithm for interleaved linearized Reed-Solomon codes, improving error correction capabilities over previous methods.

Findings

Decoding region significantly increased, especially for insertions.

Proposed list decoder can be interpreted as a probabilistic unique decoder.

Simulation suggests list size is often one up to maximal decoding radius.

Abstract

Recently, Martinez-Penas and Kschischang (IEEE Trans. Inf. Theory, 2019) showed that lifted linearized Reed-Solomon codes are suitable codes for error control in multishot network coding. We show how to construct and decode lifted interleaved linearized Reed-Solomon codes. Compared to the construction by Martinez-Penas-Kschischang, interleaving allows to increase the decoding region significantly (especially w.r.t. the number of insertions) and decreases the overhead due to the lifting (i.e., increases the code rate), at the cost of an increased packet size. The proposed decoder is a list decoder that can also be interpreted as a probabilistic unique decoder. Although our best upper bound on the list size is exponential, we present a heuristic argument and simulation results that indicate that the list size is in fact one for most channel realizations up to the maximal decoding radius.