Multishot Codes for Network Coding using Rank-Metric Codes

TL;DR

This paper develops multishot rank-metric codes for network coding channels with errors and erasures, using multilevel coding theory, and adapts encoding and decoding algorithms for practical implementation.

Contribution

It introduces a novel construction of multishot rank-metric codes for network channels, extending previous multilevel coding approaches to this setting.

Findings

Constructed multishot rank-metric codes for network channels.

Applied lifting to convert codes into network coding channel codes.

Adapted encoding and decoding algorithms for the new code construction.

Abstract

The multiplicative-additive finite-field matrix channel arises as an adequate model for linear network coding systems when links are subject to errors and erasures, and both the network topology and the network code are unknown. In a previous work we proposed a general construction of multishot codes for this channel based on the multilevel coding theory. Herein we apply this construction to the rank-metric space, obtaining multishot rank-metric codes which, by lifting, can be converted to codes for the aforementioned channel. We also adapt well-known encoding and decoding algorithms to the considered situation.