Convolutional Codes in Rank Metric with Application to Random Network Coding

TL;DR

This paper introduces convolutional codes in rank metric tailored for multi-shot random network coding, providing new constructions, decoding algorithms, and demonstrating their effectiveness in error correction within network communication.

Contribution

It presents novel (partial) unit memory convolutional codes in rank metric, along with efficient decoding algorithms and applications to random network coding.

Findings

New constructions of (P)UM codes in rank metric.

An efficient error-erasure decoding algorithm with guaranteed radius.

Application of these codes to enhance error correction in network coding.

Abstract

Random network coding recently attracts attention as a technique to disseminate information in a network. This paper considers a non-coherent multi-shot network, where the unknown and time-variant network is used several times. In order to create dependencies between the different shots, particular convolutional codes in rank metric are used. These codes are so-called (partial) unit memory ((P)UM) codes, i.e., convolutional codes with memory one. First, distance measures for convolutional codes in rank metric are shown and two constructions of (P)UM codes in rank metric based on the generator matrices of maximum rank distance codes are presented. Second, an efficient error-erasure decoding algorithm for these codes is presented. Its guaranteed decoding radius is derived and its complexity is bounded. Finally, it is shown how to apply these codes for error correction in random linear and affine network coding.