Rank Metric Decoder Architectures for Random Linear Network Coding with Error Control

TL;DR

This paper develops efficient hardware decoder architectures for rank metric codes used in error control for random linear network coding, significantly reducing complexity and enabling high-throughput implementations.

Contribution

It introduces novel, low-complexity decoder architectures for Gabidulin and KK codes, making rank metric decoding more feasible for hardware deployment.

Findings

Decoders achieve high throughput with limited error correction.

Architectures are affordable and suitable for small field implementations.

Complexity is significantly reduced compared to previous designs.

Abstract

While random linear network coding is a powerful tool for disseminating information in communication networks, it is highly susceptible to errors caused by various sources. Due to error propagation, errors greatly deteriorate the throughput of network coding and seriously undermine both reliability and security of data. Hence error control for network coding is vital. Recently, constant-dimension codes (CDCs), especially K\"otter-Kschischang (KK) codes, have been proposed for error control in random linear network coding. KK codes can also be constructed from Gabidulin codes, an important class of rank metric codes. Rank metric decoders have been recently proposed for both Gabidulin and KK codes, but they have high computational complexities. Furthermore, it is not clear whether such decoders are feasible and suitable for hardware implementations. In this paper, we reduce the complexities of rank metric decoders and propose novel decoder architectures for both codes. The synthesis results of our decoder architectures for Gabidulin and KK codes with limited error-correcting capabilities over small fields show that our architectures not only are affordable, but also achieve high throughput.