Binary Error Correcting Network Codes

TL;DR

This paper introduces a new error model and coding bounds for network coding under worst-case bit-flip errors, demonstrating the potential for improved throughput with non-coherent error-correcting codes in dynamic wireless networks.

Contribution

It proposes a novel error metric, establishes upper and lower bounds on network capacity, and develops non-coherent codes that do not require internal node error correction.

Findings

New Hamming-type upper bound on network capacity

GV-type codes enable effective error correction

Codes can be overlaid on classical network codes without internal node modifications

Abstract

We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting schemes can be arbitrarily far from achieving the optimal network throughput. We propose a new metric for errors under this model. Using this metric, we prove a new Hamming-type upper bound on the network capacity. We also show a commensurate lower bound based on GV-type codes that can be used for error-correction. The codes used to attain the lower bound are non-coherent (do not require prior knowledge of network topology). The end-to-end nature of our design enables our codes to be overlaid on classical distributed random linear network codes. Further, we free internal nodes from having to implement potentially computationally intensive link-by-link error-correction.