End-to-End Error-Correcting Codes on Networks with Worst-Case Symbol Errors

TL;DR

This paper introduces a new error-correcting code framework for networks with worst-case symbol errors, achieving near-optimal throughput without requiring internal node computations, suitable for dynamic wireless networks.

Contribution

It proposes a novel transform metric, derives classical coding bounds for network capacity, and develops efficient concatenated codes with decoding algorithms, all without needing network topology knowledge.

Findings

New transform metric for network errors

Classical coding bounds adapted to network setting

Efficient concatenated codes with decoding algorithms

Abstract

The problem of coding for networks experiencing worst-case symbol errors is considered. We 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. A new transform metric for errors under the considered model is proposed. Using this metric, we replicate many of the classical results from coding theory. Specifically, we prove new Hamming-type, Plotkin-type, and Elias-Bassalygo-type upper bounds on the network capacity. A commensurate lower bound is shown based on Gilbert-Varshamov-type codes for error-correction. The GV codes used to attain the lower bound can be non-coherent, that is, they do not require prior knowledge of the network topology. We also propose a computationally-efficient concatenation scheme. The rate achieved by our concatenated codes is characterized by a Zyablov-type lower bound. We provide a generalized minimum-distance decoding algorithm which decodes up to half the minimum distance of the concatenated codes. The end-to-end nature of our design enables our codes to be overlaid on the classical distributed random linear network codes [1]. Furthermore, the potentially intensive computation at internal nodes for the link-by-link error-correction is un-necessary based on our design.