Localized Dimension Growth in Random Network Coding: A Convolutional Approach

TL;DR

This paper introduces ARCNC, an adaptive convolutional network coding method that reduces field size requirements and improves decoding delay in network coding by dynamically adjusting local encoding kernels.

Contribution

The paper presents a novel adaptive convolutional coding algorithm that operates over small fields and adapts to unknown network topologies, enhancing efficiency and delay performance.

Findings

ARCNC operates effectively over small finite fields.

It adapts to unknown network topologies without prior knowledge.

ARCNC reduces decoding delay and memory overheads.

Abstract

We propose an efficient Adaptive Random Convolutional Network Coding (ARCNC) algorithm to address the issue of field size in random network coding. ARCNC operates as a convolutional code, with the coefficients of local encoding kernels chosen randomly over a small finite field. The lengths of local encoding kernels increase with time until the global encoding kernel matrices at related sink nodes all have full rank. Instead of estimating the necessary field size a priori, ARCNC operates in a small finite field. It adapts to unknown network topologies without prior knowledge, by locally incrementing the dimensionality of the convolutional code. Because convolutional codes of different constraint lengths can coexist in different portions of the network, reductions in decoding delay and memory overheads can be achieved with ARCNC. We show through analysis that this method performs no worse than random linear network codes in general networks, and can provide significant gains in terms of average decoding delay in combination networks.