Coding for Network Coding

TL;DR

This paper analyzes the capacity of noisy networks with randomized linear network coding, introducing a probabilistic error model and a low-complexity error correction scheme that achieves channel capacity.

Contribution

It presents a probabilistic error model for network coding and a novel low-complexity coding scheme that attains the network's capacity.

Findings

Capacity of the network channel is computed.

A new error correction scheme based on sparse graphs is proposed.

The scheme achieves capacity with quadratic complexity in information bits.

Abstract

We consider communication over a noisy network under randomized linear network coding. Possible error mechanism include node- or link- failures, Byzantine behavior of nodes, or an over-estimate of the network min-cut. Building on the work of Koetter and Kschischang, we introduce a probabilistic model for errors. We compute the capacity of this channel and we define an error-correction scheme based on random sparse graphs and a low-complexity decoding algorithm. By optimizing over the code degree profile, we show that this construction achieves the channel capacity in complexity which is jointly quadratic in the number of coded information bits and sublogarithmic in the error probability.