Multiple-access Network Information-flow and Correction Codes

TL;DR

This paper characterizes the capacity region for multiple-access network multicast with adversarial errors, proposing new capacity-achieving codes that are efficient and end-to-end, under both secret and omniscient adversary models.

Contribution

It introduces the first capacity characterization for this scenario and develops two novel polynomial-complexity codes for the omniscient adversarial model.

Findings

Capacity region characterized for both models.

Polynomial-complexity capacity-achieving code provided.

Two constructions: one based on random subspace codes, another on field extension.

Abstract

This work considers the multiple-access multicast error-correction scenario over a packetized network with $z$ malicious edge adversaries. The network has min-cut $m$ and packets of length $\ell$, and each sink demands all information from the set of sources $\sources$. The capacity region is characterized for both a "side-channel" model (where sources and sinks share some random bits that are secret from the adversary) and an "omniscient" adversarial model (where no limitations on the adversary's knowledge are assumed). In the "side-channel" adversarial model, the use of a secret channel allows higher rates to be achieved compared to the "omniscient" adversarial model, and a polynomial-complexity capacity-achieving code is provided. For the "omniscient" adversarial model, two capacity-achieving constructions are given: the first is based on random subspace code design and has complexity exponential in $\ell m$, while the second uses a novel multiple-field-extension technique and has $O(\ell m^{|\sources|})$ complexity, which is polynomial in the network size. Our code constructions are "end-to-end" in that all nodes except the sources and sinks are oblivious to the adversaries and may simply implement predesigned linear network codes (random or otherwise). Also, the sources act independently without knowledge of the data from other sources.