On Coding for Reliable Communication over Packet Networks

TL;DR

This paper introduces a capacity-achieving coding scheme for lossy packet networks that uses random linear combinations at intermediate nodes, ensuring reliable communication without decoding delays, applicable to both wireline and wireless networks.

Contribution

The paper proposes a novel coding scheme that achieves capacity in lossy networks using polynomial complexity operations, with a detailed analysis of error decay and network flow modeling.

Findings

The scheme is capacity-achieving under general loss processes.

Packet propagation follows queueing network dynamics.

Error probability decays exponentially with coding delay.

Abstract

We present a capacity-achieving coding scheme for unicast or multicast over lossy packet networks. In the scheme, intermediate nodes perform additional coding yet do not decode nor even wait for a block of packets before sending out coded packets. Rather, whenever they have a transmission opportunity, they send out coded packets formed from random linear combinations of previously received packets. All coding and decoding operations have polynomial complexity. We show that the scheme is capacity-achieving as long as packets received on a link arrive according to a process that has an average rate. Thus, packet losses on a link may exhibit correlation in time or with losses on other links. In the special case of Poisson traffic with i.i.d. losses, we give error exponents that quantify the rate of decay of the probability of error with coding delay. Our analysis of the scheme shows that it is not only capacity-achieving, but that the propagation of packets carrying "innovative" information follows the propagation of jobs through a queueing network, and therefore fluid flow models yield good approximations. We consider networks with both lossy point-to-point and broadcast links, allowing us to model both wireline and wireless packet networks.