Systematic Network Coding with the Aid of a Full-Duplex Relay

TL;DR

This paper analyzes systematic network coding in a relay channel with full-duplex relays, comparing systematic and non-systematic relays in terms of delay and decoding complexity, especially under poor channel conditions.

Contribution

It provides an analytical comparison of systematic and non-systematic relays in multi-hop wireless networks, highlighting the benefits of systematic relays for delay and complexity.

Findings

Systematic relays increase uncoded packet reception at the receiver.

Systematic relays reduce decoding complexity.

Performance benefits are significant under poor channel conditions.

Abstract

A characterization of systematic network coding over multi-hop wireless networks is key towards understanding the trade-off between complexity and delay performance of networks that preserve the systematic structure. This paper studies the case of a relay channel, where the source's objective is to deliver a given number of data packets to a receiver with the aid of a relay. The source broadcasts to both the receiver and the relay using one frequency, while the relay uses another frequency for transmissions to the receiver, allowing for a full-duplex operation of the relay. We analyze the decoding complexity and delay performance of two types of relays: one that preserves the systematic structure of the code from the source; another that does not. A systematic relay forwards uncoded packets upon reception, but transmits coded packets to the receiver after receiving the first coded packet from the source. On the other hand, a non-systematic relay always transmits linear combinations of previously received packets. We compare the performance of these two alternatives by analytically characterizing the expected transmission completion time as well as the number of uncoded packets forwarded by the relay. Our numerical results show that, for a poor channel between the source and the receiver, preserving the systematic structure at the relay (i) allows a significant increase in the number of uncoded packets received by the receiver, thus reducing the decoding complexity, and (ii) preserves close to optimal delay performance.