On the Diversity Order and Coding Gain of Multi-Source Multi-Relay Cooperative Wireless Networks with Binary Network Coding

TL;DR

This paper analyzes the diversity order and coding gain in multi-source multi-relay cooperative wireless networks with binary network coding, considering realistic fading and relay errors, providing a comprehensive framework for various topologies.

Contribution

It introduces a general analytical framework that accounts for demodulation errors, arbitrary network topologies, and binary encoding, revealing how network coding influences diversity and coding gain.

Findings

Each source's diversity order equals the network code's separation vector.

Coding gain decreases as the number of mixed packets at relays increases.

Ignoring relay errors at the destination results in approximately halving the diversity order.

Abstract

In this paper, a multi-source multi-relay cooperative wireless network with binary modulation and binary network coding is studied. The system model encompasses: i) a demodulate-and-forward protocol at the relays, where the received packets are forwarded regardless of their reliability; and ii) a maximum-likelihood optimum demodulator at the destination, which accounts for possible demodulations errors at the relays. An asymptotically-tight and closed-form expression of the end-to-end error probability is derived, which clearly showcases diversity order and coding gain of each source. Unlike other papers available in the literature, the proposed framework has three main distinguishable features: i) it is useful for general network topologies and arbitrary binary encoding vectors; ii) it shows how network code and two-hop forwarding protocol affect diversity order and coding gain; and ii) it accounts for realistic fading channels and demodulation errors at the relays. The framework provides three main conclusions: i) each source achieves a diversity order equal to the separation vector of the network code; ii) the coding gain of each source decreases with the number of mixed packets at the relays; and iii) if the destination cannot take into account demodulation errors at the relays, it loses approximately half of the diversity order.