Cooperative Strategies for the Half-Duplex Gaussian Parallel Relay Channel: Simultaneous Relaying versus Successive Relaying

TL;DR

This paper compares simultaneous and successive relaying protocols in a half-duplex Gaussian parallel relay network, proposing new schemes and analyzing their capacity and optimal relay ordering at different SNR levels.

Contribution

It introduces a composite BME-DPC scheme, derives the optimal relay ordering, and characterizes the capacity in low and high SNR regimes for the first time.

Findings

Simultaneous relaying with DDF approaches capacity at low SNR under certain conditions.

Successive relaying with DPC asymptotically achieves capacity at high SNR.

The composite BME-DPC scheme outperforms individual schemes in achievable rate.

Abstract

This study investigates the problem of communication for a network composed of two half-duplex parallel relays with additive white Gaussian noise. Two protocols, i.e., \emph{Simultaneous} and \emph{Successive} relaying, associated with two possible relay orderings are proposed. The simultaneous relaying protocol is based on \emph{Dynamic Decode and Forward (DDF)} scheme. For the successive relaying protocol: (i) a \emph{Non-Cooperative} scheme based on the \emph{Dirty Paper Coding (DPC)}, and (ii) a \emph{Cooperative} scheme based on the \emph{Block Markov Encoding (BME)} are considered. Furthermore, the composite scheme of employing BME at one relay and DPC at another always achieves a better rate when compared to the \emph{Cooperative} scheme. A \emph{"Simultaneous-Successive Relaying based on Dirty paper coding scheme" (SSRD)} is also proposed. The optimum ordering of the relays and hence the capacity of the half-duplex Gaussian parallel relay channel in the low and high signal-to-noise ratio (SNR) scenarios is derived. In the low SNR scenario, it is revealed that under certain conditions for the channel coefficients, the ratio of the achievable rate of the simultaneous relaying based on DDF to the cut-set bound tends to be 1. On the other hand, as SNR goes to infinity, it is proved that successive relaying, based on the DPC, asymptotically achieves the capacity of the network.