Lattice-coded cooperation protocol for the half-duplex Gaussian two-way relay channel

Abstract

This paper studies the Gaussian two-way relay channel (GTWRC), where two nodes exchange their messages with the help of a half-duplex relay. We investigate a cooperative transmission protocol, consisting of four phases: multiple access (MA) phase, broadcast (BC) phase, and two cooperative phases. For this setup, we propose a new transmission scheme based on superposition coding for nested lattice codes, random coding, and jointly typical decoding. This scheme divides the message of each node into two parts, referred to as satellite codeword and cloud center. Depending on the phase type, the encoder sends a linear combination of satellite codewords or cloud centers. For comparison, a rate region outer bound using a cut-set bound is provided. We show that the proposed scheme can achieve the capacity region in the high signal-to-noise ratio (SNR) regime. In addition, the achievable rate region is within 0.5 bit of the outer bound, regardless of all channel parameters. Using numerical examples, we show that our proposed scheme achieves a larger rate region than the best known 4-phase transmission strategy so far, called the Hybrid Broadcast (HBC) protocol by Kim et al. Our proposed scheme not only improves upon previous 2- and 3- and 4-phase protocols but also can perform superior at some cases to the introduced 6-phase protocol by Gong, Yue, and Wang (which has more complexity relative to our 4-phase protocol).