Distortion Exponents of Two-Way Relay Networks

In this paper, we study the transmission of Gaussian signals in a three-node two-way relay network, where two users communicate in both directions at possibly different rates, with the help of one relay. All nodes are half-duplex and equipped with single antenna. The relay employs the amplify-and-forward (AF) or decode-and-forward (DF) based cooperation protocols. We analyze the distortion exponent that characterizes the high signal-to-noise ratio (SNR) behavior of the end-to-end distortion of the reconstructed signal at each user node. The different rates of the two users necessitate the study of a new concept - the achievable distortion exponent region of the system. We first derive an outer bound on the distortion exponent region of two-way relay communications, which is tight at large bandwidth ratios. We then obtain the optimized distortion exponent pairs of simple four-phase relay strategies as well as two-phase and three-phase protocols. The results illustrate the effect of the bandwidth ratio and cooperation strategies on the optimized distortion exponents. Another contribution of the paper is that we also derive the achievable diversity-multiplexing tradeoffs (DMTs) of different two-way relay protocols.