Distortion exponents of two-way relaying cooperative networks

In this paper, we study the transmission of Gaussian signals in a three-node half-duplex bidirectional relaying network, where two users communicate in both directions with the help of one relay, and can transmit at different rates. The relay employs 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 relaying communications, which is tight at large bandwidth ratio. We then obtain the optimal distortion exponent pairs of conventional one-way relaying strategies and AF/DF based two-way relaying protocols with single-rate coding. The results illustrate the effect of the bandwidth ratio and cooperation strategies on the optimal distortion exponents.