Physical Network Coding in Two-Way Wireless Relay Channels

Abstract

It has recently been recognized that the wireless networks represent a fertile ground for devising communication modes based on network coding. A particularly suitable application of the network coding arises for the two-way relay channels, where two nodes communicate with each other assisted by using a third, relay node. Such a scenario enables application of physical network coding, where the network coding is either done (a) jointly with the channel coding or (b) through physical combining of the communication flows over the multiple access channel. In this paper we first group the existing schemes for physical network coding into two generic schemes, termed 3-step and 2-step scheme, respectively. We investigate the conditions for maximization of the two-way rate for each individual scheme: (1) the Decode-and-Forward (DF) 3-step schemes (2) three different schemes with two steps: Amplify-and-Forward (AF), JDF and Denoise-and-Forward (DNF). While the DNF scheme has a potential to offer the best two-way rate, the most interesting result of the paper is that, for some SNR configurations of the source-relay links, JDF yields identical maximal two-way rate as the upper bound on the rate for DNF.

Rate regions of a two-way Gaussian relay channel

“…Similar to [11], we classify the existing two-way relay schemes into 3-step schemes and 2-step schemes according to the number of phases to finish one round of information exchange.…”

“…When AF strategy is adopted, the relay simply amplifies the received superimposed signal from the two source nodes and forwards it to the two receivers. We name this scheme as 2S-AF [8], [11].…”

“…The achievable rate region of a general two-way relay channel is studied by Xie using random binning [10]. On the other hand, authors in [7], [8], [11]- [14] consider more practical relay strategies over Gaussian channels. In specific, the expressions of rate pairs for AF relaying are obtained in [7], [8].…”

“…Authors in [8], [13] also obtained the rate pair expressions for superposition based DF relaying, where the relay node simply applies linear combining on the two decoded and re-modulated signals. The achievable sum-rate for bit-level XOR based DF is analyzed in [11]. Therein, the optimal time control with the objective of maximizing the sum-rate is studied.…”

“…Therein, the optimal time control with the objective of maximizing the sum-rate is studied. It is worth mentioning that the asymmetry in both packet size and channel gain of the two transmitting nodes is considered in [11]. More recently, Liu and Xue characterize the achievable rate region for one particular XOR based DF with the absence of direct link [12].…”