Asymmetric Successive Compute-and-Forward and the Capacity Gap for the Gaussian Two-Way Relay Channel

The compute-and-forward strategy is one of the outstanding methods which is used for interference management in wireless relay networks where decoding linear combinations of code words is required. Recently, many efforts have been made for decoding integer and non-integer combinations [1]-[7]. The difference between the methods is the manner of handling different conditions of networks, such as equal or unequal power constraints and equal or unequal channel gains. In this work, we present a modified n-step asymmetric successive compute-and-forward strategy for the communication network where we have both unequal power constraints and unequal channel gains conditions. In the proposed method, we scale channel gains and coefficients with the square root of power constraints. In this way, despite previous methods, without the need for scaling factors in our formulation, it is still able to solve the problem of general Gaussian relay networks with unequal power constraints and unequal channel gains. We also use scaling factors in our method in order to have the ability to divide the rates between users fairly. We evaluate the ability of the modified strategy for the uplink communication of the two-way relay channel, where one relay can help communication between the two users. At the relay, we decode the linear combinations of the messages of the two users and obtain 1/2 bit/sec/Hz per user capacity gap from the cut-set bound. Through some theoretical and simulation results, we show that by appropriately adjusting parameters, different points and areas of rate regions are achievable.