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We consider a communication system where two transmitters wish to exchangeinformation through a half-duplex relay in the middle. The channels between thetransmitters and the relay have asymmetric channel gains. More specifically,the channels are assumed to be synchronized with complex inputs and complexfading coefficients with an average power constraint on the inputs to thechannels. The noise at the receivers have the same power spectral density andare assumed to be white and Gaussian. We restrict our attention to transmissionschemes where information from the two nodes are simultaneously sent to therelay during a medium access phase followed by a broadcast phase where therelay broadcasts information to both the nodes. An upper bound on the capacityfor the two phase protocol under a sum power constraint on the transmit powerfrom all the nodes is obtained as a solution to a convex optimization problem.We show that a scheme using channel inversion with lattice decoding can obtaina rate a small constant 0.09 bits from the upper bound at high signal-to-noiseratios. Numerical results show that the proposed scheme can perform very closeto the upper bound.

Power Allocation Strategies and Lattice Based Coding schemes for Bi-directional relaying