Gaussian Two-Way Channels With Discrete Inputs and Quantized Outputs
  In this paper, Gaussian two-way channel with uniform output quantization is studied. For Gaussian inputs, the optimum uniform finite-level quantizer is determined numerically for different values of Signal-to-Noise Ratio (SNR). The two-way channel with constellation-based transmitters is then investigated. A formulation for the so-called Shannon achievable region of this channel is developed and numerical computations of this region are presented for particular constellations. It is shown that if one transmitter utilizes a rotated version of the constellation used at the other transmitter, the Shannon achievable region can be enlarged 
Ershad Banijamali
cs.IT math.IT