The separability and ergodic sum-rate of parallel Gaussian interference channels

The achievable region of parallel Gaussian interference channels is investigated. The known coding schemes proposed for the the two-user Gaussian interference channel are extended to parallel Gaussian interference channels. The optimality of separate coding for two coding schemes namely, time division with power control and treat as noise, is proved. Moreover, the necessity of joint coding for simultaneous non-unique decoding and Han-Kobayashi coding is demonstrated. For all mentioned schemes, the optimal covariance matrix is shown to be diagonal. In addition, the ergodic fading interference channel is studied. The ergodic achievable sum-rate is investigated for different coding schemes and the optimality of diagonal covariance matrices is shown. It is proved that for time division with power control and simultaneous non-unique decoding, uniform power allocation over all sub-channels is sum-rate optimal.