Approximate Sum-Capacity of K-user Cognitive Interference Channels with Cumulative Message Sharing

Abstract

This paper considers the K-user cognitive interference channel with one primary and K-1 secondary/cognitive transmitters with a cumulative message sharing structure, i.e., cognitive transmitter i ϵ [2 : K] has non-causal knowledge of the messages of users with index less than i. A computable outer bound valid for any memoryless channel is proposed. The sum-rate outer bound is evaluated first for the high-SNR linear deterministic approximation of the Gaussian noise channel. This is shown to be both the sum capacity for the 3-user channel with arbitrary channel gains, and the sum-capacity for the symmetric K-user channel. Interestingly, for the K user channel, cognition at transmitters 2 to K-1 is not needed, and knowledge of all messages at the K-th transmitter only is sufficient to achieve the sum-capacity. Next, the sum-capacity of the symmetric Gaussian noise channel is characterized to within a constant additive and multiplicative gap, both of which are functions of K. As opposed to other multiuser interference channel models, a single scheme (in this case based on dirty-paper coding) suffices for both the weak and strong interference regimes. The generalized degrees of freedom (gDoF) are then derived and are shown, unlike interference and broadcast channels, to be a function of K. Interestingly, it is shown that as the number of users grows to infinity the gDoF of the K-user cognitive interference channel with cumulative message sharing tends to the gDoF of a broadcast channel with a K-antenna transmitter and K single-antenna receivers. Finally, numerical evaluations show that the actual gaps between the presented inner and outer bounds are significantly smaller than the analytically derived gaps.