On the K-user cognitive interference channel with cumulative message sharing sum-capacity

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, i ϵ [2 : K], non-causally knows all messages of the users with index less than i. We first propose a computable outer bound valid for any memoryless channel and show the sum-rate to be achievable for the symmetric K-user Linear Deterministic Channel. Interestingly, for the K-user channel having only the K-th transmitter know all other messages is sufficient to achieve the sum-capacity, i.e., cognition at transmitters 2 to K-1 is not needed. Next, the sum-capacity of the symmetric Gaussian noise channel is characterized to within a constant additive and multiplicative gap, which depend on K. As opposed to other interference channel models, a single scheme suffices for both the weak and strong interference regimes. Moreover it is only required for transmitters 2 to K-1 to have, in addition to their own message, non-causal message knowledge of the transmitter 1´s message.