Capacity Theorems for the Gaussian Zigzag Channel

We consider the two-user Gaussian zigzag channel, where there are two senders and two receivers. One of the senders transmits information to its intended receiver (without interfering with the unintended receiver) while the other sender transmits information to both receivers. We first establish achievable rates for the discrete memoryless zigzag channel under strong interference which can be extended to the Gaussian zigzag channel with strong and very strong crossover link gain (a
²
ges 1). We also determine an outer bound for the Gaussian zigzag channel under strong and very strong crossover link gain (a
²
ges 1). Moreover, we establish the capacity of the Gaussian zigzag channel under (strictly) strong crossover link gain (1 les a
²
les 1 + P
₁
)