  This paper considers the distributed information bottleneck (D-IB) problem
for a primitive Gaussian diamond channel with two relays and Rayleigh fading.
Due to the bottleneck constraint, it is impossible for the relays to inform the
destination node of the perfect channel state information (CSI) in each
realization. To evaluate the bottleneck rate, we provide an upper bound by
assuming that the destination node knows the CSI and the relays can cooperate
with each other, and also three achievable schemes with simple symbol-by-symbol
relay processing and compression. Numerical results show that the lower bounds
obtained by the proposed achievable schemes can come close to the upper bound
on a wide range of relevant system parameters.
