  This paper considers the distributed information bottleneck (D-IB) problem
for a primitive Gaussian diamond channel with two relays and MIMO Rayleigh
fading. The channel state is an independent and identically distributed
(i.i.d.) process known at the relays but unknown to the destination. The relays
are oblivious, i.e., they are unaware of the codebook and treat the transmitted
signal as a random process with known statistics. The bottleneck constraints
prevent the relays to communicate the channel state information (CSI) perfectly
to the destination. 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 two 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.
