  This paper considers the information bottleneck (IB) problem of a Rayleigh
fading multiple-input multiple-out (MIMO) channel with an oblivious relay. The
relay is constrained to operate without knowledge of the codebooks, i.e., it
performs oblivious processing. Moreover, due to the bottleneck constraint, it
is impossible for the relay to inform the destination node of the perfect
channel state information (CSI) in each channel realization. To evaluate the
bottleneck rate, we first provide an upper bound by assuming that the
destination node can get the perfect CSI at no cost. Then, we provide four
achievable schemes where each scheme satisfies the bottleneck constraint and
gives a lower bound to the bottleneck rate. In the first and second schemes,
the relay splits the capacity of the relay-destination link into two parts, and
conveys both the CSI and its observation to the destination node. Due to CSI
transmission, the performance of these two schemes is sensitive to the MIMO
channel dimension, especially the channel input dimension. To ensure that it
still performs well when the channel dimension grows large, in the third and
fourth achievable schemes, the relay only transmits compressed observation to
the destination node. Numerical results show that with simple symbol-by-symbol
oblivious relay processing and compression, the proposed achievable schemes
work well and can demonstrate lower bounds coming quite close to the upper
bound on a wide range of relevant system parameters.
