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This paper considers the information bottleneck (IB) problem of a Rayleighfading multiple-input multiple-out (MIMO) channel with an oblivious relay. Therelay is constrained to operate without knowledge of the codebooks, i.e., itperforms oblivious processing. Moreover, due to the bottleneck constraint, itis impossible for the relay to inform the destination node of the perfectchannel state information (CSI) in each channel realization. To evaluate thebottleneck rate, we first provide an upper bound by assuming that thedestination node can get the perfect CSI at no cost. Then, we provide fourachievable schemes where each scheme satisfies the bottleneck constraint andgives 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, andconveys both the CSI and its observation to the destination node. Due to CSItransmission, the performance of these two schemes is sensitive to the MIMOchannel dimension, especially the channel input dimension. To ensure that itstill performs well when the channel dimension grows large, in the third andfourth achievable schemes, the relay only transmits compressed observation tothe destination node. Numerical results show that with simple symbol-by-symboloblivious relay processing and compression, the proposed achievable schemeswork well and can demonstrate lower bounds coming quite close to the upperbound on a wide range of relevant system parameters.

Information Bottleneck for a Rayleigh Fading MIMO Channel with an Oblivious Relay