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.
Download