Trade-off between dimensionality reduction and quantization in minimum mean square error estimation

In this paper, the trade-off between dimension reduction and quantization in minimum mean square error estimation problem is investigated. With given communication bandwidth, the bits allocation problem is formulated as an optimization problem. For high dimension observation case, the optimal allocation strategy is proposed that compresses the observation to a lower dimension, then allocate the given bits to these compressed dimension. Do not waste the bandwidth on the less important dimension which would leads to bad performance.