Vector Approximate Message Passing using Information Bottleneck Optimized Lookup Tables

Recently approximate message passing algorithms have gained a lot of attention for solving problems with a known prior distribution and an observation that is described by a noisy, possibly nonlinear function of a linear transform output. There are several approximate message passing algorithms for specific problem setups. Most of those algorithms have in common that a scalar estimator with respect to the prior distribution is required. These estimators might not be available in closed form or of high computational cost. In this paper we discuss the design of lookup tables using the information bottleneck method to replace these scalar estimators. If the system setup is known, the required parameters for the design process can be determined using the state evolution framework. These parameters might be chosen heuristically if the system setup is not known a priori. For both cases numerical results are presented.