Modelling Biological Systems using a Parallel Quantized MIMO Channel

In this work, we investigate a model which is related to the class of stochastic pooling networks (SPN). These networks consist of a parallel structure of noisy and compressive sensors, which observe a common input signal. They have proven to be useful in interdisciplinary research, e.g., in physics and neurobiology. By adding a second source of parallel noise and allowing cross-connections using a channel matrix, we merge these models with the multiple-input multiple-output (MIMO) framework. In contrast to typical wireless communication scenarios, we assume the channel matrix to be changed deliberately in order to study the information processing and interconnection of neurons. We investigate which channel matrix maximizes the mutual information for the MIMO case and a single-input multipleoutput (SIMO) special case and present two convex relaxations of the original problems. Based on a modified non-negative matrix factorization (NMF) algorithm, we formulate a heuristic to obtain feasible channel matrices. Finally, we evaluate the performance of the suggested heuristic.