Conditional approximate message passing with side information

Dror Baron, Anna Ma, Deanna Needell, Cynthia Rush, Tina Woolf

Abstract: In information theory, side information (SI) is often used to increase the efficiency of communication systems. This work lays the framework for a class of Bayes-optimal signal recovery algorithms referred to as conditional approximate message passing (CAMP) that make use of available SI. CAMP involves a linear inverse problem, where noisy, linear measurements acquire an unknown input vector using a measurement matrix with independent and identically distributed entries, and the SI vector obeys a symbol-wise dependence with the input. Despite having a simple and straightforward derivation, our CAMP algorithm obtains lower mean squared error than other signal recovery algorithms that have been proposed to incorporate SI. The good performance of CAMP is due its Bayes-optimality properties, which are not present in previous approaches to SI-aided signal recovery.