Practical construction of sensing matrices for a greedy sparse recovery algorithm over finite fields

Compressed sensing aims to retrieve sparse signals from very few samples. It relies on dedicated reconstruction algorithms and well-chosen measurement matrices. In combination with network coding, which operates traditionally over finite fields, it leverages the benefits of both techniques. However, compressed sensing has been primarily investigated over the real field. F2OMP is one of the few recovery algorithms to reconstruct signals over finite fields. However, its use in practical cases is limited since its performance depends mainly on binary matrices for signal recovery. This paper reports results of extensive simulations enhancing the features of well-performing measurement matrices for F2OMP as well as methods to build them. Moreover, a modified version of the algorithm, F2OMP-loop, is proposed. It offers a compromise between performance, stability, and processing time. This allows to design a joint compressed sensing and network coding framework over finite fields.