RSCS: Minimum measurement MMV deterministic compressed sensing based on complex reed solomon coding

Compressed Sensing (CS) is an emerging field in communications and mathematics that is used to measure few measurements of long sparse vectors with the ability of lossless reconstruction. In this paper we use methods from channel coding to create the CS recovery algorithm RSCS in the Multiple Measurement Vector case (MMV) that uses a specifically constructed measurement matrix. In particular, we use a modified Reed Solomon encoding-decoding structure to measure sparsely representable vector systems down to the theoretical minimum number of measurements. We prove that the reconstruction is guaranteed, even in the low dimensional case.