Compressed sensing with Shannon-Kotel'nikov mapping in the presence of noise

Abstract

We propose a low delay/complexity sensor system based on the combination of Shannon-Kotel'nikov mapping and compressed sensing (CS). The proposed system uses a 1:2 nonlinear analog coder on the CS measurements in the presence of channel noise. It is shown that the purely-analog system, used in conjunction with either maximum a-posteriori or minimum mean square error decoding, outperforms the following reference systems in terms of signal-to-distortion ratio: 1) a conventional CS system that assumes noiseless transmission, and 2) a CS-based system which accounts for channel noise during signal reconstruction. The proposed system is also shown to be advantageous in requiring fewer sensors than the reference systems.