Analog non-linear coding for improved performance in compressed sensing

We propose a framework based on the combination of compressed sensing and non-linear coding that shows excellent robustness against noise. The key idea is the use of non-linear mappings that act as analog joint source-channel encoders, processing the compressed sensing measurements proceeding from an analog source and producing continuous amplitude samples that are transmitted directly through the noisy channel.;Specifically, we first investigate analog joint source-channel coding systems using space-filling curves and MMSE decoding. At the encoder, N source symbols are mapped into K channel symbols directly, achieving either bandwidth compression (N > K) or expansion (N < K). Different from previous work in the literature, MMSE decoding instead of ML decoding is considered, and we focus on both high and low channel signal-to-noise ratio (CSNR) regions. By using MMSE decoding, the proposed non-linear coding system clearly outperforms existing systems and presents a performance very close to the theoretical limits, even at low CSNR, as long as the curve parameters are properly optimized.;Second, the proposed non-linear analog coding scheme is combined with compressed sensing. Simulation results show that by combining non-linear coding with compressed sensing, the proposed framework clearly outperforms systems based on stand-alone compressive sensing, and it is readily applicable in practical systems such as imaging.