Turbo compressed sensing using message passing de-quantization

This paper proposes a new technique to concatenate 1-bit compressed sensing with a convolutional channel encoder for transmission of sparse signals over a memoryless AWGN channel. At the reconstruction part, an iterative decoder, referred to as turbo-CS decoder, has been proposed. At the turbo-CS decoder, the sparse signal is decoded through iterations between an a posteriori probability decoder and a softin/soft-out 1-bit compressed sensing decoder. By numerical experiments, we show that the turbo-CS decoder outperforms the state-of-the-art algorithms for 1-bit compressed sensing reconstruction in the presence of AWGN channel by more than 10 dB in terms of signal reconstruction performance.