We investigate the performance of a discrete-time all-analog-processing joint sourcechannel coding system for the transmission of i.i.d. Gaussian and Laplacian sources over AWGN channels. In the encoder, two samples of an i.i.d. source are mapped into a channel symbol using a space-filling curve. Different from previous work in the literature, MMSE decoding instead of ML decoding is considered, and we focus on both high and low channel SNR regions. The main contribution of this paper is to show that the proposed system presents a performance very close to the theoretical limits, even at low SNR, as long as the curve parameters are properly optimized.