Analog Joint Source-Channel Coding Using Non-Linear Curves and MMSE Decoding

We investigate the performance of a discrete-time all-analog-processing joint source-channel coding system for the transmission of memoryless sources over average power constrained AWGN channels. First, N:1 bandwidth compression systems are analyzed and optimized. At the encoder, N samples of an i.i.d. source are directly mapped into one channel symbol using a non-linear curve. Different from previous work in the literature, we introduce an additional degree of freedom at the encoder, 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 system presents a performance very close to the theoretical limits, even at low CSNR, as long as the system parameters are properly optimized. Then, N:K bandwidth compression systems are constructed by parallel combination of an M:1 system and a 1:1 uncoded system, and the optimal power allocation between the two constituent systems is derived in order to maximize the overall output signal-to-distortion ratio (SDR). Finally, 1:2 bandwidth expansion systems using mapping functions similar to those used in 2:1 system are investigated. Different from digital systems, the proposed scheme does not require long block lengths to achieve good performance, and shows graceful degradation when the CSNR is lower than the one used for the design.