A Distributed Digital Codec for Jointly Sparse Correlated Signals

In this paper, targeting jointly sparse correlated signals, we propose a distributed digital codec framework. First, the non-zero coefficients of each signal are quantized and then mapped onto a finite field. Subsequently, measurements obtained by compressed sensing (CS) over finite fields, where Low-density Parity-check (LDPC) matrices are adopted as CS encoding matrices, are modulated and conveyed through separate additive white Gaussian noise (AWGN) channel. Such an order for the encoder is named as "first quantization, then compressed sensing". For joint recovery, a novel joint belief propagation (JBP) algorithm is applied at the sink node, where a new type of constraint node, i.e., correlation constraint nodes is introduced, which connect two factor graphs that separately represent the CS encoding matrix of each signal. Experimental results prove that the proposed scheme outperforms the scheme that ignores the correlated information between the signals, especially when the correlation is high. Moreover, we compare the proposed framework vis-a-vis "first compressed sensing, then quantization" framework and validate the superiority in terms of recovery quality.