Efficient and Robust Distributed Digital Codec Framework for Jointly Sparse Correlated Signals

Abstract

In this paper, we propose a novel distributed digital transmission framework for two jointly sparse correlated signals. First, the non-zero coefficients of each signal are quantized by a standard quantizer or a novel distributed quantizer, as appropriate. Then, these quantized values are mapped to the elements of a finite field, except 0, while the zero coefficients are mapped to 0. Subsequently, compressed sensing over finite fields is applied to obtain measurements. We name such an order first quantization then compressed sensing. The two measurement signals are then converted to bit sequences, modulated, and transmitted through separate additive white Gaussian noise (AWGN) channels. At the central receiver, which has access to both channels, following demodulation, an innovative joint belief propagation (JBP) algorithm is performed for joint recovery. In this algorithm, we introduce a new type of constraint node, i.e., correlation constraint nodes, which connect two factor graphs that separately represent the CS encoding matrix of each signal. The experimental results prove that under the same framework the proposed scheme provides significant performance improvements compared to the scheme that ignores the correlated information between jointly sparse signals, especially when the correlation coefficient is high. Then, to answer the question of which order is better, we construct the first compressed sensing, then quantization framework, for fairness, two cutting edge jointly greedy pursuit algorithms are separately adopted at the joint decoder. Through simulations, we validate that the proposed framework provides more effective and robust transmissions.

Keywords

• Jointly sparse signals
• joint belief propagation
• distributed quantizer
• distributed compressed sensing
• LDPC matrix