Binary Compressive Sensing via Analog Fountain Coding

TL;DR

This paper introduces a novel compressive sensing method for sparse binary signals using analog fountain codes, achieving fewer measurements and robust recovery in noisy environments, with practical applications in wireless sensor networks.

Contribution

The paper proposes the AFCS scheme with a verification-based decoder and optimized measurement degree, reducing measurement requirements compared to traditional methods.

Findings

AFCS requires O(n log(1-k/n)) measurements for perfect recovery.

The verification decoder performs well in noiseless conditions.

Simulation shows AFCS outperforms conventional binary CS and L1-minimization in various SNRs.

Abstract

In this paper, a compressive sensing (CS) approach is proposed for sparse binary signals' compression and reconstruction based on analog fountain codes (AFCs). In the proposed scheme, referred to as the analog fountain compressive sensing (AFCS), each measurement is generated from a linear combination of L randomly selected binary signal elements with real weight coefficients. The weight coefficients are chosen from a finite weight set and L, called measurement degree, is obtained based on a predefined degree distribution function. We propose a simple verification based reconstruction algorithm for the AFCS in the noiseless case. The proposed verification based decoder is analyzed through SUM-OR tree analytical approach and an optimization problem is formulated to find the optimum measurement degree to minimize the number of measurements required for the reconstruction of binary sparse signals. We show that in the AFCS, the number of required measurements is of O(-n log(1-k/n)), where n is the signal length and k is the signal sparsity level. We then consider the signal reconstruction of AFCS in the presence of additive white Gaussian noise (AWGN) and the standard message passing decoder is then used for the signal recovery. Simulation results show that the AFCS can perfectly recover all non-zero elements of the sparse binary signal with a significantly reduced number of measurements, compared to the conventional binary CS and L1-minimization approaches in a wide range of signal to noise ratios (SNRs). Finally, we show a practical application of the AFCS for the sparse event detection in wireless sensor networks (WSNs), where the sensors' readings can be treated as measurements from the CS point of view.