## 1 Introduction  
Wireless sensor networks (WSNs) have attracted much interest in both academia and industry due to their advantages of low cost, ease of deployment and ubiquitous applications, ranging from military surveillance to medical monitoring [1]. Reliable wireless communication is of paramount importance to facilitate data-centric WSN applications. However, low power wireless links often lead to a high data packet loss rate [2] due to factors like channel noise, multipath, asymmetric links, inadequate antenna orientation [3] and antenna height [4]. Data collected from large-scale WSN installations are often mired with missing or garbled data values, which significantly depreciates the potential usage of the data. To deal with the high data packet loss rate, one may either transmit data only via high quality links in the connected region to ensure communication reliability; or invoke error-correcting measures, such as automatic repeat request (ARQ), in the transitional region to retransmit lost data packets (the communication area of a wireless link can be divided into three regions, which are called the connected region, the transitional region and the disconnected region). Using only high quality links in the connected region to transmit data implies shorter physical distance, which also leads to denser sensor node deployment or higher transmission power, _i.e_., shorter network lifespan. ARQ-based error correcting measures will increase transmission times and latency [5,6]. Both approaches are expensive and imperfect solutions. There are also many schemes for improving the communication performance of wireless systems, such as transmitting power control, packet length control, forward error correction (FEC), _etc_. However, FEC and power control are energy-consuming schemes [7] and are unsuitable to be implemented in low power wireless sensor nodes [8]. The scheme presented in this work is a different asymmetric communication method that shifts the computation burden from the transmission end (low power sensor nodes) to the receiving end (more powerful fusion center). Our approach leverages compressive sensing [9,10] at the receiving end to reconstruct the original sparse signal; even data packets are lost or damaged while transmitting in a lossy wireless link. In fact, with the careful packaging of the data using the appropriate packet lengths and interleaving scheme, the effect of transmission loss may be modeled as a random sampling process. As such, the original data may be reconstructed with a high probability. The notion of incorporating compressive sensing with network data transmission was discussed in [11], where the authors proposed a distributed matched source-channel communication scheme by exploiting the spatial averaging property inherent in a multiple access channel. Numerous authors have reported approaches to combine compressive sensing with wireless communication by exploiting the inherent sparseness in signals, such as temperature, \(\mathrm{CO}_{2}\) emission, seismic signal [8], image [10] and acoustical signal [12]. This work is a substantial expansion of an earlier conference proceeding paper [12], where the notion of modeling lossy wireless links as a random sampling process in compressive sensing was first presented. In this paper, we provide a careful derivation to show how the packet loss in a lossy channel may be modeled as a random sampling process of the original signal. In addition, the intricate relations between communication parameters (e.g., bit error rate, packet error rate, packet lengths) and the quality of signal reconstruction (mutual coherence) are carefully investigated. To mitigate potentialburst communication error, the interleaving scheme is incorporated at little computation and energy overhead at the transmission end. Moreover, a novel criterion, called the information acquisition rate (IAR), is proposed as a more direct and effective way to gauge the link quality rather than traditional quality metrics, such as the packet reception rate (PRR).