## 1 Introduction  
As the perceptual layer of the Internet of Things (IoT) [1; 2], wireless sensor networks (WSNs) [3] are widely deployed for purposes such as environment monitoring [4], industry automation [5] and military reconnaissance [6]. WSNs consist of many sensors and play a key role in sensing and gathering data from the surrounding environment. Because of harsh environments and energy-limited nodes, there are two key considerations in WSNs design: reliability and energy efficiency. In addition, nodes that are closer to the sink require more forwarding tasks than others, resulting in higher energy consumption as well as a reduction in the lifetime of the entire network. Compressive sensing (CS) theory [7; 8] provides a new method for reducing communication energy consumption. CS points out that, for the compressible signals in WSNs, a small collection of linear projections is sufficient to achieve near-perfect reconstruction, which reduces energy consumption and prolongs network lifetime. Thus, a considerable amount of research has been conducted concerning ways to utilize CS to gather data in WSNs. The CS-based data-gathering schemes in [9; 10; 11] obtained the member node readings utilizing fixed routing, in which ordinary nodes forward compressed data to the static sink node through multi-hops. [PERSON] et al. [9] and [PERSON] et al. [10] combined CS and routing protocols to reduce the number of transmissions. In [11; 12; 13; 14; 15], the use of sparse measurement matrix is investigated to reduce the number of nodes involved in data gathering. Introducing CS effectively reduces the energy required for communication and distributes energy consumption loads more evenly. However, if a parent node (which holds a combination of child node readings) loses its packet, then all the information from the child nodes is also lost. Hence, unreliable links have a serious impact on data gathering and make it difficult to reliable gather data reliably through a centralized sink node. Additionally, [PERSON] et al. (2016) reported that unreliable links are widespread in WSNs, where the average packet loss rate is 40-50%. Thus, assuming completely reliable links is unfeasible and oversimplifies the problem. To resolve this problem, distributed data storage (DDS) ([PERSON] et al., 2016; [PERSON] et al., 2017; [PERSON] et al., 2018) is proposed to enable reliable data gathering by employing redundancy. In contrast to a centralized sink, a mobile sink collects data from a small subset of the total nodes to recover all the data. It is worth mentioning that DDS effectively reduces the impact of packet loss on data gathering because there is no static routing, although few researchers have focused on this advantage. However, DDS requires a large number of transmission tasks to ensure sufficient redundancy, which is potentially catastrophic for nodes with energy limitations. Thus, it is imperative to investigate effective ways to apply DDS for data gathering with the dual purposes of resisting packet loss and reducing the number of transmissions. To address this problem, many studies have been carried out on this topic. In ([PERSON] et al., 2016; [PERSON] et al., 2017; [PERSON] et al., 2018), CS is combined with DDS to exploit the advantages of both technologies. The goal of [PERSON] et al. ([PERSON] et al., 2018) was to reduce the number of transmissions by exploiting the spatial correlations of nodes based on CS with the broadcast properties of wireless channels. In this scheme, the nodes store received data and broadcast the data with a given probability. The performance of data reconstruction was further improved in ([PERSON] et al., 2017). [PERSON] et al. (2017) found that the number of receptions was higher than the number of transmissions. Hence, [PERSON] et al. (2017) focused on reducing the total number of both transmissions and receptions simultaneously. In ([PERSON] et al., 2017), both the spatial and temporal correlations of nodes are exploited to reduce the number of transmissions.