## 2 Related Work
One appealing feature of the CS theory is its ability to reconstruct the original high-dimensional, inherently sparse signal by using only very few low dimensional measurements, whichprovides a promising prospect for signal recovery. This attractive feature motivated a number of works applying CS to wireless communication. The authors of [11] are the first to introduce compressed sensing into network applications. The authors propose a distributed matched source-channel communication scheme by exploiting the spatial averaging inherent in a multiple access channel. Furthermore, [11] has enlightened CS' potential application in sensor networks. Since then, there have been many research works that have concentrated on combining CS with wireless communication for transmitting these sparse signals. In the application layer, [15] proposed a CS algorithm to estimate the missing data based on the typical data loss pattern, and [7] introduced compressive sensing as a coding strategy that is applied in the application layer, which exploits redundancy in oversampling to facilitate compressive oversampling. In the routing layer, [17,18] represent the first complete design to apply compressive sampling theory to sensor data gathering for large-scale wireless sensor networks. The proposed scheme can handle abnormal sensor readings gracefully, and its load balancing characteristic is capable of extending the lifetime of the entire sensor network. In [19], the effectiveness of data gathering in WSNs is improved by introducing an autoregressive model to assess inherent sparsity and to adjust the number of measurements accordingly. In the medium access control (MAC) layer, [20] proposed compressive sensing MAC (CS-MAC) to exploit the sparse property of the sensing signal that, at a given time, only a few hosts are expected to access the channel for a data report. In CS-MAC, a central coordinator can recover a multitude of these received data in one decoding operation and then schedule multiple hosts accordingly. This result is incorporated in [21], which boosts multiple input multiple output (MIMO) capacity gain without requiring strict synchronization and coordination among distributed users. The work in [22] proposed a random access compressed sensing (RACS) scheme to analyze random access to the wireless channel. In RACS, a randomly-chosen subset of nodes participates in the sensing process and then randomly accesses the channel to report their sensing data. By using the node's carefully-designed sensing probability, RACS ensures sufficiently many data packets to be received in spite of packet collision. In the link layer, we are the first to combine CS with data loss via a lossy wireless link [12]. We modeled the packet loss during transmission as a random sampling process by utilizing knowledge of signal characteristics (sparse), then the sparse signal can be accurately transmitted through sufficient received data with lower energy consumption and latency. In this paper, considering that packet length control is an easy to implement and efficient communication performance optimization method, we further investigate packet length effect on sparse signal transmission via a lossy link based on our former work [12]. Packet length control for sparse signal transmission is investigated, which inspires us to choose different optimal packet lengths to optimize different communication demands. Furthermore, for the traditional communication technique,data interleaving is adopted to optimize sparse signal transmission performance. Further details are presented in the following sections.