Distributed compressive sensing (DCS) usually improves the signal recovery performance of multi-signal ensembles by exploiting both intra-and inter-signal correlation and sparsity structure. However, the existing DCS had proposed for a very limited ensemble of signals that has only single common information. This paper proposes a generalized DCS (GDCS) framework which can improve sparse signal detection performance given arbitrary types of common information, which are classified into full common information and partial common information after overcoming against existing limitation. Specifically, the theoretical bound on the required number of measurements under the GDCS is obtained. We also develop a practical algorithm to obtain benefits using the GDCS. At the end of this paper, it simply summarizes the potential security issues when it gets all sensing information in a sensor network. Finally, numerical results verify that the proposed algorithm reduces the required number of measurements for correlated sparse signal detection compared to the DCS algorithm. This research lays down the basis for efficient distributed signal detection so that it can improve the detection performance or it can detect the signal reliably when the number of signal observations is limited. KEYWORDS compressive sensing, distributed source coding, security sensor networks, sparsity 1 INTRODUCTION Baron et al 1 introduced distributed compressive sensing (DCS), which exploits not only just intra-correlation but also inter-correlation of signals to improve detection performance. In the work of Baron et al, 1 it assumed wireless sensor network (WSN) consisting of an arbitrary number of sensors and one sink node, where each sensor carries out compression without the cooperation of the other sensors and transmits the compressed signal to the sink node. At the sink node, it jointly reconstructs the original signals from the received signals. Here, a key of DCS is a concept of joint sparsity, defined as the sparsity of the entire signal ensemble. Three models have been considered as a joint sparse signal model in the work of Baron et al. 1 In the first model, each signal is individually sparse, and also there are common components shared by every signal vector, and it is called common information. In the second model, all signals share supports that are the locations of the nonzero coefficients. In the third model, although no signal is sparse itself, they share the large amount of common information which makes it possible to compress and recover the signals using CS. The third model can be considered as a modified version of the first model. The second joint sparsity model (JSM-2) has been actively explored in many existing literature. 2-8 A joint orthogonal matching pursuit for DCS was proposed to improve the target detection performance of MIMOradar. 4 A precognition matching pursuit which used the knowledge of common support from Frechet mean was proposed to reduce the number of required measurements in WSNs. 5 The DCS was shown to be f...