## 1 Introduction  
Multiple-input multiple-output (MIMO) represents a milestone in wireless cooperative communications, bringing efficient transmission rates and reliability. Today, virtual MIMO uses relays as virtual antennas [1], and has been widely used and rapidly developed. In cooperative communications, a typical system mainly includes three components, e.g., a source, relays, and a destination. Diversity gain is obtained when the relay nodes forward messages and the destination node combines all received signals from both the source and relay nodes. Recently, there have been several cooperative schemes proposed, such as amplify-and-forward (AF) [1], decode-and-forward (DF) [2], coded cooperation (CC) [3], and more. Traditionally, cooperative transmission has brought about several benefits, including higher date rates, lower power consumption, transmission range extension, and more, beyond those of traditional point-to-point communications [4, 5]. Various channel coding schemes with DF cooperation were proposed in [6]. Several of these were employed using Turbo codes [7; 8] and low-density parity-check (LDPC) codes [9]. Polar codes are new channel codes that can approach the Shannon limit while having low coding complexity[10]. Optimal polar code construction is generally challenging to accomplish. Therefore, many suboptimal polar code construction approaches have been proposed at different levels of computational complexity [11; 12; 13]. The use of polar codes for cooperative communications has been explored in literature as well; in [14], polar codes were proven to be applicable for degraded wiretap and relay channels, and outperformed competitive counterparts, e.g., optimally designed LDPC codes. In addition, a polar coded-cooperation network (NPCC) with joint successive cancellation (SC) decoding at the destination was proposed in [15]. It was adopted to achieve coded cooperation between two users, and offered network coding to improve the efficiency of the coded cooperation and overall BER performance. However, all of the above schemes were investigated only under a single relay cooperation. In [16], multiple relay selection cooperation was proposed to alleviate multiplex loss through optimal relay selection. The optimization objective was to find the relay with best channel quality for message forwarding. Recently, there had been several relay selection strategies in cooperative communications based on the AF and DF protocols [17; 18; 19; 20]. In [21], a practical code design for a new relay cooperation method called dynamic selective decode-and-forward (D-SDF) was proposed. In this scheme, each relay individually decides the end of the listening phase and the beginning of the cooperation phase based on different source selection rules. In [22], adaptive relay-based SDF cooperation reduced power overhead and achieved optimal outage performance (OP). However, all relays in the decoding set participated in cooperative transmission to obtain optimal interrupt performance, leading to a decline in the spectral efficiency of the entire system. For full collaboration, opportunistic relaying (OR) improved the spectrum efficiency [23]. By selecting an optimal relay to forward messages, the complexity was reduced while diversity gain, which is equivalent to full collaboration, was obtained [24]. In [25; 26], the performance of DF-based opportunistic relay selection strategies were studied with cell interference in a multi-cell environment. To solve the error propagation caused by incorrect DF relay decoding, an SDF relay protocol was proposed in [27]; the relay was able to forward source messages that were free of errors. The emergence of the SDF protocol solved the issue of decoding errors in relay nodes while maintaining participation in cooperation [28]. However, all the above schemes assume that the messages are transmitted through relay nodes at any time regardless of the quality of the trunk link, that is, an all-weather relay cooperation scheme. [PERSON] et al.