## 6 Conclusions  
In this paper, an improved PCSDF scheme is proposed with cooperative capability as the decision threshold. Optimal relay selection and OP are suggested and analyzed. The optimization of the cooperative scheme is performed with polar code construction by an optimal design-SNR and a new collaborative construction for more coding gain, which endows it with better BER and OP performance and less computational complexity. In addition, an appropriate cooperative threshold is derived to achieve optimal relay location. When the optimal relay is close to the destination node, it obtains better BER performance in the proposed cooperative scheme. Then, it can be applied in optimal relay position selection for better cooperation. Finally, the channel capacity of the entire cooperative system with different numbers of relays is provided, and a larger information rate can be obtained in the proposed scheme to approach the channel capacity. In summary, the proposed scheme uses the efficient channel capacity approaching the polar codes to assist the multi-relay SDF for better performance. Moreover, it adopts a compound relay link to exceed the cooperative threshold in order to reduce the chance of re-transmission for better performance, lower complexity, and less latency. Therefore, the proposed PCSDF scheme can be effectively adopted in multi-relay cooperative networks in practice for good OP and BER performance.  
In addition, there are other possible directions for future improvement of the optimal coded relay selection. First, polar codes with any feasible length, rather than a power of 2, can be constructed with distributed decoding for better application in coded cooperation. Second, DF or SDF cooperation used in this paper; coded cooperation (CC), soft-metric forwarding (SMF), compressed forwarding (CF), and even hybrid combinations of the above schemes can be used in the possible coded cooperation for even better performance. Finally, power allocation can be merged into the cooperation for joint optimization of the transmission resources, which could represent a promising and deep level cross-layer communication optimization in the next generation satellite based 6G IoT systems.  
Conceptualization: [PERSON] and [PERSON]; methodology: [PERSON], [PERSON] and [PERSON]; software: [PERSON] and [PERSON]; formal analysis: [PERSON] and [PERSON]; investigation: [PERSON], [PERSON] and [PERSON]; resources: [PERSON], [PERSON] and [PERSON]; data curation: [PERSON], [PERSON], [PERSON] and [PERSON]; writing--original draft preparation: [PERSON] and [PERSON]; writing--review and editing: [PERSON]; visualization: [PERSON] and [PERSON]; supervision: [PERSON]; project administration: [PERSON]; funding acquisition: [PERSON] and [PERSON]. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China under Grant U1809201, by the Fundamental Research Funds for the Provincial Universities of Zhejiang under Grant GK209907299001-003, and by the Zhejiang Provincial Natural Science Foundation of China under Grant LY20F010010.  
The authors would like to thank National Natural Science Foundation of China (NSFC), Zhejiang Provincial Natural Science Foundation of China (ZPNSFC), Zhejiang Provincial Education Department (ZPED), and Hangzhou Dianzi University for supporting this work, and [PERSON] for his active participation and expert suggestions.  
The authors declare no conflict of interest.