| Summary: | 碩士 === 國立中興大學 === 通訊工程研究所 === 99 === In this work, we investigate the problems of when it is possible for two nodes in a wireless network to communicate with each other and when this communi- cation can be assured almost surely. We answer the first problem by finding the conditions for the occurrence of percolation in a network graph. In this part, we adopt the result from bond percolation in a two-dimensional lattice to develop the conditions for percolation. As long as the probability that a sub-square is close is less than 0.5 and the number of nodes in a sub-square is at least four, percolation occurs. Following that, we establish the conditions for full connectivity in a network graph. In this part, how two adjacent sub-squares are connected differentiates this works from others. In this work, two adjacent sub-squares are connected if there exists a communicating path between them whereas a direct communication link is needed to ensure the connectivity between two adjacent sub-squares. Through induction, the full connectivity occurs almost surely if each sub-square contains at least one node and the probability of having an open sub-edge is greater than or equal to 0.3822. Simulations are conducted to validate the proposed conditions for percolation and full connectivity. In addition, we apply the proposed conditions to SINR model [1]. Based on the proposed conditions, each node can tolerate more interference than that stated in [1]. Last, we extend the derived results to the case of unreliable transmission and propose suitable conditions for percolation and full connectivity, respectively. We find when the transmission is unreliable, increasing nodes per sub-square or maintaining the probability of successful transmission above a certain threshold seems to be two possible approaches to achieve percolation and full connectivity.
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