## 3 Confidential Transmission Methods for High-Speed Power Line Carrier Communications
### High-Speed Power Line Carrier Communication Network Formation
The dominating node and dominated node states represent operational roles adopted during or after network formation, where dominating nodes function as routing nodes within the network. The specific steps for the formation of a high-speed power line carrier communication network are as follows:  
Step 1: Each carrier device in the network acquires a unique node identifier (\(ID\)) and is assigned a communication performance weight \(v(w)\) based on its signal-to-noise ratio. During initialization, all carrier devices set their state to \"undetermined\" (\(A_{v}=0\)), where \(A_{v}\) represents the three states of carrier equipment in the process of networking. When the value is 0, it means that the carrier equipment is undetermined; when the values are 1 and 2, it corresponds to the state of the dominant node and dominated node of the carrier equipment, respectively. Step 2: A carrier device initiates a networking request by broadcasting at maximum power [15], collecting the \(ID\) and weight information of other devices within its communication range. If device \(v\) has the highest weight among all one-hop neighbors in set \(M_{v}\), proceed to Step 3; otherwise, proceed to Step 4. Step 3: Update the device's state to \"dominant node\" (\(A_{v}=1\)) and broadcast its node number and state value to all one-hop neighbors. Step 4: The device updates its state based on received broadcast messages [16], categorized as follows:  
1. If any carrier device \(u\) in the network receives broadcast information \(B_{v}=1\) from the carrier device \(v\), and its current state is \"undetermined\", it updates its status to \"dominated node\" (\(A_{v}=2\)) and broadcasts its status information to devices within its communication range. 2. If any carrier device \(u\) receives broadcast information \(B_{v}=2\) from the carrier device \(v\), and its current state is \"undetermined\", it evaluates the weights of other devices in the received broadcast set \(M_{v}\). Specifically, it checks whether there exists a dominant node in subset \(Q\), (where \(Q\) represents devices with weights greater than \(v\)). If such a node exists, \(u\) updates its status to \"dominating node\" (\(A_{v}=1\)) and broadcasts its node number and status to devices within its communication range; otherwise, it continues waiting. Step 5: If all carrier devices in the network have determined their states (i.e., \(G^{\prime}=0\), where \(G^{\prime}\) denotes the set of undetermined nodes), the system enters a waiting time \(T\) before proceeding to the connectivity optimization phase. Step 6: To ensure network reliability and minimize the number of routing nodes, the following optimization rules are applied:  
1. For any dominated node \(u\), if two devices \(u_{1}\) and \(u_{2}\) within its communication range cannot connect via existing dominating nodes, \(u\) updates its status to \"dominating node\" (\(A_{u}=1\)). 2. For any dominant node \(u\), if two carrier devices \(u_{1}\) and \(u_{2}\) within its communication range can be connected through other dominant nodes (excluding \(u\) itself), the state of \(u\) is updated to a dominated node (\(A_{u}=2\)). Simultaneously, \(u\) identifies the highest-weight dominating node within its neighbor set \(M_{u}\) as its own dominating node. This algorithm determines the state of each carrier node in the high-speed power line carrier network. Each dominating node establishes connections with its corresponding dominated nodes to form subnetworks. Furthermore, any two dominated nodes are directly connected, creating a complete network where the carrier nodes act as cluster heads. Ultimately, the dominating nodes interconnect to form the high-speed power line carrier communication network.