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Petri nets applications Part 9

Tham khảo tài liệu 'petri nets applications part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Using Petri Net for Modeling and Analysis of a Encryption Scheme for Wireless Sensor Networks 311 1. Estimate the noise power Ớ2 . Then for i 1 2 . n initialize Pi b prob cị b yi . 2. Set qij b Pj b if the variable node i and the check node j are connected. 3. Update rij b using rji 0 1 1 ni ej 1 2qi j 1 rji 1 1 - rji 0 4. Update qij b using qij b KijP b n j b b 0 1 j eci i where Kij is chosen to meet qij 0 qij 1 1. 5. Compute the posterior probability of the code bit Ci using Qi b KiPi b n rij b b 0 1 jeci where Ki is chosen to ensure that Qi 0 Qi 1 1. 6. For i 1 2 . n set up c 1 if Qz 1 q 0 c 0 if Q 1 Q 0 If cHt 0 or the number of iterations equals the maximum limit stop else go to Step 2. Here H is the parity check matrix of the LDPC codes. 2.4 Petri nets A PN is identified as a particular kind of bipartite directed graph populated by three types of objects. They are places transitions and directed arcs connecting places and transitions. Formally a PN can be defined by N P T F W where a. T is the set of places T is the set of transitions P OT z b. F Q P xT u T X P is flow relationship c. W F N assigns a weight or multiplicity to each arc. Usually actions are associated to transitions and conditions are associated to places. A transition is enabled if each input place of contains at least a number of tokens equal to the weight of the arc connecting to. When an enabled transition fires it removes tokens from its input places and deposits them on its output places. PN models are suitable for representing systems that exhibit concurrence conflict and synchronization. Some important PN properties include a boundness no capacity overflow liveness freedom from deadlock conservativeness conservation of non consumable resources and reversibility cyclic behavior . The concept of liveness is closely related to the complete absence of 312 Petri Nets Applications deadlocks. A PN is said to be live if no matter what marking has been reached from the initial marking it is .