In this article, we study secure multipath routing with energy efficiency for a wireless sensor network in the presence of eavesdroppers. We consider two objectives: (1) the multipath routing scheme for maximising the energy efficiency with security constraints and (2) the multipath routing scheme for maximising the secrecy capacity. The binary erasure channel model is adopted to describe the wireless channel states among neighbouring nodes. Based on the binary erasure channel model, the problem of multipath routing degrades to a problem of bit allocation for each path. We formulate the problems and find that the problems are both quasi-convex. For the first one, it is a linear fractional optimisation problem. The optimal solution is obtained by the Charnes–Cooper transformation. For the second one, we propose an iterative algorithm to obtain the [Formula: see text]-optimal solution. The performance analysis shows that the probability of the secure bit allocation increases along with the number of multipaths and decreases along with the number of hops per path and eavesdroppers. Simulation results are presented to illustrate the proposed algorithms.
Overlapped LT codes over the binary erasure channel: analysis and design
