Wireless Sensor Network (WSN) can be deployed on bridges for Structural Health Monitoring
(SHM). SHM applications tend to produce a very high amount of data for transfer which consumes much battery
power and makes the lifetime of network very short. We propose to use network coding to improve network
efficiency and thus prolong its lifetime. A frequently overlooked disadvantage of network coding in
WSN is the link quality issue. After a message is lost or overhearing opportunity is missed due to insufficient
received signal power or excessive interference, the decoding for network coding cannot be performed at the
intermediate nodes, thus significantly degrading performance. For bridge monitoring, sensor nodes are likely
to form a linear topology such as along both sides of the bridge. To ensure proper data transfer and decoding
by use of network coding, we propose here to control transmission power as a means to adjust the number of
nodes that can overhear a message transmission by a neighboring node. Network coding gain relies on such
message overhearing. On the other hand, too much overhearing by high power transmission consumes too
much limited battery energy. By simulation, we study the tradeoffs between overhearing and power consumption
for the network-coding scheme. Specifically, we consider a bridge with fixed length and sensor
nodes are deployed at a uniform distance along one or both sides of the bridge. Each radio link is characterized
by an exponential path loss, shadowing and Rayleigh fading. Our numerical results reveal that appropriate
choices of transmission power (thus the degree of communication connectivity) can achieve the optimal
extent of overhearing for network coding gain, while minimizing the overall power consumption for the
WSN.