  This paper presents an in-depth analysis on the energy efficiency of Luby
Transform (LT) codes with Frequency Shift Keying (FSK) modulation in a Wireless
Sensor Network (WSN) over Rayleigh fading channels with pathloss. We describe a
proactive system model according to a flexible duty-cycling mechanism utilized
in practical sensor apparatus. The present analysis is based on realistic
parameters including the effect of channel bandwidth used in the IEEE 802.15.4
standard, active mode duration and computation energy. A comprehensive
analysis, supported by some simulation studies on the probability mass function
of the LT code rate and coding gain, shows that among uncoded FSK and various
classical channel coding schemes, the optimized LT coded FSK is the most
energy-efficient scheme for distance d greater than the pre-determined
threshold level d_T , where the optimization is performed over coding and
modulation parameters. In addition, although the optimized uncoded FSK
outperforms coded schemes for d < d_T , the energy gap between LT coded and
uncoded FSK is negligible for d < d_T compared to the other coded schemes.
These results come from the flexibility of the LT code to adjust its rate to
suit instantaneous channel conditions, and suggest that LT codes are beneficial
in practical low-power WSNs with dynamic position sensor nodes.
