  This paper presents the first in-depth analysis on the energy efficiency of
LT codes with Non Coherent M-ary Frequency Shift Keying (NC-MFSK), known as
green modulation [1], in a proactive Wireless Sensor Network (WSN) over
Rayleigh flat-fading channels with path-loss. We describe the proactive system
model according to a pre-determined time-based process utilized in practical
sensor nodes. The present analysis is based on realistic parameters including
the effect of channel bandwidth used in the IEEE 802.15.4 standard, and the
active mode duration. 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 NC-MFSK and various classical channel coding schemes,
the optimized LT coded NC-MFSK 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 uncoded NC-MFSK outperforms coded schemes for $d < d_T$, the energy
gap between LT coded and uncoded NC-MFSK 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.
