  This paper characterizes the second-order coding rates for lossy source
coding with side information available at both the encoder and the decoder. We
first provide non-asymptotic bounds for this problem and then specialize the
non-asymptotic bounds for three different scenarios: discrete memoryless
sources, Gaussian sources, and Markov sources. We obtain the second-order
coding rates for these settings. It is interesting to observe that the
second-order coding rate for Gaussian source coding with Gaussian side
information available at both the encoder and the decoder is the same as that
for Gaussian source coding without side information. Furthermore, regardless of
the variance of the side information, the dispersion is $1/2$ nats squared per
source symbol.
