  We extend the results of Ghourchian et al. [IEEE JSAIT-2021], to joint
source-channel coding with eavesdropping. Our work characterizes the sequential
encoding process using the cumulative rate distribution functions (CRDF) and
includes a security constraint using the cumulative leakage distribution
functions (CLF). The information leakage is defined based on the mutual
information between the source and the output of the wiretap channel to the
eavesdropper. We derive inner and outer bounds on the achievable CRDF for a
given source and CLF, and show that the bounds are tight when the distribution
achieving the capacity of the wiretap channel is the same as the one achieving
the capacity of the channel.
