  The problem of reconstructing a source sequence with the presence of decoder
side-information that is mis-synchronized to the source due to deletions is
studied in a distributed source coding framework. Motivated by practical
applications, the deletion process is assumed to be bursty and is modeled by a
Markov chain. The minimum rate needed to reconstruct the source sequence with
high probability is characterized in terms of an information theoretic
expression, which is interpreted as the amount of information of the deleted
content and the locations of deletions, subtracting "nature's secret", that is,
the uncertainty of the locations given the source and side-information. For
small bursty deletion probability, the asymptotic expansion of the minimum rate
is computed.
