We study the problem of compressing a source sequence in the presence of
side-information that is related to the source via insertions, deletions and
substitutions. We propose a simple algorithm to compress the source sequence
when the side-information is present at both the encoder and decoder. A key
attribute of the algorithm is that it encodes the edits contained in runs of
different extents separately. For small insertion and deletion probabilities,
the compression rate of the algorithm is shown to be asymptotically optimal.

The problem of broadcasting a parallel Gaussian source over an additive white
Gaussian noise broadcast channel under the mean-squared error distortion
criterion is studied.

We address the problem of securing distributed storage systems against
eavesdropping and adversarial attacks. An important aspect of these systems is
node failures over time, necessitating, thus, a repair mechanism in order to
maintain a desired high system reliability. In such dynamic settings, an
important security problem is to safeguard the system from an intruder who may
come at different time instances during the lifetime of the storage system to
observe, and possibly alter, the data stored on some nodes.

Distributed storage systems often introduce redundancy to increase
reliability. When coding is used, the repair problem arises: if a node storing
encoded information fails, in order to maintain the same level of reliability
we need to create encoded information at a new node. This amounts to a partial
recovery of the code, whereas conventional erasure coding focuses on the
complete recovery of the information from a subset of encoded packets. The
consideration of the repair network traffic gives rise to new design
challenges.

It is well known that $(n,k)$ Maximum Distance Separable (MDS) erasure codes
are optimal for storage systems due to their ability to recover from up to
$(n-k)$ node failures with minimum storage expansion. However, MDS codes come
with a significant maintenance overhead due to their expensive repair-cost for
restoring failed encoded nodes. This has recently motivated a new and superior
class of codes, called {\em Regenerating Codes}, that optimally trade off
storage cost for repair bandwidth.

Erasure coding techniques are used to increase the reliability of distributed
storage systems while minimizing storage overhead. Also of interest is
minimization of the bandwidth required to repair the system following a node
failure. In a recent paper, Wu et al. characterize the tradeoff between the
repair bandwidth and the amount of data stored per node. They also prove the
existence of regenerating codes that achieve this tradeoff.