Synchronizing edits in distributed storage networks

We consider the problem of synchronizing data in distributed storage networks under edits that include deletions and insertions. We present modifications of codes on distributed storage systems that allow updates in the parity-check values to be performed with one round of communication at low bit rates and a small storage overhead. Our main contributions are novel protocols for synchronizing both frequently updated and semi-static data, and protocols for data deduplication applications, based on intermediary coding using permutation and Vandermonde matrices.