Exact repair for distributed storage systems: Partial characterization via new bounds

The exact-repair problem for distributed storage systems is considered. Characterizing the optimal storage-vs-repair bandwidth tradeoff for such systems remains an open problem for more than four storage nodes. A new family of information theoretic lower bounds is provided for the storage-vs-repair bandwidth tradeoff. The bound recovers Tians bound for the (4, 3, 3) system, and hence suffices for exact characterization for this system. Moreover, the bound improves upon the existing lower bounds for the (5, 4, 4) system and also characterizes the partial boundary of optimal exact repair tradeoff.