Node Repair on Connected Graphs

We study the problem of erasure correction (node repair) for regenerating codes defined on graphs wherein cost transmitting information to failed node depends graphical distance from this helper vertices graph. The passed helpers traverses several graph, and savings in communication complexity can be attained if intermediate process rather than simply relaying it toward node. derive simple information-theoretic bounds amount communicated between nodes course repair. Next we show that Minimum Storage Regenerating (MSR) modified perform processing, thereby attaining lower bound exchange also consider repair when underlying graph is random, deriving conditions parameters support recovery with smaller required by relaying.