This paper considers a distributed storage system, where multiple storagenodes can be reconstructed simultaneously at a centralized location. Thiscentralized multi-node repair (CMR) model is a generalization of regeneratingcodes that allow for bandwidth-efficient repair of a single failed node. Thiswork focuses on the trade-off between the amount of data stored and repairbandwidth in this CMR model. In particular, repair bandwidth bounds are derivedfor the minimum storage multi-node repair (MSMR) and the minimum bandwidthmulti-node repair (MBMR) operating points. The tightness of these bounds areanalyzed via code constructions. The MSMR point is characterized through codesachieving this point under functional repair for general set of CMR parameters,as well as with codes enabling exact repair for certain CMR parameters. TheMBMR point, on the other hand, is characterized with exact repair codes for allCMR parameters for systems that satisfy a certain entropy accumulationproperty. Finally, the model proposed here is utilized for the secret sharingproblem, where the codes for the multi-node repair problem is used to constructcommunication efficient secret sharing schemes with the property of bandwidthefficient share repair.
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