Natalia Silberstein: "Coding for Distributed Storage Systems via Rank-Metric Codes"

In distributed storage systems (DSS) data is stored over a network of nodes in such a way that a user can retrieve the stored data even if some nodes fail. To achieve such resilience against node failures, DSS introduce data redundancy based on different coding techniques. For example, erasure codes are widely used in such systems. When a single node fails, the system reconstructs the data stored in the failed node to keep the required level of redundancy. This process of data reconstruction for a failed node is called a node repair process.

There are two important goals that guide the design of codes for DSS: reducing the repair bandwidth, i.e. the amount of data downloaded from the nodes during the node repair process, and achieving locality, i.e. reducing the number of nodes participating in the node repair process. These goals underpin the design of two families of codes for DSS called regenerating codes and locally repairable codes.

In this talk, we introduce a new approach for constructing different families of optimal codes for DSS via rank-metric codes. First, we present a construction of a new family of optimal locally repairable codes based on maximum rank distance (MRD) codes. Second, we discuss hybrid codes which minimize repair bandwidth for given locality parameters. These codes are based on a combination of locally repairable codes with regenerating codes. Finally, we consider DSS containing nodes with adversarial errors. The key challenge in such systems is the propagation of erroneous data from a single corrupted node to the rest of the system during a node repair process. We present a novel coding scheme which provides resilience against adversarial errors. This coding scheme is also based on MRD codes.