New Codes and Inner Bounds for Exact Repair in Distributed Storage Systems

We study the exact-repair tradeoff between storage and repair bandwidth in distributed storage systems (DSS). We give new inner bounds for the tradeoff region and provide code constructions that achieve these bounds.Comment: Submitted to the IEEE International Symposium on Information Theory (ISIT) 2014. This draft contains 8 pages and 4 figure

Explicit MBR All-Symbol Locality Codes

Node failures are inevitable in distributed storage systems (DSS). To enable efficient repair when faced with such failures, two main techniques are known: Regenerating codes, i.e., codes that minimize the total repair bandwidth; and codes with locality, which minimize the number of nodes participating in the repair process. This paper focuses on regenerating codes with locality, using pre-coding based on Gabidulin codes, and presents constructions that utilize minimum bandwidth regenerating (MBR) local codes. The constructions achieve maximum resilience (i.e., optimal minimum distance) and have maximum capacity (i.e., maximum rate). Finally, the same pre-coding mechanism can be combined with a subclass of fractional-repetition codes to enable maximum resilience and repair-by-transfer simultaneously

Repairable Block Failure Resilient Codes

In large scale distributed storage systems (DSS) deployed in cloud computing, correlated failures resulting in simultaneous failure (or, unavailability) of blocks of nodes are common. In such scenarios, the stored data or a content of a failed node can only be reconstructed from the available live nodes belonging to available blocks. To analyze the resilience of the system against such block failures, this work introduces the framework of Block Failure Resilient (BFR) codes, wherein the data (e.g., file in DSS) can be decoded by reading out from a same number of codeword symbols (nodes) from each available blocks of the underlying codeword. Further, repairable BFR codes are introduced, wherein any codeword symbol in a failed block can be repaired by contacting to remaining blocks in the system. Motivated from regenerating codes, file size bounds for repairable BFR codes are derived, trade-off between per node storage and repair bandwidth is analyzed, and BFR-MSR and BFR-MBR points are derived. Explicit codes achieving these two operating points for a wide set of parameters are constructed by utilizing combinatorial designs, wherein the codewords of the underlying outer codes are distributed to BFR codeword symbols according to projective planes

Update-Efficient Regenerating Codes with Minimum Per-Node Storage

Regenerating codes provide an efficient way to recover data at failed nodes in distributed storage systems. It has been shown that regenerating codes can be designed to minimize the per-node storage (called MSR) or minimize the communication overhead for regeneration (called MBR). In this work, we propose a new encoding scheme for [n,d] error- correcting MSR codes that generalizes our earlier work on error-correcting regenerating codes. We show that by choosing a suitable diagonal matrix, any generator matrix of the [n,{\alpha}] Reed-Solomon (RS) code can be integrated into the encoding matrix. Hence, MSR codes with the least update complexity can be found. An efficient decoding scheme is also proposed that utilizes the [n,{\alpha}] RS code to perform data reconstruction. The proposed decoding scheme has better error correction capability and incurs the least number of node accesses when errors are present.Comment: Submitted to IEEE ISIT 201