Secure RAID Schemes for Distributed Storage

We propose secure RAID, i.e., low-complexity schemes to store information in a distributed manner that is resilient to node failures and resistant to node eavesdropping. We generalize the concept of systematic encoding to secure RAID and show that systematic schemes have significant advantages in the efficiencies of encoding, decoding and random access. For the practical high rate regime, we construct three XOR-based systematic secure RAID schemes with optimal or almost optimal encoding and decoding complexities, from the EVENODD codes and B codes, which are array codes widely used in the RAID architecture. The schemes can tolerate up to two node failures and two eavesdropping nodes. For more general parameters we construct systematic secure RAID schemes from Reed-Solomon codes, and show that they are significantly more efficient than Shamir’s secret sharing scheme. Our results suggest that building “keyless”, information-theoretic security into the RAID architecture is practical

X-code: MDS array codes with optimal encoding

We present a new class of MDS (maximum distance separable) array codes of size n×n (n a prime number) called X-code. The X-codes are of minimum column distance 3, namely, they can correct either one column error or two column erasures. The key novelty in X-code is that it has a simple geometrical construction which achieves encoding/update optimal complexity, i.e., a change of any single information bit affects exactly two parity bits. The key idea in our constructions is that all parity symbols are placed in rows rather than columns

MDS array codes with independent parity symbols

A new family of maximum distance separable (MDS) array codes is presented. The code arrays contain p information columns and r independent parity columns, each column consisting of p-1 bits, where p is a prime. We extend a previously known construction for the case r=2 to three and more parity columns. It is shown that when r=3 such extension is possible for any prime p. For larger values of r, we give necessary and sufficient conditions for our codes to be MDS, and then prove that if p belongs to a certain class of primes these conditions are satisfied up to r ≤ 8. One of the advantages of the new codes is that encoding and decoding may be accomplished using simple cyclic shifts and XOR operations on the columns of the code array. We develop efficient decoding procedures for the case of two- and three-column errors. This again extends the previously known results for the case of a single-column error. Another primary advantage of our codes is related to the problem of efficient information updates. We present upper and lower bounds on the average number of parity bits which have to be updated in an MDS code over GF (2^m), following an update in a single information bit. This average number is of importance in many storage applications which require frequent updates of information. We show that the upper bound obtained from our codes is close to the lower bound and, most importantly, does not depend on the size of the code symbols

Efficient and Effective Schemes for Streaming Media Delivery

The rapid expansion of the Internet and the increasingly wide deployment of wireless networks provide opportunities to deliver streaming media content to users at anywhere, anytime. To ensure good user experience, it is important to battle adversary effects, such as delay, loss and jitter. In this thesis, we first study efficient loss recovery schemes, which require pure XOR operations. In particular, we propose a novel scheme capable of recovering up to 3 packet losses, and it has the lowest complexity among all known schemes. We also propose an efficient algorithm for array codes decoding, which achieves significant throughput gain and energy savings over conventional codes. We believe these schemes are applicable to streaming applications, especially in wireless environments. We then study quality adaptation schemes for client buffer management. Our control-theoretic approach results in an efficient online rate control algorithm with analytically tractable performance. Extensive experimental results show that three goals are achieved: fast startup, continuous playback in the face of severe congestion, and maximal quality and smoothness over the entire streaming session. The scheme is later extended to streaming with limited quality levels, which is then directly applicable to existing systems