Fundamental Limits on Communication for Oblivious Updates in Storage Networks

In distributed storage systems, storage nodes intermittently go offline for numerous reasons. On coming back online, nodes need to update their contents to reflect any modifications to the data in the interim. In this paper, we consider a setting where no information regarding modified data needs to be logged in the system. In such a setting, a 'stale' node needs to update its contents by downloading data from already updated nodes, while neither the stale node nor the updated nodes have any knowledge as to which data symbols are modified and what their value is. We investigate the fundamental limits on the amount of communication necessary for such an "oblivious" update process. We first present a generic lower bound on the amount of communication that is necessary under any storage code with a linear encoding (while allowing non-linear update protocols). This lower bound is derived under a set of extremely weak conditions, giving all updated nodes access to the entire modified data and the stale node access to the entire stale data as side information. We then present codes and update algorithms that are optimal in that they meet this lower bound. Next, we present a lower bound for an important subclass of codes, that of linear Maximum-Distance-Separable (MDS) codes. We then present an MDS code construction and an associated update algorithm that meets this lower bound. These results thus establish the capacity of oblivious updates in terms of the communication requirements under these settings.Comment: IEEE Global Communications Conference (GLOBECOM) 201

High Bandwidth Atomic Magnetometery with Continuous Quantum Non-demolition Measurements

We describe an experimental study of spin-projection noise in a high sensitivity alkali-metal magnetometer. We demonstrate a four-fold improvement in the measurement bandwidth of the magnetometer using continuous quantum non-demolition (QND) measurements. Operating in the scalar mode with a measurement volume of 2 cm^3 we achieve magnetic field sensitivity of 22 fT/Hz^(1/2) and a bandwidth of 1.9 kHz with a spin polarization of only 1%. Our experimental arrangement is naturally back-action evading and can be used to realize sub-fT sensitivity with a highly polarized spin-squeezed atomic vapor.Comment: 4 page

Interference Alignment in Regenerating Codes for Distributed Storage: Necessity and Code Constructions

Regenerating codes are a class of recently developed codes for distributed storage that, like Reed-Solomon codes, permit data recovery from any arbitrary k of n nodes. However regenerating codes possess in addition, the ability to repair a failed node by connecting to any arbitrary d nodes and downloading an amount of data that is typically far less than the size of the data file. This amount of download is termed the repair bandwidth. Minimum storage regenerating (MSR) codes are a subclass of regenerating codes that require the least amount of network storage; every such code is a maximum distance separable (MDS) code. Further, when a replacement node stores data identical to that in the failed node, the repair is termed as exact. The four principal results of the paper are (a) the explicit construction of a class of MDS codes for d = n-1 >= 2k-1 termed the MISER code, that achieves the cut-set bound on the repair bandwidth for the exact-repair of systematic nodes, (b) proof of the necessity of interference alignment in exact-repair MSR codes, (c) a proof showing the impossibility of constructing linear, exact-repair MSR codes for d < 2k-3 in the absence of symbol extension, and (d) the construction, also explicit, of MSR codes for d = k+1. Interference alignment (IA) is a theme that runs throughout the paper: the MISER code is built on the principles of IA and IA is also a crucial component to the non-existence proof for d < 2k-3. To the best of our knowledge, the constructions presented in this paper are the first, explicit constructions of regenerating codes that achieve the cut-set bound.Comment: 38 pages, 12 figures, submitted to the IEEE Transactions on Information Theory;v3 - The title has been modified to better reflect the contributions of the submission. The paper is extensively revised with several carefully constructed figures and example

Explicit Construction of Optimal Exact Regenerating Codes for Distributed Storage

Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a recent paper, Wu et al. characterize the tradeoff between the repair bandwidth and the amount of data stored per node. They also prove the existence of regenerating codes that achieve this tradeoff. In this paper, we introduce Exact Regenerating Codes, which are regenerating codes possessing the additional property of being able to duplicate the data stored at a failed node. Such codes require low processing and communication overheads, making the system practical and easy to maintain. Explicit construction of exact regenerating codes is provided for the minimum bandwidth point on the storage-repair bandwidth tradeoff, relevant to distributed-mail-server applications. A subspace based approach is provided and shown to yield necessary and sufficient conditions on a linear code to possess the exact regeneration property as well as prove the uniqueness of our construction. Also included in the paper, is an explicit construction of regenerating codes for the minimum storage point for parameters relevant to storage in peer-to-peer systems. This construction supports a variable number of nodes and can handle multiple, simultaneous node failures. All constructions given in the paper are of low complexity, requiring low field size in particular.Comment: 7 pages, 2 figures, in the Proceedings of Allerton Conference on Communication, Control and Computing, September 200

Gas phase hydrogen permeation in alpha titanium and carbon steels

Commercially pure titanium and heats of Armco ingot iron and steels containing from 0.008-1.23 w/oC were annealed or normalized and machined into hollow cylinders. Coefficients of diffusion for alpha-Ti and alpha-Fe were determined by the lag-time technique. Steady state permeation experiments yield first power pressure dependence for alpha-Ti and Sievert's law square root dependence for Armco iron and carbon steels. As in the case of diffusion, permeation data confirm that alpha-titanium is subject to at least partial phase boundary reaction control while the steels are purely diffusion controlled. The permeation rate in steels also decreases as the carbon content increases. As a consequence of Sievert's law, the computed hydrogen solubility decreases as the carbon content increases. This decreases in explained in terms of hydrogen trapping at carbide interfaces. Oxidizing and nitriding the surfaces of alpha-titanium membranes result in a decrease in the permeation rate for such treatment on the gas inlet surfaces but resulted in a slight increase in the rate for such treatment on the gas outlet surfaces. This is explained in terms of a discontinuous TiH2 layer

Computer Mapping of Water Quality in Saginaw Bay with LANDSAT Digital Data

The author has identified the following significant results. LANDSAT digital data and ground truth measurements for Saginaw Bay (Lake Huron), Michigan, for 31 July 1975 were correlated by stepwise linear regression and the resulting equations used to estimate invisible water quality parameters in nonsampled areas. Chloride, conductivity, total Kjeldahl nitrogen, total phosphorus, and chlorophyll a were best correlated with the ratio of LANDSAT Band 4 to Band 5. Temperature and Secchi depth correlate best with Band 5

Optimal Timer Based Selection Schemes

Timer-based mechanisms are often used to help a given (sink) node select the best helper node among many available nodes. Specifically, a node transmits a packet when its timer expires, and the timer value is a monotone non-increasing function of its local suitability metric. The best node is selected successfully if no other node's timer expires within a 'vulnerability' window after its timer expiry, and so long as the sink can hear the available nodes. In this paper, we show that the optimal metric-to-timer mapping that (i) maximizes the probability of success or (ii) minimizes the average selection time subject to a minimum constraint on the probability of success, maps the metric into a set of discrete timer values. We specify, in closed-form, the optimal scheme as a function of the maximum selection duration, the vulnerability window, and the number of nodes. An asymptotic characterization of the optimal scheme turns out to be elegant and insightful. For any probability distribution function of the metric, the optimal scheme is scalable, distributed, and performs much better than the popular inverse metric timer mapping. It even compares favorably with splitting-based selection, when the latter's feedback overhead is accounted for.Comment: 21 pages, 6 figures, 1 table, submitted to IEEE Transactions on Communications, uses stackrel.st