On erasure coding for distributed storage and streaming communications

The work presented in this thesis revolves around erasure correction coding, as applied to distributed data storage and real-time streaming communications.

First, we examine the problem of allocating a given storage budget over a set of nodes for maximum reliability. The objective is to find an allocation of the budget that maximizes the probability of successful recovery by a data collector accessing a random subset of the nodes. This optimization problem is challenging in general because of its combinatorial nature, despite its simple formulation. We study several variations of the problem, assuming different allocation models and access models, and determine the optimal allocation and the optimal symmetric allocation (in which all nonempty nodes store the same amount of data) for a variety of cases. Although the optimal allocation can have nonintuitive structure and can be difficult to find in general, our results suggest that, as a simple heuristic, reliable storage can be achieved by spreading the budget maximally over all nodes when the budget is large, and spreading it minimally over a few nodes when it is small. Coding would therefore be beneficial in the former case, while uncoded replication would suffice in the latter case.

Second, we study how distributed storage allocations affect the recovery delay in a mobile setting. Specifically, two recovery delay optimization problems are considered for a network of mobile storage nodes: the maximization of the probability of successful recovery by a given deadline, and the minimization of the expected recovery delay. We show that the first problem is closely related to the earlier allocation problem, and solve the second problem completely for the case of symmetric allocations. It turns out that the optimal allocations for the two problems can be quite different. In a simulation study, we evaluated the performance of a simple data dissemination and storage protocol for mobile delay-tolerant networks, and observed that the choice of allocation can have a significant impact on the recovery delay under a variety of scenarios.

Third, we consider a real-time streaming system where messages created at regular time intervals at a source are encoded for transmission to a receiver over a packet erasure link; the receiver must subsequently decode each message within a given delay from its creation time. For erasure models containing a limited number of erasures per coding window, per sliding window, and containing erasure bursts whose maximum length is sufficiently short or long, we show that a time-invariant intrasession code asymptotically achieves the maximum message size among all codes that allow decoding under all admissible erasure patterns. For the bursty erasure model, we also show that diagonally interleaved codes derived from specific systematic block codes are asymptotically optimal over all codes in certain cases. We also study an i.i.d. erasure model in which each transmitted packet is erased independently with the same probability; the objective is to maximize the decoding probability for a given message size. We derive an upper bound on the decoding probability for any time-invariant code, and show that the gap between this bound and the performance of a family of time-invariant intrasession codes is small when the message size and packet erasure probability are small. In a simulation study, these codes performed well against a family of random time-invariant convolutional codes under a number of scenarios.

Finally, we consider the joint problems of routing and caching for named data networking. We propose a backpressure-based policy that employs virtual interest packets to make routing and caching decisions. In a packet-level simulation, the proposed policy outperformed a basic protocol that combines shortest-path routing with least-recently-used (LRU) cache replacement.

The streaming of 1.3-2.3 MeV cosmic-ray protons during periods between prompt solar particle events

The anisotropy of 1.3 - 2.3 MeV protons in interplanetary space has been measured using the Caltech Electron/Isotope Spectrometer aboard IMP-7 for 317 6-hour periods from 72/273 to 74/2. Periods dominated by prompt solar particle events are not included. The convective and diffusive anisotropies are determined from the observed anisotropy using concurrent solar wind speed measurements and observed energy spectra. The diffusive flow of particles is found to be typically toward the sun, indicating a positive radial gradient in the particle density. This anisotropy is inconsistent with previously proposed sources of low-energy proton increases seen at 1 AU which involve continual solar acceleration.

The typical properties of this new component of low-energy cosmic rays have been determine d for this period which is near solar minimum. The particles have a median intensity of 0.06 protons/ cm^(2)-sec-sr-MeV and a mean spectral index of -3.15.The amplitude of the diffusive anisotropy is approximately proportional to the solar wind speed. The rate at which particles are diffusing toward the sun is larger than the rate at which the solar wind is convecting the particles away from the sun. The 20 to 1 proton to alpha ratio typical of this new component has been reported by Mewaldt, et al. (1975b).

A propagation model with κ_(rr) assumed independent of radius and energy is used to show that the anisotropy could be due to increases similar to those found by McDonald, et al. (1975) at ~3 AU. The interplanetary Fermi-acceleration model proposed by Fisk (1976) to explain the increases seen near 3 AU is not consistent with the ~12 per cent diffusive anisotropy found.

The dependence of the diffusive anisotropy on various parameters is shown. A strong dependence of the direction of the diffusive anisotropy on the concurrently measured magnetic field direction is found, indicating a κ_⊥ less than κ_∥ to be typical for this large data set.