Increasing Availability in Distributed Storage Systems via Clustering

We introduce the Fixed Cluster Repair System (FCRS) as a novel architecture for Distributed Storage Systems (DSS), achieving a small repair bandwidth while guaranteeing a high availability. Specifically we partition the set of servers in a DSS into $s$ clusters and allow a failed server to choose any cluster other than its own as its repair group. Thereby, we guarantee an availability of $s-1$. We characterize the repair bandwidth vs. storage trade-off for the FCRS under functional repair and show that the minimum repair bandwidth can be improved by an asymptotic multiplicative factor of $2/3$ compared to the state of the art coding techniques that guarantee the same availability. We further introduce Cubic Codes designed to minimize the repair bandwidth of the FCRS under the exact repair model. We prove an asymptotic multiplicative improvement of $0.79$ in the minimum repair bandwidth compared to the existing exact repair coding techniques that achieve the same availability. We show that Cubic Codes are information-theoretically optimal for the FCRS with $2$ and $3$ complete clusters. Furthermore, under the repair-by-transfer model, Cubic Codes are optimal irrespective of the number of clusters

KK Users Caching Two Files: An Improved Achievable Rate

Caching is an approach to smoothen the variability of traffic over time. Recently it has been proved that the local memories at the users can be exploited for reducing the peak traffic in a much more efficient way than previously believed. In this work we improve upon the existing results and introduce a novel caching strategy that takes advantage of simultaneous coded placement and coded delivery in order to decrease the worst case achievable rate with $2$ files and $K$ users. We will show that for any cache size $\frac{1}{K}<M<1$ our scheme outperforms the state of the art

Compute-and-Forward: Finding the Best Equation

Compute-and-Forward is an emerging technique to deal with interference. It allows the receiver to decode a suitably chosen integer linear combination of the transmitted messages. The integer coefficients should be adapted to the channel fading state. Optimizing these coefficients is a Shortest Lattice Vector (SLV) problem. In general, the SLV problem is known to be prohibitively complex. In this paper, we show that the particular SLV instance resulting from the Compute-and-Forward problem can be solved in low polynomial complexity and give an explicit deterministic algorithm that is guaranteed to find the optimal solution.Comment: Paper presented at 52nd Allerton Conference, October 201

GDSP: A Graphical Perspective on the Distributed Storage Systems

The classical distributed storage problem can be modeled by a k-uniform {\it complete} hyper-graph where vertices represent servers and hyper-edges represent users. Hence each hyper-edge should be able to recover the full file using only the memories of the vertices associated with it. This paper considers the generalization of this problem to {\it arbitrary} hyper-graphs and to the case of multiple files, where each user is only interested in one, a problem we will refer to as the graphical distributed storage problem (GDSP). Specifically, we make progress in the analysis of minimum-storage codes for two main subproblems of the GDSP which extend the classical model in two independent directions: the case of an arbitrary graph with multiple files, and the case of an arbitrary hyper-graph with a single file

New Shortest Lattice Vector Problems of Polynomial Complexity

The Shortest Lattice Vector (SLV) problem is in general hard to solve, except for special cases (such as root lattices and lattices for which an obtuse superbase is known). In this paper, we present a new class of SLV problems that can be solved efficiently. Specifically, if for an $n$-dimensional lattice, a Gram matrix is known that can be written as the difference of a diagonal matrix and a positive semidefinite matrix of rank $k$ (for some constant $k$), we show that the SLV problem can be reduced to a $k$-dimensional optimization problem with countably many candidate points. Moreover, we show that the number of candidate points is bounded by a polynomial function of the ratio of the smallest diagonal element and the smallest eigenvalue of the Gram matrix. Hence, as long as this ratio is upper bounded by a polynomial function of $n$, the corresponding SLV problem can be solved in polynomial complexity. Our investigations are motivated by the emergence of such lattices in the field of Network Information Theory. Further applications may exist in other areas.Comment: 13 page

Caching and Distributed Storage:Models, Limits and Designs

A simple task of storing a database or transferring it to a different point via a communication channel turns far more complex as the size of the database grows large. Limited bandwidth available for transmission plays a central role in this predicament. In two broad contexts, Content Distribution Networks (CDN) and Distributed Storage Systems (DSS), the adverse effect of the growing size of the database on the transmission bandwidth can be mitigated by exploiting additional storage units. Characterizing the optimal tradeoff between the transmission bandwidth and the storage size is the central quest to numerous works in the recent literature, including this thesis. In a DSS, individual servers fail routinely and must be replicated by downloading data from the remaining servers, a task referred to as the repair process. To render this process of repairing failed servers more straightforward and efficient, various forms of redundancy can be introduced in the system. One of the benchmarks by which the reliability of a DSS is measured is availability, which refers to the number of disjoint sets of servers that can help to repair any failed server. We study the interaction of this parameter with the amount of traffic generated during the repair process (the repair bandwidth) and the storage size. In particular, we propose a novel DSS architecture which can achieve much smaller repair bandwidth for the same availability, compared to the state of the art. In the context of CDNs, the network can be highly congested during certain hours of the day and almost idle at other times. This variability of traffic can be reduced by utilizing local storage units that prefetch the data while the network is idle. This approach is referred to as caching. In this thesis we analyze a CDN that has access to independent data from various content providers. We characterize the best caching strategy in terms of the aggregate peak traffic under the constraint that coding across contents from different libraries is prohibited. Furthermore we prove that under certain set of conditions this restriction is without loss of optimality

A Novel Centralized Strategy for Coded Caching with Non-uniform Demands

Despite significant progress in the caching literature concerning the worst case and uniform average case regimes, the algorithms for caching with nonuniform demands are still at a basic stage and mostly rely on simple grouping and memory-sharing techniques. In this work we introduce a novel centralized caching strategy for caching with nonuniform file popularities. Our scheme allows for assigning more cache to the files which are more likely to be requested, while maintaining the same sub-packetization for all the files. As a result, in the delivery phase it is possible to perform linear codes across files with different popularities without resorting to zero-padding or concatenation techniques. We will describe our placement strategy for arbitrary range of parameters. The delivery phase will be outlined for a small example for which we are able to show a noticeable improvement over the state of the art.Comment: 4 pages, 3 figures, submitted to the 2018 International Zurich Seminar on Information and Communicatio