On the Existence of Optimal Exact-Repair MDS Codes for Distributed Storage

The high repair cost of (n,k) Maximum Distance Separable (MDS) erasure codes has recently motivated a new class of codes, called Regenerating Codes, that optimally trade off storage cost for repair bandwidth. In this paper, we address bandwidth-optimal (n,k,d) Exact-Repair MDS codes, which allow for any failed node to be repaired exactly with access to arbitrary d survivor nodes, where k<=d<=n-1. We show the existence of Exact-Repair MDS codes that achieve minimum repair bandwidth (matching the cutset lower bound) for arbitrary admissible (n,k,d), i.e., k<n and k<=d<=n-1. Our approach is based on interference alignment techniques and uses vector linear codes which allow to split symbols into arbitrarily small subsymbols.Comment: 20 pages, 6 figure

Rate-efficient Visual Correspondences using Random Projections,” to appear

We consider the problem of establishing visual correspondences in a distributed and rate-efficient fashion by broadcasting compact descriptors. Establishing visual correspondences is a critical task before other vision tasks can be performed in a wireless camera network. We propose the use of coarsely quantized random projections of descriptors to build binary hashes, and use the Hamming distance between binary hashes as the matching criterion. In this work, we derive the analytic relationship of Hamming distance between the binary hashes to Euclidean distance between the original descriptors. We present experimental verification of our result, and show that for the task of finding visual correspondences, sending binary hashes is more rate-efficient than prior approaches. 1

Informationtheoretic bounds on model selection for Gaussian markov random fields

Abstract—The problem of graphical model selection is to estimate the graph structure of an unknown Markov random field based on observed samples from the graphical model. For Gaussian Markov random fields, this problem is closely related to the problem of estimating the inverse covariance matrix of the underlying Gaussian distribution. This paper focuses on the information-theoretic limitations of Gaussian graphical model selection and inverse covariance estimation in the highdimensional setting, in which the graph size p and maximum node degree d are allowed to grow as a function of the sample size n. Our first result establishes a set of necessary conditions on n(p, d) for any recovery method to consistently estimate the underlying graph. Our second result provides necessary conditions for any decoder to produce an estimate b Θ of the true inverse covariance matrix Θ satisfying ‖ b Θ − Θ ‖ &lt; δ in the elementwise ℓ∞-norm (which implies analogous results in the Frobenius norm as well). Combined with previously known sufficient conditions for polynomial-time algorithms, these results yield sharp characterizations in several regimes of interest. I