On sequences of projections of the cubic lattice

In this paper we study sequences of lattices which are, up to similarity, projections of $\mathbb{Z}^{n+1}$ onto a hyperplane $\bm{v}^{\perp}$, with $\bm{v} \in \mathbb{Z}^{n+1}$ and converge to a target lattice $\Lambda$ which is equivalent to an integer lattice. We show a sufficient condition to construct sequences converging at rate $O(1/ |\bm{v}|^{2/n})$ and exhibit explicit constructions for some important families of lattices.Comment: 16 pages, 5 figure

Reliability of Erasure Coded Storage Systems: A Geometric Approach

We consider the probability of data loss, or equivalently, the reliability function for an erasure coded distributed data storage system under worst case conditions. Data loss in an erasure coded system depends on probability distributions for the disk repair duration and the disk failure duration. In previous works, the data loss probability of such systems has been studied under the assumption of exponentially distributed disk failure and disk repair durations, using well-known analytic methods from the theory of Markov processes. These methods lead to an estimate of the integral of the reliability function. Here, we address the problem of directly calculating the data loss probability for general repair and failure duration distributions. A closed limiting form is developed for the probability of data loss and it is shown that the probability of the event that a repair duration exceeds a failure duration is sufficient for characterizing the data loss probability. For the case of constant repair duration, we develop an expression for the conditional data loss probability given the number of failures experienced by a each node in a given time window. We do so by developing a geometric approach that relies on the computation of volumes of a family of polytopes that are related to the code. An exact calculation is provided and an upper bound on the data loss probability is obtained by posing the problem as a set avoidance problem. Theoretical calculations are compared to simulation results.Comment: 28 pages. 8 figures. Presented in part at IEEE International Conference on BigData 2013, Santa Clara, CA, Oct. 2013 and to be presented in part at 2014 IEEE Information Theory Workshop, Tasmania, Australia, Nov. 2014. New analysis added May 2015. Further Update Aug. 201

The Firm-Level Credit Multiplier

We study the effect of asset tangibility on corporate financing and investment decisions. Financially constrained firms benefit the most from investing in tangible assets because those assets help relax constraints, allowing for further investment. Using a dynamic model, we characterize this effect – which we call firm-level credit multiplier – and show how asset tangibility increases the sensitivity of investment to Tobin’s Q for financially constrained firms. Examining a large sample of manufacturers over the 1971-2005 period as well as simulated data, we find support for our theory’s tangibility–investment channel. We further verify that our findings are driven by firms’ debt issuance activities. Consistent with our empirical identification strategy, the firm-level credit multiplier is absent from samples of financially unconstrained firms and samples of financially constrained firms with low spare debt capacity.

Canonical Realization of (2+1)-dimensional Bondi-Metzner-Sachs symmetry

We construct canonical realizations of the $\mathfrak{bms}_3$ algebra as symmetry algebras of a free Klein-Gordon (KG) field in $2+1$ dimensions, for both the massive and massless case. We consider two types of realizations, one on-shell, written in terms of the Fourier modes of the scalar field, and the other one off-shell with non-local transformations written in terms of the KG field and its momenta. These realizations contain both supertranslations and superrotations, for which we construct the corresponding Noether charges.Comment: Version accepted for publication in PRD. Expanded title and expanded discussion about superrotations in the massive cas

Semantically Secure Lattice Codes for Compound MIMO Channels

We consider compound multi-input multi-output (MIMO) wiretap channels where minimal channel state information at the transmitter (CSIT) is assumed. Code construction is given for the special case of isotropic mutual information, which serves as a conservative strategy for general cases. Using the flatness factor for MIMO channels, we propose lattice codes universally achieving the secrecy capacity of compound MIMO wiretap channels up to a constant gap (measured in nats) that is equal to the number of transmit antennas. The proposed approach improves upon existing works on secrecy coding for MIMO wiretap channels from an error probability perspective, and establishes information theoretic security (in fact semantic security). We also give an algebraic construction to reduce the code design complexity, as well as the decoding complexity of the legitimate receiver. Thanks to the algebraic structures of number fields and division algebras, our code construction for compound MIMO wiretap channels can be reduced to that for Gaussian wiretap channels, up to some additional gap to secrecy capacity.Comment: IEEE Trans. Information Theory, to appea

Curves on torus layers and coding for continuous alphabet sources

In this paper we consider the problem of transmitting a continuous alphabet discrete-time source over an AWGN channel. The design of good curves for this purpose relies on geometrical properties of spherical codes and projections of $N$-dimensional lattices. We propose a constructive scheme based on a set of curves on the surface of a 2N-dimensional sphere and present comparisons with some previous works.Comment: 5 pages, 4 figures. Accepted for presentation at 2012 IEEE International Symposium on Information Theory (ISIT). 2th version: typos corrected. 3rd version: some typos corrected, a footnote added in Section III B, a comment added in the beggining of Section V and Theorem I adde