Scanning tunnelling spectroscopy of electron resonators

The electronic structure of artificial Mn atom arrays on Ag(111) is characterized in detail with scanning tunnelling spectroscopy and spectroscopic imaging at low temperature. We demonstrate the degree to which variations in geometry may be used to control spatial and spectral distributions of surface state electrons confined within the arrays, how these are influenced by atoms placed within the structure and how the ability to induce spectral features at specific energies may be exploited through lineshape analyses to deduce quasiparticle lifetimes near the Fermi level. Through extensive comparison of $dI/dV$ maps and spectra we demonstrate the utility of a model based upon two-dimensional s-wave scatterers for describing and predicting the characteristics of specific resonators

On Secure Network Coding with Nonuniform or Restricted Wiretap Sets

The secrecy capacity of a network, for a given collection of permissible wiretap sets, is the maximum rate of communication such that observing links in any permissible wiretap set reveals no information about the message. This paper considers secure network coding with nonuniform or restricted wiretap sets, for example, networks with unequal link capacities where a wiretapper can wiretap any subset of $k$ links, or networks where only a subset of links can be wiretapped. Existing results show that for the case of uniform wiretap sets (networks with equal capacity links/packets where any $k$ can be wiretapped), the secrecy capacity is given by the cut-set bound, and can be achieved by injecting $k$ random keys at the source which are decoded at the sink along with the message. This is the case whether or not the communicating users have information about the choice of wiretap set. In contrast, we show that for the nonuniform case, the cut-set bound is not achievable in general when the wiretap set is unknown, whereas it is achievable when the wiretap set is made known. We give achievable strategies where random keys are canceled at intermediate non-sink nodes, or injected at intermediate non-source nodes. Finally, we show that determining the secrecy capacity is a NP-hard problem.Comment: 24 pages, revision submitted to IEEE Transactions on Information Theor

Connecting Multiple-unicast and Network Error Correction: Reduction and Unachievability

We show that solving a multiple-unicast network coding problem can be reduced to solving a single-unicast network error correction problem, where an adversary may jam at most a single edge in the network. Specifically, we present an efficient reduction that maps a multiple-unicast network coding instance to a network error correction instance while preserving feasibility. The reduction holds for both the zero probability of error model and the vanishing probability of error model. Previous reductions are restricted to the zero-error case. As an application of the reduction, we present a constructive example showing that the single-unicast network error correction capacity may not be achievable, a result of separate interest.Comment: ISIT 2015. arXiv admin note: text overlap with arXiv:1410.190

Lossy Compression with Privacy Constraints: Optimality of Polar Codes

A lossy source coding problem with privacy constraint is studied in which two correlated discrete sources $X$ and $Y$ are compressed into a reconstruction $\hat{X}$ with some prescribed distortion $D$. In addition, a privacy constraint is specified as the equivocation between the lossy reconstruction $\hat{X}$ and $Y$. This models the situation where a certain amount of source information from one user is provided as utility (given by the fidelity of its reconstruction) to another user or the public, while some other correlated part of the source information $Y$ must be kept private. In this work, we show that polar codes are able, possibly with the aid of time sharing, to achieve any point in the optimal rate-distortion-equivocation region identified by Yamamoto, thus providing a constructive scheme that obtains the optimal tradeoff between utility and privacy in this framework.Comment: Submitted for publicatio