On joint detection and decoding of linear block codes on Gaussian vector channels

Optimal receivers recovering signals transmitted across noisy communication channels employ a maximum-likelihood (ML) criterion to minimize the probability of error. The problem of finding the most likely transmitted symbol is often equivalent to finding the closest lattice point to a given point and is known to be NP-hard. In systems that employ error-correcting coding for data protection, the symbol space forms a sparse lattice, where the sparsity structure is determined by the code. In such systems, ML data recovery may be geometrically interpreted as a search for the closest point in the sparse lattice. In this paper, motivated by the idea of the "sphere decoding" algorithm of Fincke and Pohst, we propose an algorithm that finds the closest point in the sparse lattice to the given vector. This given vector is not arbitrary, but rather is an unknown sparse lattice point that has been perturbed by an additive noise vector whose statistical properties are known. The complexity of the proposed algorithm is thus a random variable. We study its expected value, averaged over the noise and over the lattice. For binary linear block codes, we find the expected complexity in closed form. Simulation results indicate significant performance gains over systems employing separate detection and decoding, yet are obtained at a complexity that is practically feasible over a wide range of system parameters

Trickle-down processes and their boundaries

It is possible to represent each of a number of Markov chains as an evolving sequence of connected subsets of a directed acyclic graph that grow in the following way: initially, all vertices of the graph are unoccupied, particles are fed in one-by-one at a distinguished source vertex, successive particles proceed along directed edges according to an appropriate stochastic mechanism, and each particle comes to rest once it encounters an unoccupied vertex. Examples include the binary and digital search tree processes, the random recursive tree process and generalizations of it arising from nested instances of Pitman's two-parameter Chinese restaurant process, tree-growth models associated with Mallows' phi model of random permutations and with Schuetzenberger's non-commutative q-binomial theorem, and a construction due to Luczak and Winkler that grows uniform random binary trees in a Markovian manner. We introduce a framework that encompasses such Markov chains, and we characterize their asymptotic behavior by analyzing in detail their Doob-Martin compactifications, Poisson boundaries and tail sigma-fields.Comment: 62 pages, 8 figures, revised to address referee's comment

GeoNotes: A Location-based Information System for Public Spaces

The basic idea behind location-based information systems is to connect information pieces to positions in outdoor or indoor space. Through position technologies such as Global Positioning System (GPS), GSM positioning, Wireless LAN positioning o

Potential Networks, Contagious Communities, and Understanding Social Network Structure

In this paper we study how the network of agents adopting a particular technology relates to the structure of the underlying network over which the technology adoption spreads. We develop a model and show that the network of agents adopting a particular technology may have characteristics that differ significantly from the social network of agents over which the technology spreads. For example, the network induced by a cascade may have a heavy-tailed degree distribution even if the original network does not. This provides evidence that online social networks created by technology adoption over an underlying social network may look fundamentally different from social networks and indicates that using data from many online social networks may mislead us if we try to use it to directly infer the structure of social networks. Our results provide an alternate explanation for certain properties repeatedly observed in data sets, for example: heavy-tailed degree distribution, network densification, shrinking diameter, and network community profile. These properties could be caused by a sort of `sampling bias' rather than by attributes of the underlying social structure. By generating networks using cascades over traditional network models that do not themselves contain these properties, we can nevertheless reliably produce networks that contain all these properties. An opportunity for interesting future research is developing new methods that correctly infer underlying network structure from data about a network that is generated via a cascade spread over the underlying network.Comment: To Appear in Proceedings of the 22nd International World Wide Web Conference(WWW 2013