Simplified random network codes for multicast networks

Thesis (M. Eng. and S.B.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (p. 43).Network coding is a method of data transmission across a network which involves coding at intermediate nodes. Network coding is particularly attractive for multicast. Building on the work done on random linear network codes, we develop a constrained, simplified code construction suitable for multicast in wireless networks. We analyze bounds on sufficient code size and code success probability via an algebraic framework for network coding. We also present simulation results that compare generalized random network codes with our code construction. Issues unique to the simplified code are explored and a relaxation of the code to improve code performance is discussed.by Anna H. Lee.M.Eng.and S.B

On some new approaches to practical Slepian-Wolf compression inspired by channel coding

This paper considers the problem, first introduced by Ahlswede and Körner in 1975, of lossless source coding with coded side information. Specifically, let X and Y be two random variables such that X is desired losslessly at the decoder while Y serves as side information. The random variables are encoded independently, and both descriptions are used by the decoder to reconstruct X. Ahlswede and Körner describe the achievable rate region in terms of an auxiliary random variable. This paper gives a partial solution for the optimal auxiliary random variable, thereby describing part of the rate region explicitly in terms of the distribution of X and Y

Low-Complexity Approaches to Slepian–Wolf Near-Lossless Distributed Data Compression

This paper discusses the Slepian–Wolf problem of distributed near-lossless compression of correlated sources. We introduce practical new tools for communicating at all rates in the achievable region. The technique employs a simple “source-splitting” strategy that does not require common sources of randomness at the encoders and decoders. This approach allows for pipelined encoding and decoding so that the system operates with the complexity of a single user encoder and decoder. Moreover, when this splitting approach is used in conjunction with iterative decoding methods, it produces a significant simplification of the decoding process. We demonstrate this approach for synthetically generated data. Finally, we consider the Slepian–Wolf problem when linear codes are used as syndrome-formers and consider a linear programming relaxation to maximum-likelihood (ML) sequence decoding. We note that the fractional vertices of the relaxed polytope compete with the optimal solution in a manner analogous to that observed when the “min-sum” iterative decoding algorithm is applied. This relaxation exhibits the ML-certificate property: if an integral solution is found, it is the ML solution. For symmetric binary joint distributions, we show that selecting easily constructable “expander”-style low-density parity check codes (LDPCs) as syndrome-formers admits a positive error exponent and therefore provably good performance

Quasi-Gaussian Statistics of Hydrodynamic Turbulence in 3/4+\epsilon dimensions

The statistics of 2-dimensional turbulence exhibit a riddle: the scaling exponents in the regime of inverse energy cascade agree with the K41 theory of turbulence far from equilibrium, but the probability distribution functions are close to Gaussian like in equilibrium. The skewness \C S \equiv S_3(R)/S^{3/2}_2(R) was measured as \C S_{\text{exp}}\approx 0.03. This contradiction is lifted by understanding that 2-dimensional turbulence is not far from a situation with equi-partition of enstrophy, which exist as true thermodynamic equilibrium with K41 exponents in space dimension of $d=4/3$. We evaluate theoretically the skewness \C S(d) in dimensions ${4/3}\le d\le 2$, show that \C S(d)=0 at $d=4/3$, and that it remains as small as \C S_{\text{exp}} in 2-dimensions.Comment: PRL, submitted, REVTeX 4, 4 page

Executive summary of the joint position paper on renal denervation of the Cardiovascular and Interventional Radiological Society of Europe (CIRSE) and the European Society of Hypertension (ESH)

No abstract available

The Fokker-Planck equation for bistable potential in the optimized expansion

The optimized expansion is used to formulate a systematic approximation scheme to the probability distribution of a stochastic system. The first order approximation for the one-dimensional system driven by noise in an anharmonic potential is shown to agree well with the exact solution of the Fokker-Planck equation. Even for a bistable system the whole period of evolution to equilibrium is correctly described at various noise intensities.Comment: 12 pages, LATEX, 3 Postscript figures compressed an

A controlled study of cold dust content in galaxies from z=0−2z=0-2

At $z=1-3$, the formation of new stars is dominated by dusty galaxies whose far-IR emission indicates they contain colder dust than local galaxies of a similar luminosity. We explore the reasons for the evolving IR emission of similar galaxies over cosmic time using: 1) Local galaxies from GOALS $(L_{\rm IR}=10^{11}-10^{12}\,L_\odot)$; 2) Galaxies at $z\sim0.1-0.5$ from the 5MUSES ($L_{\rm IR}=10^{10}-10^{12}\,L_\odot$); 3) IR luminous galaxies spanning $z=0.5-3$ from GOODS and Spitzer xFLS ($L_{\rm IR}>10^{11}\,L_\odot$). All samples have Spitzer mid-IR spectra, and Herschel and ground-based submillimeter imaging covering the full IR spectral energy distribution, allowing us to robustly measure $L_{\rm IR}^{\rm\scriptscriptstyle SF}$, $T_{\rm dust}$, and $M_{\rm dust}$ for every galaxy. Despite similar infrared luminosities, $z>0.5$ dusty star forming galaxies have a factor of 5 higher dust masses and 5K colder temperatures. The increase in dust mass is linked with an increase in the gas fractions with redshift, and we do not observe a similar increase in stellar mass or star formation efficiency. $L_{160}^{\rm\scriptscriptstyle SF}/L_{70}^{\rm\scriptscriptstyle SF}$, a proxy for $T_{\rm dust}$, is strongly correlated with $L_{\rm IR}^{\rm\scriptscriptstyle SF}/M_{\rm dust}$ independently of redshift. We measure merger classification and galaxy size for a subsample, and there is no obvious correlation between these parameters and $L_{\rm IR}^{\rm \scriptscriptstyle SF}/M_{\rm dust}$ or $L_{160}^{\rm\scriptscriptstyle SF}/L_{70}^{\rm\scriptscriptstyle SF}$. In dusty star forming galaxies, the change in $L_{\rm IR}^{\rm\scriptscriptstyle SF}/M_{\rm dust}$ can fully account for the observed colder dust temperatures, suggesting that any change in the spatial extent of the interstellar medium is a second order effect.Comment: Accepted for publication in ApJ. 21 pages, 11 figure

The impact of the mixing properties within the Antarctic stratospheric vortex on ozone loss in spring

Calculations of equivalent length from an artificial advected tracer provide new insight into the isentropic transport processes occurring within the Antarctic stratospheric vortex. These calculations show two distinct regions of approximately equal area: a strongly mixed vortex core and a broad ring of weakly mixed air extending out to the vortex boundary. This broad ring of vortex air remains isolated from the core between late winter and midspring. Satellite measurements of stratospheric H2O confirm that the isolation lasts until at least mid-October. A three-dimensional chemical transport model simulation of the Antarctic ozone hole quantifies the ozone loss within this ring and demonstrates its isolation. In contrast to the vortex core, ozone loss in the weakly mixed broad ring is not complete. The reasons are twofold. First, warmer temperatures in the broad ring prevent continuous polar stratospheric cloud (PSC) formation and the associated chemical processing (i.e., the conversion of unreactive chlorine into reactive forms). Second, the isolation prevents ozone-rich air from the broad ring mixing with chemically processed air from the vortex core. If the stratosphere continues to cool, this will lead to increased PSC formation and more complete chemical processing in the broad ring. Despite the expected decline in halocarbons, sensitivity studies suggest that this mechanism will lead to enhanced ozone loss in the weakly mixed region, delaying the future recovery of the ozone hole