Optimal Feedback Communication via Posterior Matching

In this paper we introduce a fundamental principle for optimal communication over general memoryless channels in the presence of noiseless feedback, termed posterior matching. Using this principle, we devise a (simple, sequential) generic feedback transmission scheme suitable for a large class of memoryless channels and input distributions, achieving any rate below the corresponding mutual information. This provides a unified framework for optimal feedback communication in which the Horstein scheme (BSC) and the Schalkwijk-Kailath scheme (AWGN channel) are special cases. Thus, as a corollary, we prove that the Horstein scheme indeed attains the BSC capacity, settling a longstanding conjecture. We further provide closed form expressions for the error probability of the scheme over a range of rates, and derive the achievable rates in a mismatch setting where the scheme is designed according to the wrong channel model. Several illustrative examples of the posterior matching scheme for specific channels are given, and the corresponding error probability expressions are evaluated. The proof techniques employed utilize novel relations between information rates and contraction properties of iterated function systems.Comment: IEEE Transactions on Information Theor

Our Troubled Health Care System: Why Is It So Hard to Fix? Nineteenth Annual Herbert Lourie Memorial Lecture on Health Policy.

This brief draws heavily on Judith Feder, 2004, "Crowd-Out and the Politics of Health Reform," The Journal of Law, Medicine, and Ethids 32(3): 461-464. We all know that affordable health care is now back on the political agenda, and it's about time! Because all of us--families, businesses, and governments--are struggling with the ever-increasing costs of care. Every year about a million people are added to the rolls of the uninsured. In 2006, it was even more, over 2 million. The number of people without health insurance coverage has reached more than 47 million. People *with* insurance are seeing their benefits dwindle and their health care costs consume their wabes. Even people with health insurance find themselves unable to pay their medical bills and going without needed care. The bottom line is that, increasingly, our health insurance system fails to protect us when we get sick.health insurance, uninsurance, cost of medical care

Relativistic effects on LEED intensities from Au(111)

Comparison of relativistically and nonrelativistically calculated intensity versus energy profiles in low energy electron diffraction (LEED) from the (111) surface of Au (Z = 79) reveals that relativistic corrections are quite significant. They can however, be obtained in very good approximation by quasirelativistic calculations, in which spin-averaged relativistic phase shifts are used as input for the nonrelativistic multiple scattering formalism. Further, relativistic effects on intensities are found to be comparable to differences arising from different approximations to the exchange part of the ion core potential

On the calculation of the minimax-converse of the channel coding problem

A minimax-converse has been suggested for the general channel coding problem by Polyanskiy etal. This converse comes in two flavors. The first flavor is generally used for the analysis of the coding problem with non-vanishing error probability and provides an upper bound on the rate given the error probability. The second flavor fixes the rate and provides a lower bound on the error probability. Both converses are given as a min-max optimization problem of an appropriate binary hypothesis testing problem. The properties of the first converse were studies by Polyanskiy and a saddle point was proved. In this paper we study the properties of the second form and prove that it also admits a saddle point. Moreover, an algorithm for the computation of the saddle point, and hence the bound, is developed. In the DMC case, the algorithm runs in a polynomial time.Comment: Extended version of a submission to ISIT 201

Pay Equity Legislation

[Excerpt] The issue of pay equity has attracted substantial attention in recent Congresses. A number of measures, including bills that would provide additional remedies, mandate “equal pay for equivalent jobs,” or require studies on pay inequity, have been introduced in each of the last several congressional sessions. In the 111th Congress, similar legislation has been introduced, including the Paycheck Fairness Act (H.R. 12/S. 182/S. 3772), the Fair Pay Act (H.R. 2151/S. 904), and the Title VII Fairness Act (S. 166). In addition, on January 29, 2009, President Obama signed the Lilly Ledbetter Fair Pay Act of 2009 (H.R. 11/S. 181). This legislation supersedes the 2007 Supreme Court decision in Ledbetter v. Goodyear Tire & Rubber Co., Inc., by amending Title VII to clarify that the time limit for suing employers for pay discrimination begins each time they issue a paycheck. Although the House of Representatives passed both the Ledbetter legislation and the Paycheck Fairness Act as a combined package, the Senate did not combine the two bills and has not yet taken up the latter for a vote. Recently, however, Senator Reid reintroduced the Paycheck Fairness Act as S. 3772, and the bill has been placed on the Senate calendar

Impact study on the application of vinasse to cambisol and vertic luvisol in Ethiopia

To study an impact on the application of vinasse to Cambisol and vertic Luvisol in Ethiopia, we used HP1 an hydrogeochemical models to assess the medium-term risks of the use of that agricultural practice by a Sugar Factory. The three water input scenarios tested play a major role in soil function and simulated soil changes after a vinasse input. There is always drainage in all three types of soil; it varies from slight (50 mm/yr) to fairly substantial (1000 mm/yr). However, the latter value is related to a scenario (i) that does not take rainfall into account in irrigation management and (ii) that ignores losses of water before it reaches the soil. Overall the conditions seem optimal, strictly from the water supply standpoint, for limiting the risk of salinization. Under the initial conditions, the irrigation water used was not heavily loaded with salts (ca. 4.5 mS/cm) and the soil exchange complex was 80% saturated with calcium because of the calcareous origin of the parent rock. The behaviour of the three soils is fairly similar overall. The input of vinasse, at a dose equivalent to 340 kg/ha of potassium, causes a significant increase in the concentrations of chemical elements in the soil solution but also greater leaching of these chemical elements out of the soil profile. Over time, the distribution of cations in the CEC does not change very much and appears to settle on noncritical values. Sodium, then potassium, partially replaces magnesium and calcium in the CEC, but ultimately the change is slight. The percentage of calcium in the CEC never falls below 75%. Saturation indices determine whether the physico-chemical conditions are such that minerals (halite, calcite, gypsum, etc.) will precipitate out and cause salinization. Our simulations show that when vinasse inputs are done at a normal dose (equivalent to 340 kg/ha of potassium), the risk of precipitation of minerals is nil, especially when water inputs are properly calculated (low drainage). However, when the inputs are doubled (equivalent to 580 kg/ha of potassium), several minerals are near supersaturation and therefore liable to precipitate out. The volumes of water supplied are also immaterial, since when drainage is slight, anhydrite and gypsum are the substances liable to precipitate out, and when it is greater, K-jarosite will. Therefore, whatever the water input scenario tested, we recommend against vinasse inputs at a dose equivalent to 580 kg/ha of potassium. On the other hand, for all three types of soil, vinasse inputs at a dose equivalent to 340 kg/ha of potassium present no medium-term risk of soil salinization. Moreover, at these same doses, no parameter (chemical composition, breakdown of elements in the CEC, SI, etc.) tends toward a critical threshold. (Texte intégral