Distortion Minimization in Gaussian Layered Broadcast Coding with Successive Refinement

A transmitter without channel state information (CSI) wishes to send a delay-limited Gaussian source over a slowly fading channel. The source is coded in superimposed layers, with each layer successively refining the description in the previous one. The receiver decodes the layers that are supported by the channel realization and reconstructs the source up to a distortion. The expected distortion is minimized by optimally allocating the transmit power among the source layers. For two source layers, the allocation is optimal when power is first assigned to the higher layer up to a power ceiling that depends only on the channel fading distribution; all remaining power, if any, is allocated to the lower layer. For convex distortion cost functions with convex constraints, the minimization is formulated as a convex optimization problem. In the limit of a continuum of infinite layers, the minimum expected distortion is given by the solution to a set of linear differential equations in terms of the density of the fading distribution. As the bandwidth ratio b (channel uses per source symbol) tends to zero, the power distribution that minimizes expected distortion converges to the one that maximizes expected capacity. While expected distortion can be improved by acquiring CSI at the transmitter (CSIT) or by increasing diversity from the realization of independent fading paths, at high SNR the performance benefit from diversity exceeds that from CSIT, especially when b is large.Comment: Accepted for publication in IEEE Transactions on Information Theor

Universal Lossless Compression with Unknown Alphabets - The Average Case

Universal compression of patterns of sequences generated by independently identically distributed (i.i.d.) sources with unknown, possibly large, alphabets is investigated. A pattern is a sequence of indices that contains all consecutive indices in increasing order of first occurrence. If the alphabet of a source that generated a sequence is unknown, the inevitable cost of coding the unknown alphabet symbols can be exploited to create the pattern of the sequence. This pattern can in turn be compressed by itself. It is shown that if the alphabet size $k$ is essentially small, then the average minimax and maximin redundancies as well as the redundancy of every code for almost every source, when compressing a pattern, consist of at least 0.5 log(n/k^3) bits per each unknown probability parameter, and if all alphabet letters are likely to occur, there exist codes whose redundancy is at most 0.5 log(n/k^2) bits per each unknown probability parameter, where n is the length of the data sequences. Otherwise, if the alphabet is large, these redundancies are essentially at least O(n^{-2/3}) bits per symbol, and there exist codes that achieve redundancy of essentially O(n^{-1/2}) bits per symbol. Two sub-optimal low-complexity sequential algorithms for compression of patterns are presented and their description lengths analyzed, also pointing out that the pattern average universal description length can decrease below the underlying i.i.d.\ entropy for large enough alphabets.Comment: Revised for IEEE Transactions on Information Theor

Multi-Period Trading via Convex Optimization

We consider a basic model of multi-period trading, which can be used to evaluate the performance of a trading strategy. We describe a framework for single-period optimization, where the trades in each period are found by solving a convex optimization problem that trades off expected return, risk, transaction cost and holding cost such as the borrowing cost for shorting assets. We then describe a multi-period version of the trading method, where optimization is used to plan a sequence of trades, with only the first one executed, using estimates of future quantities that are unknown when the trades are chosen. The single-period method traces back to Markowitz; the multi-period methods trace back to model predictive control. Our contribution is to describe the single-period and multi-period methods in one simple framework, giving a clear description of the development and the approximations made. In this paper we do not address a critical component in a trading algorithm, the predictions or forecasts of future quantities. The methods we describe in this paper can be thought of as good ways to exploit predictions, no matter how they are made. We have also developed a companion open-source software library that implements many of the ideas and methods described in the paper

GSE, data management system programmers/User' manual

The GSE data management system is a computerized program which provides for a central storage source for key data associated with the mechanical ground support equipment (MGSE). Eight major sort modes can be requested by the user. Attributes that are printed automatically with each sort include the GSE end item number, description, class code, functional code, fluid media, use location, design responsibility, weight, cost, quantity, dimensions, and applicable documents. Multiple subsorts are available for the class code, functional code, fluid media, use location, design responsibility, and applicable document categories. These sorts and how to use them are described. The program and GSE data bank may be easily updated and expanded

Battery selection for space experiments

This paper will delineate the criteria required for the selection of batteries as a power source for space experiments. Four basic types of batteries will be explored, lead acid, silver zinc, alkaline manganese and nickel cadmium. A detailed description of the lead acid and silver zinc cells while a brief exploration of the alkaline manganese and nickel cadmium will be given. The factors involved in battery selection such as packaging, energy density, discharge voltage regulation, and cost will be thoroughly examined. The pros and cons of each battery type will be explored. Actual laboratory test data acquired for the lead acid and silver zinc cell will be discussed. This data will include discharging under various temperature conditions, after three months of storage and with different types of loads. A description of the required maintenance for each type of battery will be investigated. The lifetime and number of charge/discharge cycles will be discussed

Single freeform surface design for prescribed input wavefront and target irradiance

In beam shaping applications, the minimization of the number of necessary optical elements for the beam shaping process can benefit the compactness of the optical system and reduce its cost. The single freeform surface design for input wavefronts, which are neither planar nor spherical, is therefore of interest. In this work, the design of single freeform surfaces for a given zero-\'etendue source and complex target irradiances is investigated. Hence, not only collimated input beams or point sources are assumed. Instead, a predefined input ray direction vector field and irradiance distribution on a source plane, which has to be redistributed by a single freeform surface to give the predefined target irradiance, is considered. To solve this design problem, a partial differential equation (PDE) or PDE system, respectively, for the unknown surface and its corresponding ray mapping is derived from energy conservation and the ray-tracing equations. In contrast to former PDE formulations of the single freeform design problem, the derived PDE of Monge-Amp\`ere type is formulated for general zero-\'etendue sources in cartesian coordinates. The PDE system is discretized with finite differences and the resulting nonlinear equation system solved by a root-finding algorithm. The basis of the efficient solution of the PDE system builds the introduction of an initial iterate constuction approach for a given input direction vector field, which uses optimal mass transport with a quadratic cost function. After a detailed description of the numerical algorithm, the efficiency of the design method is demonstrated by applying it to several design examples. This includes the redistribution of a collimated input beam beyond the paraxial approximation, the shaping of point source radiation and the shaping of an astigmatic input wavefront into a complex target irradiance distribution.Comment: 11 pages, 10 figures version 2: Equation (7) was corrected; additional minor changes/improvement

Battery selection for Space Shuttle experiments

This paper will delineate the criteria required for the selection of batteries as a power source for space experiments. Four basic types of batteries will be explored, lead acid, silver zinc, alkaline manganese, and nickel cadmium. A detailed description of the lead acid and silver zinc cells and a brief exploration of the alkaline manganese and nickel cadmium will be given. The factors involved in battery selection such as packaging, energy density, discharge voltage regulation, and cost will be thoroughly examined. The pros and cons of each battery type will be explored. Actual laboratory test data acquired for the lead acid and silver zinc cell will be discussed. This data will include discharging under various temperature conditions, after three months of storage, and with different types of loads. The lifetime and number of charge/discharge cycles will also be discussed. A description of the required maintenance for each type of battery will be investigated