From a background of RC interconnect models in layout-to-circuit extraction, this paper compares two realizable model reduction methodologies based on generalized Y# transformation. The first method represents admittances through a rational function in the s-domain, where the numerator and denominator polynomials are truncated at a user-defined order. During the Y# transformation, common factors in the numerator and denominator are identified and cancelled. The rational form of the admittances allows realization through e.g. Brune synthesis. The second method represents admittances through a moments expansion up to a user-defined order. It also allows synthesis after a Pade matching step. In that sense, the methods are equivalent. Nevertheless, a comparison shows that the former performs better in the frequency domain.

This paper presents a new method to automatically generate posynomial symbolic expressions for the performance characteristics of analog integrated circuits. The coefficient set as well as the exponent set of the posynomial expression are determined based on SPICE simulation data with device-level accuracy. We will prove that this problem corresponds to solving a non--convex optimization problem without local minima. The presented method is capable of generating posynomial performance expressions for both linear and nonlinear circuits and circuit characteristics. This approach allows to automatically generate an accurate sizing model that composes a geometric program that fully describes the analog circuit sizing problem. The automatic generation avoids the time--consuming nature of hand--crafted analytic model generation. Experimental results illustrate the capabilities and effectiveness of the presented modeling technique.

The notion of convexity underlies important results in many parts of mathematics such as optimization, analysis, combinatorics, probability and number theory. The geometric foundations of the theory of convex sets date back to work of Minkowski, Carathéodory, and Fenchel around 1900. Since then, this area has expanded into a large number of directions and now includes topics such as high-dimensional spaces, convex analysis, polyhedral geometry, computational convexity, approximation methods and others. In the context of optimization, both theory and empirical evidence show that problems with convex constraints allow efficient algorithms. Many applications in the sciences and engineering involve optimization, and it is always extremely advantageous when the underlying feasible regions are convex and have practically useful representations as convex sets. A situation in which convexity has been well-understood is the study of convex polyhedra, which are the solution sets of finitely many linear inequalities [27, 86]. A context in algebraic geometry in which convexity arises is the theory of toric varieties. These are algebraic varieties derived from polyhedra [49, 73]. Both convex polyhedra and toric varieties have satisfactory computational techniques associated to them. Linear optimization over polyhedra is linear programming which admits interior-point algorithms that run in polynomial time. More generally, polyhedra can be

We consider random access in wireless networks under the physical interference model, wherein the receiver is capable of power-based capture, i.e., a packet can be decoded correctly in the presence of multiple transmissions if the received Signal to Interference and Noise Ratio exceeds a threshold. We propose a splitting algorithm that varies the transmission powers of users on the basis of quaternary channel feedback (idle, success, capture, collision). We show that our algorithm achieves a maximum stable throughput of 0.5518. Simulation results demonstrate that our algorithm achieves higher throughput and lower delay thanthat of the First Come First Servesplitting algorithmwith uniformtransmission power.

Abstract not found

We present a method for designing operational amplifiers using reversed geometric programming, which is an extension of geometric programming that allows both convex and non-convex constraints. Adding a limited set of non-convex constraints can improve the accuracy of convex equationbased optimization, without compromising global optimality. These constraints allow increased accuracy for critical modeling equations, such as the relationship between gm and Ips. To demonstrate the design methodology, a foldedcascode amplifier is designed in a 0.18'pm technology for varying speed requirements and is compared with simnlations and designs obtained from geometric programming. Categories and Subject Descriptors:

In this article we shall study some basic properties of posynomial rings with particular emphasis on rings Pos(K, Q)[¯x], and Pos(K, Z)[¯x]. The latter ring is the well known ring of Laurent polynomials. 1

Abstract—Throughput and per-packet delay can present strong trade-offs that are important in the cases of delay sensitive applications. We investigate such trade-offs using a random linear network coding scheme for one or more receivers in single hop wireless packet erasure broadcast channels. We capture the delay sensitivities across different types of network applications using a class of delay metrics based on the norms of packet arrival times. With these delay metrics, we establish a unified framework to characterize the rate and delay requirements of applications and to optimize system parameters. In the single receiver case, we demonstrate the trade-off between average packet delay, which we view as the inverse of throughput, and maximum inorder inter-arrival delay for various system parameters. For a single broadcast channel with multiple receivers having different delay constraints and feedback delays, we jointly optimize the coding parameters and time-division scheduling parameters at the transmitter. We formulate the optimization problem as a Generalized Geometric Program (GGP). This approach allows the transmitter to adjust adaptively the coding and scheduling parameters for efficient allocation of network resources under varying delay constraints. In the case where the receivers are served by multiple non-interfering wireless broadcast channels, the same optimization problem is formulated as a Signomial Program, which is NP-hard in general. We provide approximation methods using successive formulation of geometric programs and show the convergence of approximations.