Optimal wire and transistor sizing for circuits with non-tree topology

Abstract

a b b a s @ i s l . s t a n f o r d . e d u AbstractConventional methods for optimal sizing of wires and transistors use linear RC circuit models and the Elmore delay as a measure of signal delay. If the RC circuit has a tree topology the sizing problem reduces to a convex optimization problem which can be solved using geometric programming. The tree topology restriction precludes the use of these methods in several sizing problems of significant importance to highperformance deep submicron design including, for example, circuits with loops of resistors, e.g., clock distribution meshes, and circuits with coupling capacitors, e.g., buses with crosstalk between the lines. The paper proposes a new optimization method which can be used to address these problems. The method uses the dominant time constant as a measure of signal propagation delay in an RC circuit, instead of Elmore delay. Using this measure, sizing of any RC circuit can be cast as a convex optimization problem which can be solved using the recently developed efficient interior-point methods for semidefinite programming. The method is applied to two important sizing problems -sizing of clock meshes, and sizing of buses in the presence of crosstalk.

Enhancing Sparsity by Reweighted ℓ 1 Minimization

“…The difficulty is that errors occur upon transmission so that a fraction of the transmitted codeword may be corrupted in a completely arbitrary and unknown fashion. In this setup, the authors in [31] showed that one could transmit n pieces of information reliably by encoding the information as Φx 0 where Φ ∈ R m×n , m ≥ n, is a suitable coding matrix, and by solving min x∈R n y − Φx ℓ 1 (11) upon receiving the corrupted codeword y = Φx 0 + e; here, e is the unknown but sparse corruption pattern. The conclusion of [31] is then that the solution to this program recovers x 0 exactly provided that the fraction of errors is not too large.…”

“…Some examples of ℓ 1 type methods for sparse design in engineering include Vandenberghe et al [11,12] for designing sparse interconnect wiring, and Hassibi et al [13] for designing sparse control system feedback gains. In [14], Dahleh and Diaz-Bobillo solve controller synthesis problems with an ℓ 1 criterion, and observe that the optimal closed-loop responses are sparse.…”

Compressed Sensing With Quantized Measurements

“…In statistics, the idea of regularization is used in the well known Lasso algorithm [7] for feature selection. Other uses of based methods include total variation denoising in image processing [8], [9], circuit design [10], [11], sparse portfolio optimization [12], and trend filtering [13]. Several recent papers address the problem of quantized compressed sensing.…”

Mixed state estimation for a linear Gaussian Markov model

“…Some recent examples include compressed sensing [16] and sparse decoding [17]. Other applications that use convex relaxations include portfolio optimization with transaction costs [18], controller design [19], circuit design [20], and sensor selection [21]. In our previous work [22] we used a convex relaxation technique for the problem of fault identification in a static setting.…”