237907
IC power distribution challenges
With each technology generation, delivering a time-varying current with reduced nominal supply voltage variation is becoming more difficult due to increasing current and power requirements. The power delivery network design becomes much more complex and requires accurate analysis and optimizations at all levels of abstraction in order to meet the specifications. We describe techniques for estimation of the supply voltage variations that can be used in the design of the power delivery network. We also describe the decoupling capacitor hierarchy that provides a low impedance to the increasing high-frequency current demand and limits the supply voltage variations. Techniques for high-level power estimation that can be used for performance vs. power trade-offs to reduce the current and power requirements of the circuit are also presented.
12123652
Analysis of blocking dynamic circuits
In order for dynamic circuits to operate correctly, their inputs must be monotonically rising during evaluation. Blocking dynamic circuits satisfy this constraint by delaying evaluation until all inputs have been properly setup relative to the evaluation clock. By viewing dynamic gates as latches, we demonstrate that the optimal delay of a blocking dynamic gate may occur when the setup time is negative. With blocking dynamic circuits, cascading low-skew dynamic gates allows each dynamic gate to tolerate a degraded input level. The larger noise margin provides greater flexibility with the delay vs. noise margin trade-off (i.e. the circuit robustness vs. speed tradeoff). This paper generalizes blocking dynamic circuits and provides a systematic approach for assigning clock phases, given delay and noise margin constraints. Using this framework, one can analyze any logic network consisting of blocking dynamic circuits.
6282895
Timing analysis including clock skew
Clock skew is an increasing concern for high-speed circuit designers. Circuit designers use transparent latches and skew-tolerant domino circuits to hide clock skew from the critical path and take advantage of shared portions of the clock network to budget less skew between nearby elements than across the entire die, but current timing analysis algorithms do not handle correlated clock skews. This paper extends the Sakallah-Mudge-Olukotun (SMO) latch-based timing analysis to include different amounts of clock skew between different elements. The key change is that departure times from each latch must be defined with respect to launching clocks so that the skew between the launching and receiving clocks can be determined at each receiver. The exact analysis leads to an explosion in the number of timing constraints, but most constraints are not tight in practical situations and a modified version of the Szymanski-Shenoy relaxation algorithm gives exact results with only a small increase in runtime. The timing analysis formulation also captures the effects of skew on edge-triggered flip-flops, domino circuits, and min-delay constraints. Our exact algorithm, applied to a supercomputer node controller with over 12000 clocked elements, finds the system can run 50-90 ps faster than a single skew analysis would predict and requires searching fewer than 4% more latch departures than conventional algorithms. With the less conservative skew budgets enabled by better timing analysis, we expect clocked systems will remain viable to multi-GHz frequencies.
1870907
Macro-modeling concepts for the chip electrical interface
The power delivery network is made up of passive elements in the distribution network, as well as the active transistor loads. A chip typically has three types of power supplies that require attention: core, I/O, and analog. Core circuits consist of digital circuits and have the largest current demand. In addition to all of the system issues/models for the core, modeling the I/O subsystem has the additional requirement of modeling return paths and discontinuities. The analog circuits present yet a different challenge to the macro-modeling of the supply network because they place a tight demand on supply variations. This paper presents a design methodology on how to generate macro-models of the entire chip electrical interface. This methodology can be used by the chip, package, and system designers and is being used to design high-reliability servers.
53748903
A Framework for Designing Reusable Analog Circuits
7771298
Robust stability of a class of nonlinear time-varying discrete systems
This paper studies the problem of robust absolute stability of a class of nonlinear discrete-time systems with time-varying matrix uncertainties of polyhedral type and multiple time-varying sector nonlinearities. By using the variational method and the Lyapunov Second Method, criteria for robust absolute stability are obtained in different forms for the given class of systems. Specifically, we determine the parametric class of Lyapunov functions which defines the necessary and sufficient conditions of robust absolute stability. We apply these Lyapunov functions to derive an algebraic criterion for robust absolute stability in the form of solvability conditions of a set of matrix equations.
24184742
On Distance Two Labellings of Graphs
18721223
Phase analysis of circadian-related genes in two tissues
BackgroundRecent circadian clock studies using gene expression microarray in two different tissues of mouse have revealed not all circadian-related genes are synchronized in phase or peak expression times across tissues in vivo. Instead, some circadian-related genes may be delayed by 4–8 hrs in peak expression in one tissue relative to the other. These interesting biological observations prompt a statistical question regarding how to distinguish the synchronized genes from genes that are systematically lagged in phase/peak expression time across two tissues.ResultsWe propose a set of techniques from circular statistics to analyze phase angles of circadian-related genes in two tissues. We first estimate the phases of a cycling gene separately in each tissue, which are then used to estimate the paired angular difference of the phase angles of the gene in the two tissues. These differences are modeled as a mixture of two von Mises distributions which enables us to cluster genes into two groups; one group having synchronized transcripts with the same phase in the two tissues, the other containing transcripts with a discrepancy in phase between the two tissues. For each cluster of genes we assess the association of phases across the tissue types using circular-circular regression. We also develop a bootstrap methodology based on a circular-circular regression model to evaluate the improvement in fit provided by allowing two components versus a one-component von-Mises model.ConclusionWe applied our proposed methodologies to the circadian-related genes common to heart and liver tissues in Storch et al. [2], and found that an estimated 80% of circadian-related transcripts common to heart and liver tissues were synchronized in phase, and the other 20% of transcripts were lagged about 8 hours in liver relative to heart. The bootstrap p-value for being one cluster is 0.063, which suggests the possibility of two clusters. Our methodologies can be extended to analyze peak expression times of circadian-related genes across more than two tissues, for example, kidney, heart, liver, and the suprachiasmatic nuclei (SCN) of the hypothalamus.
769378
Efficient Distribution of Key Chain Commitments for Broadcast Authentication in Distributed Sensor Networks
Broadcast authentication is a fundamental security service in distributed sensor networks. A scheme named $\mu$TESLA has been proposed for efficient broadcast authentication in such networks. However, $\mu$TESLA requires initial distribution of certain information based on unicast between the base station and each sensor node before the actual authentication of broadcast messages. Due to the limited bandwidth in wireless sensor networks, this initial unicast-based distribution severely limits the application of $\mu$TESLA in large sensor networks. This paper presents a novel technique to replace the unicast-based initialization with a broadcast-based one. As a result, $\mu$TESLA can be used in a sensor network with a large amount of sensors, as long as the message from the base station can reach these sensor nodes. This paper further explores several techniques that improve the performance, the robustness, as well as the security of the proposed method. The resulting protocol satisfies several nice properties, including low overhead, tolerance of message loss, scalability to large networks, and resistance to replay attacks as well as some known Denial of Service (DOS) attacks.
53235721
Establishing pairwise keys in distributed sensor networks
Pairwise key establishment is a fundamental security service in sensor networks; it enables sensor nodes to communicate securely with each other using cryptographic techniques. However, due to the resource constraints on sensor nodes, it is not feasible to use traditional key management techniques such as public key cryptography and key distribution center (KDC). A number of key predistribution techniques have been proposed for pairwise key establishment in sensor networks recently. To facilitate the study of novel pairwise key predistribution techniques, this paper develops a general framework for establishing pairwise keys between sensor nodes using bivariate polynomials. This paper then proposes two efficient instantiations of the general framework: a random subset assignment key predistribution scheme, and a hypercube-based key predistribution scheme. The analysis shows that both schemes have a number of nice properties, including high probability, or guarantee to establish pairwise keys, tolerance of node captures, and low storage, communication, and computation overhead. To further reduce the computation at sensor nodes, this paper presents an optimization technique for polynomial evaluation, which is used to compute pairwise keys. This paper also reports the implementation and the performance of the proposed schemes on MICA2 motes running TinyOS, an operating system for networked sensors. The results indicate that the proposed techniques can be applied efficiently in resource-constrained sensor networks.