Fault-Tolerant Clock Synchronization with High Precision

Kinali, Attila; Huemer, Florian; Lenzen, Christoph

doi:10.1109/isvlsi.2016.88

“…While the softwarehardware based implementations of TTP and FlexRay achieve a precision in the order of microseconds, higher operating frequencies ultimately require a pure hardware implementation. Recently, an implementation of the algorithm of Lundelius Welch and Lynch based on an FPGA has been presented by Kinali et al [19]. All known implementations, however, synchronize potentially metastable inputs before computations -a technique that becomes less reliable with increasing operating frequencies, since less time is available for metastability resolution.…”

Section: Components For Clock Synchronizationmentioning

confidence: 99%

Metastability-Containing Circuits

Friedrichs

¹

,

Függer

²

,

Lenzen

³

2018

IEEE Trans. Comput.

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In digital circuits, metastability can cause deteriorated signals that neither are logical 0 or logical 1, breaking the abstraction of Boolean logic. Unfortunately, any way of reading a signal from an unsynchronized clock domain or performing an analog-to-digital conversion incurs the risk of a metastable upset; no digital circuit can deterministically avoid, resolve, or detect metastability (Marino, 1981). Synchronizers, the only traditional countermeasure, exponentially decrease the odds of maintained metastability over time. Trading synchronization delay for an increased probability to resolve metastability to logical 0 or 1, they do not guarantee success.We propose a fundamentally different approach: It is possible to contain metastability by finegrained logical masking so that it cannot infect the entire circuit. This technique guarantees a limited degree of metastability in -and uncertainty about -the output.At the heart of our approach lies a time-and value-discrete model for metastability in synchronous clocked digital circuits. Metastability is propagated in a worst-case fashion, allowing to derive deterministic guarantees, without and unlike synchronizers. The proposed model permits positive results and passes the test of reproducing Marino's impossibility results. We fully classify which functions can be computed by circuits with standard registers. Regarding masking registers, we show that they become computationally strictly more powerful with each clock cycle, resulting in a non-trivial hierarchy of computable functions.Demonstrating the applicability of our approach, we present the first fault-tolerant distributed clock synchronization algorithm that deterministically guarantees correct behavior in the presence of metastability. As a consequence, clock domains can be synchronized without using synchronizers, enabling metastability-free communication between them.

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Self-stabilizing Byzantine Clock Synchronization with Optimal Precision

Khanchandani

¹

,

Lenzen

²

2016

Lecture Notes in Computer Science

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In the Byzantine-tolerant clock synchronization problem, the goal is to synchronize the clocks of n fully connected nodes. The clocks run at rates between 1 and ϑ > 1, and messages have a delay (including computation) between d − U and d. Moreover, up to f < n/3 of the nodes can fail by deviating arbitrarily from the protocol, i.e., are Byzantine. Despite this interference, correct nodes need to generate distinguished events (or pulses) almost simultaneously and periodically. The quality of the solution is measured by the skew, which is the maximum real time difference between corresponding pulses. In the self-stabilizing setting, in addition we allow for transient failures, possibly of all nodes. Once transient faults have ceased and at most f nodes remain faulty, the system should start generating synchronized pulses again. We design a self-stabilizing solution to this problem with asymptotically optimal skew. We achieve our goal by refining and extending the protocol of Lynch and Welch and make the following contributions in the process.-We give a simple analysis of the Lynch and Welch protocol with improved bounds on skew and tolerable difference in clock rates by rebuilding upon the main ingredient of their protocol, called approximate agreement. -We give a modified version of the protocol so that the frequency and amount of communication between the nodes is reduced. The modification adds a step to adjust the clock rates by another application of approximate agreement. The skew bound achieved is asymptotically optimal for suitable choices of parameters. -We present a method to add self-stabilization to the above protocols while preserving their skew bounds. The heart of the method is a coupling scheme that leverages a self-stabilizing protocol with a larger skew.

show abstract

Self-Stabilizing Byzantine Clock Synchronization with Optimal Precision

Khanchandani

¹

,

Lenzen

²

2018

Self Cite

View full text Add to dashboard Cite

In the Byzantine-tolerant clock synchronization problem, the goal is to synchronize the clocks of n fully connected nodes. The clocks run at rates between 1 and ϑ > 1, and messages have a delay (including computation) between d − U and d. Moreover, up to f < n/3 of the nodes can fail by deviating arbitrarily from the protocol, i.e., are Byzantine. Despite this interference, correct nodes need to generate distinguished events (or pulses) almost simultaneously and periodically. The quality of the solution is measured by the skew, which is the maximum real time difference between corresponding pulses. In the self-stabilizing setting, in addition we allow for transient failures, possibly of all nodes. Once transient faults have ceased and at most f nodes remain faulty, the system should start generating synchronized pulses again. We design a self-stabilizing solution to this problem with asymptotically optimal skew. We achieve our goal by refining and extending the protocol of Lynch and Welch and make the following contributions in the process.-We give a simple analysis of the Lynch and Welch protocol with improved bounds on skew and tolerable difference in clock rates by rebuilding upon the main ingredient of their protocol, called approximate agreement. -We give a modified version of the protocol so that the frequency and amount of communication between the nodes is reduced. The modification adds a step to adjust the clock rates by another application of approximate agreement. The skew bound achieved is asymptotically optimal for suitable choices of parameters. -We present a method to add self-stabilization to the above protocols while preserving their skew bounds. The heart of the method is a coupling scheme that leverages a self-stabilizing protocol with a larger skew.

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Fault-Tolerant Clock Synchronization with High Precision

Cited by 5 publications

References 15 publications

Metastability-Containing Circuits

Metastability-Containing Circuits

Self-stabilizing Byzantine Clock Synchronization with Optimal Precision

Self-Stabilizing Byzantine Clock Synchronization with Optimal Precision

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