Segment Delay Learning From Quantized Path Delay Measurements

Our understanding on a silicon chip is limited due to low measurement resolution or model-silicon miscorrelation including variations. This paper shows that chips are better understood by combining noisy measurement results and model information through a mathematical algorithm. Our proposed method learns segment delays in logic circuits from quantized path delay measurements using ridge regression. During the learning process, we take advantage of both nominal segment delays and the delay sensitivity with respect to variations. We also interpret the ridge regression in Bayesian context and in doing so, propose an analytic formula to set the regularization parameter of the ridge regression. For the silicon measurement environments where low measurement resolution is the dominant source of measurement noise, this formula allows us to predict post-silicon results more accurately and speed up the algorithm eliminating inefficient and inaccurate cross-validation. We also demonstrate our method in enhancing the resolution of already measured path delays. We learn segment delays from quantized path delay measurements and predict the path delays prior to the quantization. Our simulation results show that the predicted path delays are much closer to actual values than the measured values and the nominal values.