2012 12th IEEE International Conference on Nanotechnology (IEEE-NANO) The International Conference Centre Birmingham 20-23 August 20112, Birmingham, United Kingdom Degradation Stochastic Resonance (DSR) in AD-AVG Architectures Nivard Aymerich, Sorin Cotofana and Antonio Rubio Ahstrct- This paper introduces for the frst time the Degra dation Stochastic Resonance (DRS) efct observed in the Adaptive Averaging ( AD-AVG) architecture. This phenomenon, closely related to the well-known Suprathreshold Stochastic Resonance ( SSR), infuences the AD-AVG behavior for specifc noise conditions and causes a yield improving efct over the degradation in time. In this article we analyze this counter intuitive efect and explain the most relevant features. We observe, for example, that the yield of 20-input AD-AVG with 0.4 V of noise in the variability monitor increases from 0.93 to 0.97 after particular amounts of degradation. I. INTRODUCTION New emerging device technologies may sufer from a reduced device quality. Along with the benefts of smaller size, low power consumption and high performance, future technologies are expected to have associated higher levels of process and environmental variations as well as performance degradation due to the high stress of materials [1], [ 2], [ 3], [4]. The development of fault-tolerant architectures emerges as a key research topic at the present. Currently, most of the fault-tolerant techniques rely on the use of majority gates [5], [6]. A successful alternative to majority gates is the averaging cell (AVG) [7], [8], [9], which exhibits higher reliability at lower cost based on the average of the input replicas. This approach is quite effective in case the inputs are subject to independent drifts with similar magnitude. However, this condition is no longer valid for the current technologies. To optimize the AVG architecture in heterogeneous drift environments we proposed the Adaptive Average cell (AD AVG) [10]. This enhanced AVG technique is capable of tolerating non homogeneous input drifts and the effects of degradation by cleverly adapting the input weight values. The AD-AVG has been analyzed in detail in previous papers [10], but recently it has been discovered an interesting but not so intuitive effect that deserves a specifc justifcation. In this paper we describe for the frst time a stochastic resonance phenomenon discovered in the behavior of the AD-AVG at specifc conditions. This counter-intuitive effect takes places in the AVG structure as result of the infuence of degradation in the hardware combined with the noise affect ing the variability monitor used to reconfgure the averaging weights. The so-called Degradation Stochastic Resonance (DSR) efect is related to the well-known Suprathreshold Stochastic Resonance (SSR), which was frst analyzed by Stocks in 2000 [11]. DSR basically involves an enhancement in the behavior of a signal processing system (AD-AVG) subject to noise and degradation. In the following sections we present the AD-AVG structure, the statistical models used to analyze its behavior and demonstrate the impact of DSR efect in the reliability of this fault-tolerant architecture. II. THE A DAPTIVE AVERAGING CELL (AD-AVG) The AD-AVG architecture, graphically depicted in Fig ure 1, is a fault-tolerant technique based on hardware re dundancy. It calculates the most probable value of a binary variable from a set of error-prone physical replicas. The AD AVG is demonstrated to tolerate high amounts of heteroge neous variability and accumulated degradation in the physical replicas [10]. g Fig. 1. Adaptive Averaging ceU (AD-AVG) architecture. The AD-AVG operation is based on a weighted average of R input replicas Yi of a binary variable y. i = 1, ... ,R (1) Each replica Yi is afected by an independent drif T)i that alters the ideal value y. The Yi signals are represented in the system by continuous voltage levels, where 0 and Vee stand for ideal logical values '0' and '1', respectively. Without loss of generality we use Vee = 1 V. The AD-AVG output f is an estimation of Y according to ( 2). R Y ' = L CiYi i =l , { Vee Y= o if y ' > Vee/2 if y ' < Vee/2 ( 2) We model drif magnitudes as Gaussian random variables with null mean and different standard deviation levels T)i r N(O, ai) . The averaging weights Ci are normalized to the unity, i.e., 2!1 Ci = 1, and their optimal values for the reliability purpose are: 2 a y l mn Ci = -- 2 - a i i = 1, ... ,R. ( 3) Where a; , mn corresponds to the minimum achievable weighted average variance. The input variances aT are es timated by means of a variability monitor that is subject to noise. We refer to the level of noise in the monitor with the parameter as. The averaging weights are reconfgured according to the input variance estimators and the optimal averaging weight values. A detailed presentation and discus sion about the optimal averaging weights' formula can be found in [10].