A Bio-inspired Redundant Sensing Architecture
Sensing is the process of deriving signals from the environment that allows artificial systems to interact with the physical world. The Shannon theorem specifies the maximum rate at which information can be acquired [1]. However, this upper bound is hard to achieve in many man-made systems. The biological visual systems, on the other hand, have highly efficient signal representation and processing mechanisms that allow precise sensing. In this work, we argue that redundancy is one of the critical characteristics for such superior performance. We show architectural advantages by utilizing redundant sensing, including correction of mismatch error and significant precision enhancement. For a proof-of-concept demonstration, we have designed a heuristic-based analog-to-digital converter -a zero-dimensional quantizer. Through Monte Carlo simulation with the error probabilistic distribution as a priori, the performance approaching the Shannon limit is feasible. In actual measurements without knowing the error distribution, we observe at least 2-bit extra precision. The results may also help explain biological processes including the dominance of binocular vision, the functional roles of the fixational eye movements, and the structural mechanisms allowing hyperacuity.
The authors introduce an architecture for introducing redundancy in the reference value sets used by various ADC techniques (e.g. SAR). These degrees of freedom potentially allow one to optimize the combinations of references used to generate a threshold/comparison-point so as to minimize the error from component mismatch. An ADC circuit has been fabricated to implement such techniques, and they are indeed found to reduce mismatch error.
Update in response to author's rebuttal: Many thanks to the authors for taking the time to consider my points and to respond to them. In general, I would say that I look forward to seeing a revised version of the paper that makes the adjustments the authors promise, but the promised changes are sufficiently significant that (sight unseen) I only feel comfortable bumping up the technical quality by a point. My detailed responses to the responses, in order: -I do understand it is difficult to discuss too much prior work in the redundancy-for-mismatch-reduction space given the 9 page limitation. Nonetheless there is a complete absence of this at present in the paper, which may even count as a fatal flaw. (As an aside, note that McNeill's (JSSC 2005) work does *not* increase either power consumption or chip area (therein lies the innovation), although the authors are absolutely correct in noting that off-chip calibration power/space is unaccounted for. This is the kind of "Related work" discussion I would have appreciated seeing in the paper.) -While it is reassuring that the authors are planning to introduce more implementation details, my interest is less in the detailed implementation details and more in better motivation for the algorithmic choices that are made. With that said, if the paper were to spend more time discussing their (significant) contributions on the hardware implementation end, what I see as flaws in the algorithmic presentation would be far more forgivable. -The language may be simple, but it is surprisingly difficult to extract the core algorithmic ideas from a reading of the paper. This could very well be a reading comprehension issue on my end, but I doubt it. -Understood and agreed on the purpose of the simulation/implementation, and glad to hear that the authors are considering contrasting to stronger baselines. -I appreciate the clarification re: eq (5). It does make more sense to me now. -The author's listing of their assumptions in their rebuttal is much appreciated, but it is very difficult to parse from the paper. A similarly rational motivation for the structure of their design (N0/N1/etc.), as they promise, would also help a great deal. -Scalar quantization is 1-dimensional quantization. I remain unclear on why the authors are referring to it as zero-dimensional quantization (a term I neither understand nor have heard before --- and a simple google search seems to confirm its lack of usage in the literature).  Positives:  -The fundamental idea explored by the authors --- the use of redundancy to reduce mismatch errors --- is a compelling one. I would add that they are far from the first to explore this fertile area; see, for instance, McNeill's work (JSSC 2005, “Split ADC” Architecture for Deterministic Digital Background Calibration of a 16-bit 1-MS/s ADC). Their approach in adjusting which components to utilize represents a significant improvement over post-processing calibration. As the authors note, there are numerous situations where information is simply beyond recovering in the latter case. -While I am generally suspicious of "neural" analogies, the authors do an admirable job of drawing inspiration from the human visual system while optimizing a clear practical objective. -The authors implement their proposed solution not only in software and through simulations, but by fabricating an actual circuit. This adds tremendously to the credibility of their results. With that said, the authors do not go into details about their hardware implementation or its validation, and the focus of my review is on their algorithmic work (the authors themselves note that the hardware implementation is to be described elsewhere).  (bigger) areas for improvement: -Fundamentally, I do not feel that the justification and explanation of the authors' algorithmic contributions is up to the NIPS standard. More on this below. -A lesser concern is the virtual lack of comparison to alternatives/nontrivial-baselines, either in terms of mismatch error vs quantization error, or in terms of the power/area tradeoff the authors frequently make reference to. This makes it very difficult to objectively evaluate the authors' contributions. -The model for binary coding introduced in Sec 2.2 is extremely difficult to follow ---one has to read through multiple times just to understand the terminology. What is a unit cell, versus a reference, versus a component? I was only able to piece this together through a combination of domain knowledge and guesswork from the expressions.  -Furthermore, there is a lack of motivation for the binary coding approach beyond its use in "artificial systems" (it's relevant for SAR etc., but the authors provide no references or examples for this). This is critical, as the entire space of optimizations the authors are concerned with exist within this paradigm. -The model for component noise (eq. (5)) is supplied without any justification, either in words or in citations. Why, for instance, does the variance scale with the mean? Why not the standard deviation? -The description of the scheme in Section 3 is extraordinarily painful to decode. I would feel genuinely uncomfortable seeing this manuscript published the way this is currently written. One has to read the section twice to even understand the basic architecture that is being used, and terminology is used without any introduction/definition (e.g. the use of \hat{c} versus c --- there may even be a typo on line 269 as the \hat is used in the argument but not the subscript, but I would not be able to swear by this, as the \hat significance is never provided.). -Related to the above, the form of the proposed solution (eq. (8)) is not sufficiently motivated or justified. A red flag: not only do the authors never explain the purpose/intuition behind parameters N_0/N_1/s_1, but they later turn to simulations (lines 310-313) just to explain their impact on the solution. If there are simple  insights that lead one to the system designed by the authors, this manuscript certainly does not make them clear. -Results reported for DNL/INL make for fantastic confirmations that the techniques proposed work in practice. With that said, confirmation of functionality is insufficient in a space as crowded as this one (mismatch calibration/correction), and performance needs to be compared against nontrivial and informative baselines.  (smaller) areas/points for improvement: -The authors frequently refer to scalar quantization as zero-dimensional. Unless I am missing something big, I believe they mean one-dimensional. -Eq. (6): should NOT index c_i by i, since that index is being used with a different interpretation by X_i. -line 213: should be fig. 3(a).  -What is fig. 3a showing? Expected absolute error over many samples, or a single sample? -line 241: \in [0,1] should be \in \{0,1\}, as the former refers to the unit interval.