Statistical inference with unreliable binary observations

We describe a novel statistical inference approach to data conversion for mixed-signal interfaces. We propose a data conversion architecture in which a signal is observed by a set of sensors with uncertain parameters, such as highly scaled comparator circuits in an analog-to-digital converter. These sensor outputs are not used to form a quantized representation of the signal but are used directly to make decisions in statistical inference problems such as parameter estimation, classification, and signal detection. We derive a mathematical model of this system and apply information-theoretic tools to describe the achievable performance of such a converter in information processing systems. In particular, we find asymptotic expressions for Fisher information and Kullback-Leibler divergence in terms of the design parameters and the sensor statistics. Simulations of parameter estimation, classification, and symbol detection systems show that these architectures can achieve strong performance even when the devices have significant process variations. We also discuss practical system design and implementation issues including sensor calibration and propose a lower-complexity suboptimal estimation architecture. The analytical and simulation results suggest that it is both possible and practical to build information processing systems using unreliable mixed-signal components