Delta–Sigma Cellular Automata for Analog VLSI Random Vector Generation

We present a class of analog cellular automata for parallel analog random vector generation, including theory on the randomness properties, scalable parallel very large scale integration (VLSI) architectures, and experimental results from an analog VLSI prototype with 64 channels. Linear congruential coupling between cells produces parallel channels of uniformly distributed random analog values, with statistics that are uncorrelated both across channels and over time. The cell for each random channel essentially implements a switched-capacitor delta–sigma modulator, and measures 100 m 120 m in 2 m CMOS technology. The 64 cells are connected as a MASH cascade in a chain or ring topology on a two-dimensional (2-D) grid, and can be rearranged for use in various VLSI applications that require a parallel supply of random analog vectors, such as analog encryption and secure communications, analog builtin self-test, stochastic neural networks, and simulated annealing optimization and learning.