Fully Analog Noise-Resilient Dynamical Systems Storing Binary Sequence

Abstract

This paper presents fully analog noise-resilient dynamical systems for storing a binary sequence. The proposed dynamical system is a gradient descent dynamical system based on a potential energy function defined based on a parity check matrix of a binary linear code. We assume that the dynamical system operates with stochastic disturbances such as thermal noises. We formulate the whole system, including stochastic disturbances, using stochastic differential equations (SDE). From a discretized stochastic difference equation, i.e., the Euler-Maruyama equation, we can study the covariance evolution of error vectors regarding the random walk of the system state around an equilibrium state. Some numerical evaluations for the (7,4) Hamming code and related codes indicate the robustness of the proposed dynamical system against the stochastic disturbances.