Noise shaping pulse - density modulation in inhibitory neural networks with subthreshold VLSI neuron circuits

An inhibitory network model that performs noise-shaping pulse-density modulation [1] was implemented with subthreshold analog MOS circuits, aiming at the development of ultralow-power Σ∆-type AD converters. Through circuit simulations, we evaluate the effects of the noise shaping produced by the network circuit. Keywords—VLSI, pulse density modulation, noise shaping, chaotic neural networks 1 Model and Method The network consists of N integrate-and-fire neurons (IFNs) with all-to-all inhibitory connections [1]. A common analog input is given to all the IFNs, while 1-bit digital output is given by the sum of firing events of the IFNs. Static and dynamic noises are introduced into the analog input and the reset potential of IFNs after each firing, respectively. Since the wiring complexity of the network; i.e., O(N) in [1], can be reduced to O(N) by introducing a global inhibitor [2], we designed a network circuit as shown in Fig. 1. The static and dynamic noises are given to the circuit as device mismatches of current sources (Ii) and external random (Poisson) spikes, respectively. Similarly, instead of applying dynamic noises to the circuits externally, we tried to use neuron’s intrinsic noises by using chaotic neuron units based on 3variable Lotka-Volterra system [3]. The network dynamics are given by ̇ x1,i = (h− x1,i − c x2,i − k yi)x1,i, ̇ x2,i = (a h− b x1,i − x2,i − yi)x2,i, ẏi = (−r h + α kx1,i + β x2,i)yi, h = Ii − w N N ∑