LIF and Simplified SRM Neurons Encode Signals Into Spikes via a Form of Asynchronous Pulse Sigma-Delta Modulation

We show how two spiking neuron models encode continuous-time signals into spikes (action potentials, time-encoded pulses, or point processes) using a special form of sigma-delta modulation (SDM). In particular, we show that the well-known leaky integrate-and-fire (LIF) neuron and the simplified spike response model (SRM₀) neuron encode the continuous-time signals into spikes via a proposed asynchronous pulse SDM (APSDM) scheme. The encoder is clock free using level-crossing sampling with a single-level quantizer, unipolar signaling, differential coding, and pulse-shaping filters. The decoder, in the form of a low-pass filter or bandpass smoothing filter, can be fed with the spikes to reconstruct an estimate of the signal. The density of the spikes reflects the amplitude of the encoded signal. Numerical examples illustrating the concepts and the signaling efficiency of APSDM vis-à-vis SDM for comparable reconstruction accuracies are presented. We anticipate these results will facilitate the design of spiking neurons and spiking neural networks as well as cross fertilizations between the fields of neural coding and the SDM.