Analysis of Encoding Degradation in Spiking Sensors Due to Spike Delay Variation

Abstract

Spiking sensors such as the silicon retina and cochlea encode analog signals into massively parallel asynchronous spike train output where the information is contained in the precise spike timing. The variation of the spike timing that arises from spike transmission degrades signal encoding quality. Using the signal-to-distortion ratio (SDR) metric with nonlinear spike train decoding based on frame theory, two particular sources of delay variation including comparison delay $T_{\mathbf {DC}}$ and queueing delay $T_{\mathbf {DQ}}$ are evaluated on two encoding mechanisms which have been used for implementations of silicon array spiking sensors: asynchronous delta modulation and self-timed reset. As specific examples, $T_{\mathbf {DC}}$ is obtained from a 2T current-mode comparator, and $T_{\mathbf {DQ}}$ is obtained from an M/D/1 queue for 1-D sensors like the silicon cochlea and an $\text {M}^{\mathrm {\mathbf {X}}}$ /D/1 queue for 2-D sensors like the silicon retina. Quantitative relations between the SDR and the circuit and system parameters of spiking sensors are established. The analysis method presented in this work will be useful for future specifications-guided designs of spiking sensors.