A Non-Uniform Quantization Framework for Time-Encoding Machines

TL;DR

This paper introduces a non-uniform quantization scheme for time encoding machines that leverages the inherent non-uniform distribution of firing intervals, significantly improving efficiency and accuracy over uniform quantization methods.

Contribution

It develops a power-law-based non-uniform quantization framework tailored to the firing interval distribution in TEMs, outperforming uniform quantization in power and error metrics.

Findings

NUQ outperforms UQ under the same bit budget.

TEM--NUQ achieves lower error at half the transmission cost.

Distribution-aware quantization enhances efficiency and accuracy.

Abstract

Time encoding machines (TEMs) provide an event-driven alternative to classical uniform sampling, enabling power-efficient representations without a global clock. While prior work analyzed uniform quantization (UQ) of firing intervals, we show that these intervals are inherently non-uniformly distributed, motivating the use of non-uniform quantization (NUQ). We derive the probability distribution of firing intervals for a class of bandlimited signals and design a power-law-based NUQ scheme tailored to this distribution. Simulations demonstrate that NUQ significantly outperforms UQ under the same bit budget. We also compare TEMs with non-uniform sampling (NUS), where both amplitudes and timings require quantization, and show that TEM--NUQ achieves lower error at half the transmission cost. These results highlight the advantages of distribution-aware quantization and establish TEM--NUQ as an efficient alternative to conventional UQ and NUS schemes.