ACIF-TEM: Adaptive Compressed IF-TEM

• Adaptive Compressed IF-TEM (ACIF-TEM) is a clockless, adaptive architecture that combines dynamic bias tuning and segmented analog compression to digitize amplitude-bounded signals efficiently.
• It synergistically merges features of Adaptive IF-TEM and Compressed IF-TEM, reducing oversampling and quantization error while achieving up to 60% lower bit-rates compared to traditional methods.
• ACIF-TEM employs a two-step pulse-shrinking TDC and iterative reconstruction to maintain high precision, making it ideal for energy-constrained edge sensing and distributed acquisition systems.

Adaptive Compressed Integrate-and-Fire Time Encoding Machine (ACIF-TEM) is a signal acquisition architecture that synergistically combines adaptive sampling and analog compression within a fully integrated, clockless time-to-digital conversion framework. Building upon the power-efficient Integrate-and-Fire Time Encoding Machine (IF-TEM), ACIF-TEM integrates adaptive bias control from Adaptive IF-TEM (AIF-TEM) and pre-quantization analog compression from Compressed IF-TEM (CIF-TEM), with each component reinforcing the performance and efficiency of the other. ACIF-TEM is shown to realize substantial bit- and energy-reductions compared to all prior IF-TEM variants, particularly in practical audio-band and quasi-stationary signal regimes (Karp et al., 4 Nov 2025).

1. Signal Model and Motivations

ACIF-TEM targets amplitude-bounded and bandlimited analog signals $x(t)$, satisfying $|x(t)|\leq c_{\max}$ and $X(\omega)=0$ for $|\omega|>\Omega$, with total finite energy $E$. In standard analog-to-digital conversion, Nyquist sampling at $2\Omega$ Hz leads to uniform bit allocation and power-intensive, high-rate digital circuitry. IF-TEM offers a clockless, asynchronous alternative by integrating $x(t)$ plus a static bias until a threshold is reached and emitting nonuniform firing times, with subsequent intervals $T_n = t_n - t_{n-1}$ encoding local signal amplitude (Karp et al., 4 Nov 2025).

However, classical IF-TEM reveals two core inefficiencies. First, a constant bias $b_{\mathrm{IF}} > c_{\max}$ results in oversampling during low-amplitude periods. Second, the time-to-digital converter (TDC) must quantize over the full dynamic range $\Delta t_{\max} - \Delta t_{\min}$, leading to non-optimal bit usage. These limitations motivate adaptive and compressed variants.

2. Component Architectures: AIF-TEM and CIF-TEM

Adaptive IF-TEM (AIF-TEM)

AIF-TEM addresses oversampling inefficiency by dynamically tuning the bias $|x(t)|\leq c_{\max}$0 to local amplitude statistics. At each firing $|x(t)|\leq c_{\max}$1, the bias is set with a margin: $|x(t)|\leq c_{\max}$2, using a Max-Amplitude Predictor (MAP) that estimates the maximum $|x(t)|\leq c_{\max}$3 over a preceding window. This adaptation ensures the integrator output remains strictly increasing and the inter-firing interval $|x(t)|\leq c_{\max}$4 is tightly bounded: $|x(t)|\leq c_{\max}$5 where $|x(t)|\leq c_{\max}$6 is an integrator gain and $|x(t)|\leq c_{\max}$7 the comparator threshold. Amplitude adaptation reduces average oversampling and enables local control over both rate and quantization (Omar et al., 2024).

Compressed IF-TEM (CIF-TEM)

CIF-TEM applies a compression transformation prior to quantization by partitioning the interval range $|x(t)|\leq c_{\max}$8 into $|x(t)|\leq c_{\max}$9 segments. Each $X(\omega)=0$0 is mapped to a segment index $X(\omega)=0$1 and a residual $X(\omega)=0$2 via

$X(\omega)=0$3

with only infrequent index updates (i.e., $X(\omega)=0$4) incurring additional bits. The residual is then uniformly quantized within its segment, substantially reducing quantization error and total bit-rate over conventional IF-TEM for stationary or slowly varying signals (Tarnopolsky et al., 2022).

3. ACIF-TEM: Integrated Synergistic Design

ACIF-TEM fuses AIF-TEM's bias adaptation and CIF-TEM's segmental compression into a unified workflow. In Stage 1, the MAP-driven adaptive bias produces a dynamically range-restricted set of intervals $X(\omega)=0$5. In Stage 2, a bias-driven segmentator—tied to local amplitude statistics—parcels the remaining interval range into $X(\omega)=0$6 segments. Both adaptation and compression logic are physically integrated in a clockless, two-step pulse-shrinking (2PS) TDC, eliminating the need for high-frequency clocks and extra latches.

Notably, segment granularity in ACIF-TEM is computed as

$X(\omega)=0$7

where $X(\omega)=0$8 is the run-time estimate of local amplitude variance and $X(\omega)=0$9 the total quantization levels. This self-tuning ensures locally optimal trade-offs between segment width and quantization precision. Updates occur every $|\omega|>\Omega$0 events, amortizing computational overhead and ensuring adaptation tracks abrupt signal changes (Karp et al., 4 Nov 2025).

2PS TDC Operation

Each firing interval $|\omega|>\Omega$1 passes through $|\omega|>\Omega$2 coarse and $|\omega|>\Omega$3 fine shrinking stages. The output is reconstructed as

$|\omega|>\Omega$4

where $|\omega|>\Omega$5, $|\omega|>\Omega$6, and $|\omega|>\Omega$7. Bit usage is minimized since only the segment index (coarse) and fine position need to be stored per event.

4. Sampling–Quantization Analysis and Reconstruction

The ACIF-TEM reconstruction pipeline employs standard IF-TEM inversion algorithms: the (possibly nonlinear) mapping from digitized $|\omega|>\Omega$8 to the analog signal $|\omega|>\Omega$9 is solved using iterative kernel expansions over sinc-basis centered at appropriately chosen time points, with convergence conditions enforced by construction via bias and segmentation strategies.

Distortion decomposes as $E$0, with quantization error for the two-step TDC bounded by $E$1. The overall bit-rate is analytically characterized as

$E$2

where $E$3 denotes ACIF-TEM's oversampling ratio, $E$4 the number of Nyquist-rate samples, and $E$5 the segment-change probability. In all cases, $E$6 and $E$7 for the same quantization resolution (Karp et al., 4 Nov 2025).

5. Empirical Performance and Comparative Evaluation

Empirical evaluation on audio signals (44.1 kHz bandwidth) demonstrates that ACIF-TEM achieves fixed MSE targets with substantially reduced bit usage compared to all baselines. For MSE $E$8 dB, the key metrics are as follows:

Sampler	Oversampling	Bits/event	Total bits	Compression
IF-TEM	$E$9	9	100 M	baseline
AIF-TEM	$2\Omega$0	7	78 M	22% vs IF-TEM
CIF-TEM	$2\Omega$1	7	70 M	30% vs IF-TEM
ACIF-TEM	$2\Omega$2	4	40 M	60% vs IF-TEM

“Bits per event” includes segment, residual, and amortized bias update bits. ACIF-TEM yields a 3-bit/event reduction compared to AIF-TEM and 60% total bit-rate reduction compared to IF-TEM (Karp et al., 4 Nov 2025). Direct-comparison experiments confirm that similar MSE levels require 1–2 fewer bits in ACIF-TEM than CIF-TEM, and that ACIF-TEM matches or exceeds “oracle” MAP performance (Omar et al., 2024, Tarnopolsky et al., 2022).

6. Implementation Considerations and Limitations

The ACIF-TEM architecture is fully asynchronous due to the 2PS TDC design, leading to low power dissipation and high immunity to process-voltage-temperature variations; no high-frequency clock is required. Correct operation requires the MAP block to conservatively estimate local amplitude maxima, as underestimation can violate the fundamental sampling criterion $2\Omega$3 and compromise reconstruction.

Segment update interval $2\Omega$4 trades off between control-loop stability and adaptation speed. In rapidly varying signals, run-length savings in segment index transmissions diminish, moderately attenuating compression efficiency. For extremely low-amplitude signals, the segment number $2\Omega$5 drops to its minimum and ACIF-TEM reduces to a simple TDC (Karp et al., 4 Nov 2025).

7. Context and Relation to Broader Research

ACIF-TEM extends the paradigm of asynchronous, nonuniform analog-to-digital sampling by integrating adaptive, compressive, and fully digital-efficient techniques within a unified converter. The synergistic design resolves both oversampling and quantization inefficiency. ACIF-TEM stands distinct from other variable-bias, variable-threshold, and event-based analog encoders by guaranteeing geometric convergence in iterative reconstruction while achieving bit-minimal, MSE-constrained operation on real signals (Yashaswini et al., 22 Jan 2026, Omar et al., 2024).

A plausible implication is that ACIF-TEM architectures are particularly attractive in edge sensing, neural recording, and bandwidth-constrained distributed acquisition systems where nonstationary signal variation and energy budget are critical constraints. However, adaptation speed and estimator reliability remain practical limitations, especially in hostile or fast-fluctuating environments.

In summary, ACIF-TEM provides a rigorously analyzed, empirically validated, and hardware-realistic solution for compressed, adaptive, and asynchronous analog-to-digital conversion in modern information processing pipelines (Karp et al., 4 Nov 2025, Tarnopolsky et al., 2022, Omar et al., 2024).