# Fold First, Detect Directly: Communication Symbol Detection Without Unfolding for Low-Bitrate Modulo-ADCs

arXiv: https://arxiv.org/abs/2609.11298 · HTML: https://mlsanity.com/paper/2609.11298/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 10 Sep 2026.

## Builds on (most cited first, 13 of 13)

- [Unlimited Sampling from Theory to Practice: Fourier-Prony Recovery and Prototype ADC](https://mlsanity.com/paper/2105.05818/) (2021)
- [Data-driven Estimation of Sinusoid Frequencies](https://mlsanity.com/paper/1906.00823/) (2019)
- [Above the Nyquist Rate, Modulo Folding Does Not Hurt](https://mlsanity.com/paper/1903.12289/) (2019)
- [Back in the US-SR: Unlimited Sampling and Sparse Super-Resolution with its Hardware Validation](https://mlsanity.com/paper/2207.13230/) (2022)
- [Residual Recovery Algorithm For Modulo Sampling](https://mlsanity.com/paper/2110.03335/) (2021)
- [The Surprising Benefits of Hysteresis in Unlimited Sampling: Theory, Algorithms and Experiments](https://mlsanity.com/paper/2111.12675/) (2021)
- [λ-MIMO: Massive MIMO via Modulo Sampling](https://mlsanity.com/paper/2210.10193/) (2022)
- [Robust Unlimited Sampling Beyond Modulo](https://mlsanity.com/paper/2206.14656/) (2022)
- [Unlimited Sampling of Bandpass Signals: Computational Demodulation via Undersampling](https://mlsanity.com/paper/2307.04917/) (2023)
- [A Learning-Based Framework for Line-Spectra Super-resolution](https://mlsanity.com/paper/1811.05844/) (2018)
- [Spiked Covariance Estimation from Modulo-Reduced Measurements](https://mlsanity.com/paper/2110.01150/) (2021)
- [A Hardware Prototype of Wideband High-Dynamic Range ADC](https://mlsanity.com/paper/2301.09609/) (2023)
- [Blind-Adaptive Quantizers](https://mlsanity.com/paper/2409.04077/) (2024)

## Abstract (arXiv)

Modulo-folding analog-to-digital converters (MF-ADCs) enable low-dynamic-range quantizers to sample high-amplitude signals without clipping. However, downstream processing traditionally relies on waveform unfolding algorithms, which require high oversampling rates and are highly sensitive to noise. For communication receivers, where the goal is symbol detection rather than signal reconstruction, unfolding is a redundant intermediate step. In this paper, we propose an unfolding-free maximum-likelihood symbol-detection framework for oversampled MF-ADCs in the presence of joint channel and quantization noise. By leveraging modulo wrap cancellation, we derive an exact, single-term Mahalanobis-distance metric that operates directly on folded observations. To handle long sequences, we introduce a parallelized block search algorithm that reduces computational complexity to scale linearly with sequence length. Simulations show our detector significantly outperforms existing unfolding baselines and approaches unclipped conventional ADC performance.