Online Conformal Compression for Zero-Delay Communication with Distortion Guarantees

TL;DR

This work introduces Online Conformal Compression (OCC), a zero-delay lossy compression scheme that uses a shared autoregressive predictor at both encoder and decoder to achieve deterministic per-sequence outage guarantees under a $0-1$ distortion with target $\alpha$. OCC relies on online conformal prediction to turn predictor outputs into adaptive prediction sets $\hat{\mathcal{X}}_t$, updating thresholds $\gamma_t$ to ensure long-run coverage while signaling outages in either synchronous or asynchronous transmission modes. The authors prove a distortion bound of $\alpha + \frac{1+\eta_1}{\eta_1 T^{1-\beta}}$ for learning rates $\eta_t = \eta_1 t^{-eta}$, $\beta \in [0,1)$, and validate the method on English text, showing OCC achieves compression rates close to an offline hindsight optimum and outperforms dropout-based baselines, especially in the synchronous setting. The results demonstrate OCC’s potential for adaptive, reliable, and low-latency lossy compression in online systems, with robust performance under non-stationary data distributions.

Abstract

We investigate a lossy source compression problem in which both the encoder and decoder are equipped with a pre-trained sequence predictor. We propose an online lossy compression scheme that, under a 0-1 loss distortion function, ensures a deterministic, per-sequence upper bound on the distortion (outage) level for any time instant. The outage guarantees apply irrespective of any assumption on the distribution of the sequences to be encoded or on the quality of the predictor at the encoder and decoder. The proposed method, referred to as online conformal compression (OCC), is built upon online conformal prediction--a novel method for constructing confidence intervals for arbitrary predictors. Numerical results show that OCC achieves a compression rate comparable to that of an idealized scheme in which the encoder, with hindsight, selects the optimal subset of symbols to describe to the decoder, while satisfying the overall outage constraint.

Figures (3)

• Figure 1: Block diagram representing the operation of the proposed online conformal compression (OCC) strategy for zero-delay coding with anytime deterministic outage guarantees.
• Figure 2: Average compression rate and outage rate versus the outage requirement $\alpha$.
• Figure 3: Average compression rate and outage rate versus the time index $t$.

Theorems & Definitions (3)

• Lemma 1
• proof
• Theorem 1