Strong Converse Exponent for Remote Lossy Source Coding

TL;DR

This work resolves the exponential strong converse for remote lossy source coding by precisely characterizing the correct-reconstruction exponent $E(R, \Delta)$. The authors derive a unified formula $E(R, \Delta) = \min_{Q_{XY}} D(Q_{XY}\|P_{XY}) + E(Q_{XY}, R, \Delta)$ with $E(Q_{XY}, R, \Delta) = \min_{Q_{\hat{X}|XY}: \mathbb{E}[d(X,\hat{X})]\le \Delta} I_Q(X;\hat{X}|Y) + |I_Q(Y;\hat{X}) - R|^{+}$, and prove both achievability and converse using the method of types. They establish that $E(R, \Delta) > 0$ whenever $R < R_r(P_{XY}, \Delta)$ and prove continuity in $R$, while also showing how the result recovers Csiszár–Körner's lossy coding and Kang et al.'s biometric authentication results as special cases. The analysis employs a type-based coding scheme with Berger’s type covering lemma and yields a simple, alternate converse, linking indirect rate-distortion with the information-spectrum framework. These findings illuminate the fundamental limits of remote sensing and biometric verification under distortion constraints and provide a robust tool for assessing reliability at finite rates.

Abstract

Past works on remote lossy source coding studied the rate under average distortion and the error exponent of excess distortion probability. In this work, we look into how fast the excess distortion probability converges to 1 at small rates, also known as exponential strong converse. We characterize its exponent by establishing matched upper and lower bounds. From the exponent, we also recover two previous results on lossy source coding and biometric authentication.

Theorems & Definitions (11)

• Theorem 1
• proof
• Proposition 1
• proof
• Corollary 1
• Corollary 2
• proof
• Lemma 1
• Remark 1
• Lemma 2