Gaussian source compression rates precisely quantified with new math

Exact Second-Order Asymptotics for the Gaussian Gray--Wyner Problem

Information Theory

Summary

Compressing sounds or signals that come from two connected sources is a tricky problem. The authors focus on signals that behave like a Gaussian distribution, which is common in nature and engineering. They improved understanding by finding exact formulas for how much information can be compressed without losing too much quality, considering not just the average case but also more detailed behavior when compressing large amounts of data. Their new math tool groups signals by how their power spreads, helping to better guarantee compression quality. This work sharpens how engineers can design systems that compress related data efficiently with reliable quality.

What this means in practice

  • For data compression engineers: Design compression schemes for correlated Gaussian data with guaranteed distortion probabilities.
  • For signal processing teams: Optimize lossy compression of jointly distributed signals in communication or storage systems using precise second-order rate tradeoffs.

A theory result. No direct application yet.

Authors

Lin Zhou, Lei Yu

Abstract

We revisit the Gray-Wyner problem of lossy compression of bivariate Gaussian sources under the quadratic distortion measure and derive the exact second-order asymptotics. Specifically, we first identify the boundary rate tuples using the explicit first-order asymptotics by Yu (TIT 2023) and then characterize the tradeoff among three second-order coding rates subject to a constraint on the joint excess-distortion probability. Our main contribution is the achievability proof, where we derive a covariance shell covering lemma that is analogous to the type covering lemma for the discrete case. In particular, our covering lemma classifies the source sequences into power shell types via their empirical covariance matrix. For each such power shell type, we derive sufficient conditions on the compression rates so that covering within distortion levels are achievable. Finally, asymptotical analysis via the Berry-Esseen theorem yields the desired result.
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