Gaussian source rate-distortion function

Squared-error rate-distortion function of an iid zero-mean Gaussian source.

Specification version 1Published 2006-07-181 evidence records

About this problem

The question, scope, and sources behind this Registry record.

Formal question

Determine the minimum rate for an iid Gaussian source of variance sigma squared under mean-squared error D.

Scope & constraints

source: iid zero-mean Gaussian
logBase: 2
variance: sigma^2
distortion: mean squared error

Primary sources

Elements of Information Theory, second edition — Gaussian source rate-distortion function Chapters 2, 5, 7, 10, 13 and 15

What we know

Current frontiers derived from accepted Claims.

Exact established valueR(D) = (1/2) log2(sigma^2/D) for 0<D<sigma^2; 0 for D>=sigma^2

The accepted equality closes this optimization result.

Claims

Assertions tied to evidence, attribution, and review.

2026

CLM-INFO-003212= R(D) = (1/2) log2(sigma^2/D) for 0<D<sigma^2; 0 for D>=sigma^2EXACT VALUEThe cited theorem establishes R(D) = (1/2) log2(sigma^2/D) for 0<D<sigma^2; 0 for D>=sigma^2 under the current specification; this does not assert universal empirical attainability.Source: Elements of Information Theory, second edition — Gaussian source rate-distortion function ↗

PROVEN

Timeline

The frontier as it changed over time.

How this frontier is derived

Only accepted Claims matching the current specification contribute to the displayed bounds. Strict inequalities remain open; contradictory Claims require editorial review.

—No breakthrough events recorded yetEvents appear here when an accepted Claim tightens a bound or closes the frontier.