Wyner–Ziv rate-distortion bound

Rate-distortion function with correlated side information only at the decoder.

Specification version 1Published 1976-01-011 evidence records

About this problem

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

Formal question

Determine minimum lossy source-coding rate when correlated side information Y is available only to the decoder.

Scope & constraints

sources: iid pairs (X,Y)
markovChain: U-X-Y
reconstruction: Xhat=g(U,Y)
finiteAlphabets: true
expectedDistortion: <=D

Primary sources

The rate-distortion function for source coding with side information at the decoder — Wyner–Ziv rate-distortion bound Main theorem

What we know

Current frontiers derived from accepted Claims.

Exact established valueR_WZ(D) = min [I(X;U)-I(Y;U)]

The accepted equality closes this optimization result.

Claims

Assertions tied to evidence, attribution, and review.

2026

CLM-INFO-003217= R_WZ(D) = min [I(X;U)-I(Y;U)]EXACT VALUEThe cited theorem establishes R_WZ(D) = min [I(X;U)-I(Y;U)] under the current specification; this does not assert universal empirical attainability.Source: The rate-distortion function for source coding with side information at the decoder — Wyner–Ziv rate-distortion bound ↗

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.

Specification

What question is being asked?

Constraints: sources=iid pairs (X,Y) · markovChain=U-X-Y · reconstruction=Xhat=g(U,Y) · finiteAlphabets=true · expectedDistortion=<=D

Read full specification ↗

Corrections & disputes

Record history

No unresolved corrections or disputes are recorded for this published version.

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Editorial status

Evidence-backed record

1 accepted Claim, with 1 linked evidence records.

Human-reviewed · No AI-only claims

Verified prizes & bounties

Active verified incentives

No active verified bounties are linked to this Limit.

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Reproducibility

Machine-checked history

No accepted machine-checked reproductions are recorded for this Limit.

Cite this LimitLimits Registry. LR-003217. Wyner–Ziv rate-distortion bound. 2026.