Physically degraded broadcast-channel capacity region

Two-user capacity region for a physically degraded discrete memoryless broadcast channel.

Specification version 1Published 1973-03-011 evidence records

About this problem

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

Formal question

Determine the two-user capacity region when X-Y-Z forms a physically degraded broadcast channel.

Scope & constraints

channel: two-user discrete memoryless broadcast
unionOver: p(u,x)
degradedMarkovChain: U-X-Y-Z
generalBroadcastChannelExcluded: true

Primary sources

Random coding theorem for broadcast channels with degraded components — Physically degraded broadcast-channel capacity region Capacity-region theorem

What we know

Current frontiers derived from accepted Claims.

Exact established valueR1 <= I(X;Y|U), R2 <= I(U;Z)

The accepted equality closes this optimization result.

Claims

Assertions tied to evidence, attribution, and review.

2026

CLM-INFO-003206= R1 <= I(X;Y|U), R2 <= I(U;Z)EXACT VALUEThe cited theorem establishes R1 <= I(X;Y|U), R2 <= I(U;Z) under the current specification; this does not assert universal empirical attainability.Source: Random coding theorem for broadcast channels with degraded components — Physically degraded broadcast-channel capacity region ↗

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: channel=two-user discrete memoryless broadcast · unionOver=p(u,x) · degradedMarkovChain=U-X-Y-Z · generalBroadcastChannelExcluded=true

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-003206. Physically degraded broadcast-channel capacity region. 2026.