Discrete memoryless multiple-access capacity region

Capacity region of a stationary memoryless multiple-access channel.

Specification version 1Published 1972-01-011 evidence records

About this problem

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

Formal question

Determine the closure of simultaneously achievable user-rate tuples for a discrete memoryless multiple-access channel.

Scope & constraints

channel: discrete memoryless MAC
unionOver: p(q) product_i p(x_i|q)
timeSharing: Q
allUserSubsets: true

Primary sources

The capacity region of a channel with two senders and two receivers — Discrete memoryless multiple-access capacity region Multiple-access capacity theorem

What we know

Current frontiers derived from accepted Claims.

Exact established valuesum_{i in S} R_i <= I(X_S;Y|X_{S^c},Q), all S

The accepted equality closes this optimization result.

Claims

Assertions tied to evidence, attribution, and review.

2026

CLM-INFO-003205= sum_{i in S} R_i <= I(X_S;Y|X_{S^c},Q), all SEXACT VALUEThe cited theorem establishes sum_{i in S} R_i <= I(X_S;Y|X_{S^c},Q), all S under the current specification; this does not assert universal empirical attainability.Source: The capacity region of a channel with two senders and two receivers — Discrete memoryless multiple-access 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=discrete memoryless MAC · unionOver=p(q) product_i p(x_i|q) · timeSharing=Q · allUserSubsets=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-003205. Discrete memoryless multiple-access capacity region. 2026.