DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generated

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Finite degraded wiretap channel

Definition

A finite wiretap channel Finite discrete memoryless wiretap channel and code model is degraded from Bob to Eve if there is a finite stochastic kernel $V (z ∣ y)$ from Bob's output alphabet to Eve's output alphabet such that

$W (y, z ∣ x) = W_{Y} (y ∣ x) V (z ∣ y) for every x, y, z .$

Equivalently, for every input law $P_{X}$ , the induced joint law is $P_{X} (x) W_{Y} (y ∣ x) V (z ∣ y)$ . The requirement specifies the joint coupling of Bob's and Eve's outputs, not only their separate marginal channels.

Depends on

Used by

A degraded binary erasure wiretap channel Example
Secrecy capacity of a finite degraded wiretap channel Theorem

Dependency tree · two levels

5 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Abbas El Gamal and Young-Han Kim, Network Information Theory, arXiv:1001.3404v3 (standard reference, not scraped)
Paul Cuff, Princeton ELE 538: Information Theoretic Security, Lecture 11 (standard reference, not scraped)