CCapacity Atlas
erasure-wiretap-channel

Erasure wiretap channel with noiseless legitimate reception

A noiseless legitimate receiver and an erasure eavesdropper have a simple strong-secrecy capacity.

Wiretap Binary Finite alphabet Discrete memoryless Erasure Degraded Secrecy Secrecy capacity Exact

Channel and question

Input
Binary channel inputs generated using private randomness.
Output
The legitimate receiver sees the input. The eavesdropper sees an input or erasure.
Law
The legitimate channel is the identity. The eavesdropper channel is a BEC of erasure probability epsilon.
Quantity
Erasure wiretap channel with noiseless legitimate reception capacity \(C_s\), measured in secret bits per channel use.

Criterion. Vanishing legitimate average error and unnormalized information leakage.

  • 0 <= epsilon <= 1. Erasures are iid and independent of message and private seed.
  • The seed is uniform, finite, private and independent of the uniform message.
  • Legitimate average error and unnormalized I(M;Z^n) both tend to zero.

Current status

\[C_s=\varepsilon\]
Known results and bounds for Erasure wiretap channel with noiseless legitimate reception
ResultRelationMethodYear
Exact\(C_s=\varepsilon\)Random binning and the degraded wiretap converse.1975

Formal verification

Lean coverageFormally stated

Concrete operational definitions and admitted research statements are present. Existing proofs are preserved. New statements require mathematical review and proof completion.

Claims

  • Strong-secrecy capacity when the legitimate channel is noiseless and Eve sees erasures.
    operational-capacity · exact capacity · solved · Formally stated · v1
Lean declarations (1)

References

  1. Aaron D. Wyner (1975). The Wire-Tap Channel. Bell System Technical Journal. DOI 10.1002/j.1538-7305.1975.tb02040.x.
  2. Matthieu R. Bloch and J. Nicholas Laneman (2013). Strong Secrecy from Channel Resolvability. IEEE Transactions on Information Theory.

Discussion

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Related problems

Degraded Gaussian wiretap channel

A Gaussian receiver has a lower noise variance than the eavesdropper, yielding a closed-form secrecy capacity.

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General finite wiretap channel

The unconstrained finite wiretap channel has a single-auxiliary secrecy-capacity characterization without a degradedness assumption.

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Binary Z-channel Z-channel

One binary symbol is transmitted perfectly while the other can flip in only one direction.

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