Broadcast Channels with Privacy Leakage Constraints
Ziv Goldfeld, Gerhard Kramer, Haim H. Permuter

TL;DR
This paper investigates the capacity limits of broadcast channels with privacy leakage constraints, deriving bounds and demonstrating how secrecy requirements influence achievable communication rates.
Contribution
It introduces new inner and outer bounds on the leakage-capacity region for broadcast channels with privacy constraints, generalizing previous results and employing a novel Uniform Approximation Lemma.
Findings
Bounds match for semi-deterministic and degraded BCs
Inner bound recovers Marton's region without leakage constraints
Leakage-capacity regions vary with secrecy scenarios
Abstract
The broadcast channel (BC) with one common and two private messages with leakage constraints is studied, where leakage rate refers to the normalized mutual information between a message and a channel symbol string. Each private message is destined for a different user and the leakage rate to the other receiver must satisfy a constraint. This model captures several scenarios concerning secrecy, i.e., when both, either or neither of the private messages are secret. Inner and outer bounds on the leakage-capacity region are derived when the eavesdropper knows the codebook. The inner bound relies on a Marton-like code construction and the likelihood encoder. A Uniform Approximation Lemma is established that states that the marginal distribution induced by the encoder on each of the bins in the Marton codebook is approximately uniform. Without leakage constraints the inner bound recovers…
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