Equivocation A Special Case of Distortion-based Characterization.

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Presentation transcript:

Equivocation A Special Case of Distortion-based Characterization

Wiretap Channel [Wyner 75]

Confidential Messages [Csiszar, Korner 78]

Merhav 2008

Villard-Piantanida 2010

Other Examples of rate-equivocation Gunduz-Erkip-Poor 2008 Lia-H. El-Gamal 2008 Tandon-Ulukus-Ramchandran 2009 …

Another Approach

Causal Disclosure (case 1)

Causal Disclosure (case 2)

Causal Disclosure (case 3)

What if lossy compression were defined with respect to information measures? R H(X^n|M) Not as interesting as R(D)

Log-loss Distortion Reconstruction space of Z is the set of distributions.

Best Reconstruction Yields Entropy

Result 1 from Secrecy R-D Theory

Result 2 from Secrecy R-D Theory

Result 3 from Secrecy R-D Theory

Equivocation is a blunt special case General optimal secrecy performance requires a specific encoding scheme. These equivocation bounds can be achieved with: – Random binning – Time-sharing – Almost any reasonable method

Summary Equivocation in secrecy is in general a special case of rate-distortion theory for secrecy systems with causal disclosure. The equivocation special case does not shed light on good coding structures in general.