State Leakage and Coordination With Causal State Knowledge at the Encoder

We revisit the problems of state masking and state amplification through the lens of empirical coordination. Specifically, we characterize the rate-equivocation-coordination trade-offs regions of a state-dependent channel in which the encoder has causal and strictly causal state knowledge. We also extend this characterization to the cases of two-sided state information and noisy channel feedback. Our approach is based on the notion of core of the receiver’s knowledge, which we introduce to capture what the decoder can infer about all the signals involved in the model. Finally, we exploit the aforementioned results to solve a channel state estimation zero-sum game in which the encoder prevents the decoder to estimate the channel state accurately.

[1]  Tristan Tomala,et al.  Persuasion with Limited Communication Capacity , 2017, J. Econ. Theory.

[2]  Mael Le Treust,et al.  Empirical coordination with two-sided state information and correlated source and state , 2015, ISIT.

[3]  Mael Le Treust Empirical coordination with channel feedback and strictly causal or causal encoding , 2015, ISIT.

[4]  Shlomo Shamai,et al.  Information Rates Subject to State Masking , 2007, IEEE Transactions on Information Theory.

[5]  Penélope Hernández,et al.  Optimal use of communication resources , 2006 .

[6]  Young-Han Kim,et al.  State Amplification , 2008, IEEE Transactions on Information Theory.

[7]  Neri Merhav,et al.  Channel Coding in the Presence of Side Information , 2008, Found. Trends Commun. Inf. Theory.

[8]  Haim H. Permuter,et al.  Coordination Capacity , 2009, IEEE Transactions on Information Theory.

[9]  Maël Le Treust,et al.  Joint Empirical Coordination of Source and Channel , 2014, IEEE Transactions on Information Theory.

[10]  Urbashi Mitra,et al.  Causal State Communication , 2012, IEEE Transactions on Information Theory.

[11]  Thomas M. Cover,et al.  Elements of information theory (2. ed.) , 2006 .

[12]  Shlomo Shamai,et al.  Gaussian State Amplification with Noisy Observations , 2015, IEEE Transactions on Information Theory.

[13]  Matthieu R. Bloch,et al.  Coordination in Distributed Networks via Coded Actions With Application to Power Control , 2015, IEEE Transactions on Information Theory.

[14]  Tristan Tomala,et al.  Secret Correlation in Repeated Games with Imperfect Monitoring , 2007, Math. Oper. Res..

[15]  Rida Laraki,et al.  Informationally optimal correlation , 2008, Math. Program..

[16]  Lei Zhao,et al.  Coordination using implicit communication , 2011, 2011 IEEE Information Theory Workshop.

[17]  Anant Sahai,et al.  Information Embedding and the Triple Role of Control , 2013, IEEE Transactions on Information Theory.

[18]  Tobias J. Oechtering,et al.  Coordination Coding with Causal Decoder for Vector-valued Witsenhausen Counterexample Setups , 2019, 2019 IEEE Information Theory Workshop (ITW).

[19]  Max H. M. Costa,et al.  Writing on dirty paper , 1983, IEEE Trans. Inf. Theory.

[20]  Paul W. Cuff,et al.  Hybrid codes needed for coordination over the point-to-point channel , 2011, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[21]  Gregory W. Wornell,et al.  Communication Subject to State Obfuscation , 2020 .

[22]  Paul W. Cuff,et al.  Rate-distortion theory for secrecy systems , 2013, 2013 IEEE International Symposium on Information Theory.

[23]  Serap A. Savari,et al.  Communicating Probability Distributions , 2007, IEEE Transactions on Information Theory.

[24]  Tristan Tomala,et al.  Empirical Distributions of Beliefs Under Imperfect Observation , 2006, Math. Oper. Res..

[25]  Sennur Ulukus,et al.  State amplification and state masking for the binary energy harvesting channel , 2014, 2014 IEEE Information Theory Workshop (ITW 2014).

[26]  Imre Csiszár,et al.  Information Theory - Coding Theorems for Discrete Memoryless Systems, Second Edition , 2011 .

[27]  M. Sion On general minimax theorems , 1958 .

[28]  Amos Lapidoth,et al.  The Rate-and-State Capacity with Feedback , 2018, IEEE Transactions on Information Theory.

[29]  Sriram Vishwanath,et al.  State Amplification Subject to Masking Constraints , 2016, IEEE Transactions on Information Theory.

[30]  Mung Chiang,et al.  Channel capacity and state estimation for state-dependent Gaussian channels , 2005, IEEE Transactions on Information Theory.

[31]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[32]  Matthieu R. Bloch,et al.  Empirical coordination, state masking and state amplification: Core of the decoder's knowledge , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[33]  Nicolas Vieille,et al.  How to play with a biased coin? , 2002, Games Econ. Behav..

[34]  Claude E. Shannon,et al.  Channels with Side Information at the Transmitter , 1958, IBM J. Res. Dev..

[35]  Maël Le Treust,et al.  Strategic Communication with Side Information at the Decoder , 2019, ArXiv.

[36]  Maël Le Treust Correlation between channel state and information source with empirical coordination constraint , 2014, 2014 IEEE Information Theory Workshop (ITW 2014).

[37]  Joseph A. O'Sullivan,et al.  Information-theoretic analysis of information hiding , 2003, IEEE Trans. Inf. Theory.