Can Marton Coding Alone Ensure Individual Secrecy?

For communications in the presence of eavesdroppers, random components are often used in code design to camouflage information from eavesdroppers. In broadcast channels without eavesdroppers, Marton coding comprises random components which allow correlation between auxiliary random variables representing independent messages. In this paper, we study if Marton coding alone can ensure individual secrecy in the two-receiver discrete memoryless broadcast channel with a passive eavesdropper. Our results show that this is possible and Marton coding guarantees individual secrecy in accordance to the principle of Wyner secrecy coding. However, this comes with a penalty of requiring stricter channel conditions.

[1]  Claude E. Shannon,et al.  Communication theory of secrecy systems , 1949, Bell Syst. Tech. J..

[2]  Martin E. Hellman,et al.  A note on Wyner's wiretap channel (Corresp.) , 1977, IEEE Trans. Inf. Theory.

[3]  Imre Csiszár,et al.  Broadcast channels with confidential messages , 1978, IEEE Trans. Inf. Theory.

[4]  Lawrence Ong,et al.  The Secure Two-Receiver Broadcast Channel With One-Sided Receiver Side Information , 2018, 2018 IEEE Information Theory Workshop (ITW).

[5]  Holger Boche,et al.  Joint and individual secrecy in broadcast channels with receiver side information , 2014, 2014 IEEE 15th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC).

[6]  Holger Boche,et al.  On the Individual Secrecy Capacity Regions of the General, Degraded, and Gaussian Multi-Receiver Wiretap Broadcast Channel , 2016, IEEE Transactions on Information Forensics and Security.

[7]  Holger Boche,et al.  Secrecy measures for broadcast channels with receiver side information: Joint vs individual , 2014, 2014 IEEE Information Theory Workshop (ITW 2014).

[8]  Aydin Sezgin,et al.  Secrecy in broadcast channels with receiver side information , 2011, 2011 Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR).

[9]  Aydin Sezgin,et al.  Individual Secrecy for Broadcast Channels With Receiver Side Information , 2017, IEEE Transactions on Information Theory.

[10]  Aydin Sezgin,et al.  Individual Secrecy for the Broadcast Channel , 2017, IEEE Transactions on Information Theory.

[11]  Lawrence Ong,et al.  A Simplified Coding Scheme for the Broadcast Channel with Complementary Receiver Side Information under Individual Secrecy Constraints , 2018, ArXiv.

[12]  Holger Boche,et al.  Robust Broadcasting of Common and Confidential Messages Over Compound Channels: Strong Secrecy and Decoding Performance , 2014, IEEE Transactions on Information Forensics and Security.

[13]  Abbas El Gamal,et al.  Network Information Theory , 2021, 2021 IEEE 3rd International Conference on Advanced Trends in Information Theory (ATIT).

[14]  Abbas El Gamal,et al.  3-Receiver broadcast channels with common and confidential messages , 2009, 2009 IEEE International Symposium on Information Theory.

[15]  Katalin Marton,et al.  A coding theorem for the discrete memoryless broadcast channel , 1979, IEEE Trans. Inf. Theory.

[16]  A. D. Wyner,et al.  The wire-tap channel , 1975, The Bell System Technical Journal.