Capacity Bounds for Broadcast Channels With Confidential Messages

This paper studies capacity bounds for discrete memoryless broadcast channels with confidential messages. Two private messages as well as a common message are transmitted; the common message is to be decoded by both receivers, while each private message is only for its intended receiver. In addition, each private message is to be kept secret from the unintended receiver where secrecy is measured by equivocation. Both inner and outer bounds are proposed to the rate equivocation region for broadcast channels with confidential messages. The proposed inner bound generalizes Csiszar and Korner's rate equivocation region for broadcast channels with a single confidential message, Liu 's achievable rate region for broadcast channels with perfect secrecy, Marton's and Gel'fand-Pinsker's achievable rate region for general broadcast channels. The proposed outer bounds, together with the inner bound, help establish the rate equivocation region of several classes of discrete memoryless broadcast channels with confidential messages, including the less noisy, deterministic, and semideterministic broadcast channels. Furthermore, specializing to the general broadcast channel by removing the confidentiality constraint, the proposed outer bounds reduce to new capacity outer bounds for the discrete memory broadcast channel.

[1]  Yingbin Liang,et al.  Rate Regions for Relay Broadcast Channels , 2006, IEEE Transactions on Information Theory.

[2]  A. Sridharan.  Broadcast Channels , 2022 .

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

[4]  Chandra Nair.  An outer bound for 2-receiver discrete memoryless broadcast channels , 2008, ArXiv.

[5]  Imre Csiszár,et al.  Secrecy capacities for multiple terminals , 2004, IEEE Transactions on Information Theory.

[6]  G. Kramer,et al.  Capacity Theorems for Cooperative Relay Broadcast Channels , 2006, 2006 40th Annual Conference on Information Sciences and Systems.

[7]  Ender Tekin,et al.  The Gaussian Multiple Access Wire-Tap Channel with Collective Secrecy Constraints , 2006, 2006 IEEE International Symposium on Information Theory.

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

[9]  Hesham El Gamal,et al.  The Relay–Eavesdropper Channel: Cooperation for Secrecy , 2006, IEEE Transactions on Information Theory.

[10]  Edward C. van der Meulen,et al.  A proof of Marton's coding theorem for the discrete memoryless broadcast channel , 1981, IEEE Trans. Inf. Theory.

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

[12]  Yasutada Oohama,et al.  Coding for relay channels with confidential messages , 2001, Proceedings 2001 IEEE Information Theory Workshop (Cat. No.01EX494).

[13]  Yingbin Liang,et al.  Equivalence of two inner bounds on the capacity region of the broadcast channel , 2008, 2008 46th Annual Allerton Conference on Communication, Control, and Computing.

[14]  Gerhard Kramer,et al.  Topics in Multi-User Information Theory , 2008, Found. Trends Commun. Inf. Theory.

[15]  Hiroshi Sato,et al.  An outer bound to the capacity region of broadcast channels (Corresp.) , 1978, IEEE Trans. Inf. Theory.

[16]  Abbas El Gamal,et al.  An outer bound to the capacity region of the broadcast channel , 2006, ISIT.

[17]  Abbas El Gamal,et al.  An Outer Bound to the Capacity Region of the Broadcast Channel , 2006, 2006 IEEE International Symposium on Information Theory.

[18]  Ami Wiesel,et al.  On the Gaussian MIMO Wiretap Channel , 2007, 2007 IEEE International Symposium on Information Theory.

[19]  Ender Tekin,et al.  The Gaussian multiple access wire-tap channel: wireless secrecy and cooperative jamming , 2007, 2007 Information Theory and Applications Workshop.

[20]  Chandra Nair,et al.  On the inner and outer bounds for 2-receiver discrete memoryless broadcast channels , 2008, 2008 Information Theory and Applications Workshop.

[21]  Shlomo Shamai,et al.  Capacity outer bounds for broadcast channels , 2008, 2008 IEEE Information Theory Workshop.

[22]  Thomas M. Cover,et al.  Comments on Broadcast Channels , 1998, IEEE Trans. Inf. Theory.

[23]  H. Vincent Poor,et al.  Multiple-Access Channels With Confidential Messages , 2008, IEEE Transactions on Information Theory.

[24]  Hesham El Gamal,et al.  On the Secrecy Capacity of Fading Channels , 2006, 2007 IEEE International Symposium on Information Theory.

[25]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

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

[27]  H. Vincent Poor,et al.  Generalized Multiple Access Channels with Confidential Messages , 2006, 2006 IEEE International Symposium on Information Theory.

[28]  Roy D. Yates,et al.  Secret Communication via Multi-antenna Transmission , 2007, 2007 41st Annual Conference on Information Sciences and Systems.

[29]  Bin Dai,et al.  Wiretap Channel With Side Information , 2006, ArXiv.

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

[31]  Nan Liu,et al.  Towards the Secrecy Capacity of the Gaussian MIMO Wire-Tap Channel: The 2-2-1 Channel , 2007, IEEE Transactions on Information Theory.

[32]  Roy D. Yates,et al.  Discrete Memoryless Interference and Broadcast Channels With Confidential Messages: Secrecy Rate Regions , 2007, IEEE Transactions on Information Theory.

[33]  Shlomo Shamai,et al.  Secure Communication Over Fading Channels , 2007, IEEE Transactions on Information Theory.

[34]  Ender Tekin,et al.  The General Gaussian Multiple-Access and Two-Way Wiretap Channels: Achievable Rates and Cooperative Jamming , 2007, IEEE Transactions on Information Theory.