Achieving secrecy capacity of the wiretap channel and broadcast channel with a confidential component

We show that capacity of the general (not necessarily degraded or symmetric) wiretap channel under a “strong secrecy constraint” can be achieved using an explicit scheme based on polar codes. We also extend our construction to the case of broadcast channels with confidential messages defined by Csiszar and Korner, achieving the entire capacity region of this communication model. This submission is an extended abstract of the paper by the same authors (see arXiv:1410.3422).

[1]  Erdal Arikan,et al.  Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels , 2008, IEEE Transactions on Information Theory.

[2]  Sik K. Leung-Yan-Cheong.  On a special class of wiretap channels (Corresp.) , 1977, IEEE Trans. Inf. Theory.

[3]  Shlomo Shamai,et al.  Secrecy-achieving polar-coding , 2010, 2010 IEEE Information Theory Workshop.

[4]  S. K. Leung-Yan-Cheong.  On a special class of wiretap channels , 1976 .

[5]  Mikael Skoglund,et al.  Nested Polar Codes for Wiretap and Relay Channels , 2010, IEEE Communications Letters.

[6]  Junya Honda,et al.  Polar Coding Without Alphabet Extension for Asymmetric Models , 2013, IEEE Transactions on Information Theory.

[7]  Erdal Arikan,et al.  Source polarization , 2010, 2010 IEEE International Symposium on Information Theory.

[8]  Victor K.-W. Wei,et al.  Generalized Hamming weights for linear codes , 1991, IEEE Trans. Inf. Theory.

[9]  Alexander Vardy,et al.  Achieving the Secrecy Capacity of Wiretap Channels Using Polar Codes , 2010, IEEE Transactions on Information Theory.

[10]  Joseph M. Renes,et al.  Polar codes for private classical communication , 2012, 2012 International Symposium on Information Theory and its Applications.

[11]  Emre Telatar,et al.  On the rate of channel polarization , 2008, 2009 IEEE International Symposium on Information Theory.

[12]  Joseph M. Renes,et al.  Polar Codes for Private and Quantum Communication Over Arbitrary Channels , 2012, IEEE Transactions on Information Theory.

[13]  Ueli Maurer,et al.  Information-Theoretic Key Agreement: From Weak to Strong Secrecy for Free , 2000, EUROCRYPT.

[14]  U. Maurer.  The Strong Secret Key Rate of Discrete Random Triples , 1994 .

[15]  Onur Ozan Koyluoglu,et al.  Polar coding for secure transmission and key agreement , 2010, PIMRC.

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

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

[18]  Alexander Vardy,et al.  A new polar coding scheme for strong security on wiretap channels , 2013, 2013 IEEE International Symposium on Information Theory.