Achieving the secrecy capacity of wiretap channels using polar codes

IEEE Transactions on Information Theory

Volumn 57, Issue 10, 2011, Pages 6428-6443

  Mahdavifar, Hessam ^a   Vardy, Alexander ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Channel polarization; information theoretic security; polar codes; secrecy capacity; strong security; wiretap channel

Indexed keywords

CHANNEL POLARIZATIONS; INFORMATION-THEORETIC SECURITY; POLAR CODES; SECRECY CAPACITY; STRONG SECURITY; WIRETAP CHANNEL;

INFORMATION THEORY; RELIABILITY;

CHANNEL CODING;

EID: 80053941690     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2162275     Document Type: Article

References (43)

1. M. Andersson, V. Rathi, R. Thobaben, J. Kliewer, and M. Skoglund, "Nested polar codes for wiretap and relay channels," IEEE Commun. Lett., 14, no. 8, 752-754, Aug. 2010.
2. E.Arikan, "A performance comparison of polar codes and Reed-Muller codes," IEEE Commun. Lett., 12, no. 6, 447-449, Jun. 2008.
3. E. Arikan, "Channel polarization: A method for constructing capacityachieving codes for symmetric binary-input memoryless channels," IEEE Trans. Inf. Theory, 55, no. 7, 3051-3073, Jul. 2009.
4. E. Arikan and E. Telatar, "On the rate of channel polarization," in Proc. IEEE Int. Symp. Information Theory, Jun.-Jul. 2009, 1493-1495.
5. M. Bellare, S. Tessaro, and A. Vardy, A cryptographic treatment of the wiretap channel. Apr. 2010, preprint.
6. M. Bellare,A. Desai, E. Jokipii, and P. Rogaway, "A concrete security treatment of symmetric encryption," in Proc. IEEE Symp. Foundations Computer Science, Miami Beach, FL, Oct. 1997, 394-403.
7. C. Bennett, G. Brassard, C. Crépeau, and U. M. Maurer, "Generalized privacy amplification," IEEE Trans. Inf. Theory, 41, no. 6, 1915-1923, Nov. 1995.
8. M. Cheraghchi, F. Didier, and A. Shokrollahi, "Invertible extractors and wiretap protocols," in Proc. IEEE Int. Symp. Information Theory, Seoul, Korea, 2009, 1934-1938.
9. G. Cohen and G. Zémor, "The wire-tap channel applied to biometrics," in Proc. Int. Symp. Information Theory and its Applications, Parma, Italy, Oct. 2004.
10. G. Cohen and G. Zémor, "Syndrome-coding for the wiretap channel revisited," in Proc. IEEE Information Theory Workshop, Chengdu, China, Oct. 2006, 33-36.
11. T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. Hoboken, NJ: Wiley, 2006.
12. I. Csiszár and J. Körner, "Broadcast channels with confidential messages," IEEE Trans. Inf. Theory, IT-24, no. 3, 339-348, May 1978.
13. I. Dumer and K. Shabunov, "Soft-decision decoding of Reed-Muller codes: Recursive lists," IEEE Trans. Inf. Theory, 52, no. 3, 1260-1266, Mar. 2006.
14. R. G. Gallager, Information Theory and Reliable Communication. Hoboken, NJ: Wiley, 1968.
15. S. Goldwasser and S. Micali, "Probabilistic encryption," J. Comput. Syst. Sci., 28, 270-299, Apr. 1984.
16. S. Hassani and R. L. Urbanke, "On the scaling of polar codes: The behavior of polarized channels," in Proc. IEEE Int. Symp. Information Theory, Austin, TX, Jun. 2010, 874-878.
17. E. Hof and S. Shamai, "Secrecy-achieving polar-coding," in Proc. IEEE Information Theory Workshop, Dublin, Ireland, Aug.-Sep. 2010, 1-5.
18. N. Hussami, R. L. Urbanke, and S. B. Korada, "Performance of polar codes for channel and source coding," in Proc. IEEE Int. Symp. Information Theory, Seoul, Korea, Jun. 2009, 1488-1492.
19. S. B. Korada, "Polar Codes for Channel and Source Coding," Ph.D. dissertation, EPFL, Lausanne, Switzerland, 2009.
20. S. B. Korada, E. Sasoglu, and R. L. Urbanke, "Polar codes: Characterization of exponent, bounds, and constructions," in Proc. IEEE Int. Symp. Information Theory, Seoul, Korea, Jun. 2009, 1483-1487.
21. O. O. Koyluoglu and H. El Gamal, "Polar coding for secure transmission and key agreement," in Proc. IEEE Int. Symp. Personal Indoor and Mobile Radio Comm., Istanbul, Turkey, Sep. 2010, 2698-2703.
22. S. Leung-Yan-Cheong, "On a special class of wire-tap channels," IEEE Trans. Inf. Theory, IT-23, no. 5, 625-627, Sep. 1977.
23. S. Leung-Yan-Cheong and M. E. Hellman, "The Gaussian wire-tap channel," IEEE Trans. Inf. Theory, IT-24, no. 4, 451-456, Jul. 1978.
24. Y. Liang, H. V. Poor, and S. Shamai, "Information theoretic security," Found. and Trends in Commun. and Inf. Theory, 5, no. 4-5, 355-580, 2008.
25. H. Mahdavifar and A. Vardy, "Achieving the secrecy capacity of wiretap channels using polar codes," preprint, Dec. 31, 2009, arxiv.org/ abs/1001.0210.
26. H. Mahdavifar and A. Vardy, "Achieving the secrecy capacity of wiretap channels using polar codes," in Proc. IEEE Int. Symp. Information Theory, Austin, TX, Jun. 2010, 913-917.
27. R. Masstsumoto, "On the randomness in the encoder," Jun. 2010, private communication.
28. U. M. Maurer, "The strong secret key rate of discrete random triples," in Communication and Cryptography-Two Sides of One Tapestry, R. Blahut, Ed. et al., Boston, MA, 1994, 271-285.
29. U. M. Maurer and S. Wolf, "Information-theoretic key agreement: From weak to strong secrecy for free," in Lecture Notes in Computer Science. Berlin, Germany: Springer, 2000, 1807, 351-368.
30. R. Mori and T. Tanaka, "Performance and construction of polar codes on symmetric binary-input memoryless channels," in Proc. IEEE Int. Symp. Information Theory, Seoul, Korea, Jun. 2009, 1496-1500.
31. R. Mori and T. Tanaka, "Performance of polar codes with the construction using density evolution," IEEE Commun. Lett., 13, no. 7, 519-521, Jul. 2009.
32. D. K.Mynbaev and L. L. Scheiner, Fiber-Optic Communications Technology. Englewood Cliffs, NJ: Prentice-Hall, 2000.
33. L. H. Ozarow and A. D.Wyner, "Wire-tap channel II," Bell Lab. Tech. J., 63, no. 10, 2135-2157, Dec. 1984.
34. Y. Polyanskiy, H. V. Poor, and S. Verdú, "Channel coding rate in the finite blocklength regime," IEEE Trans. Inf. Theory, 56, no. 5, 2307-2359, May 2010.
35. E. Sasoglu, E. Telatar, and E. Arikan, "Polarization for arbitrary discrete memoryless channels," in Proc. IEEE Information Theory Workshop, Taormina, Italy, Oct. 2009, 144-148.
36. V. Strassen, "Asymptotische abschätzungen in Shannon's informationstheorie," in Proc. 3rd Conf. Information Theory, Statistical Decision Functions, and Random Processes, Prague, Czechoslovakia, 1964, 689-732.
37. A. Suresh, A. Subramanian, A. Thangaraj, M. Bloch, and S. W. McLaughlin, "Strong secrecy for erasure wiretap channels," in Proc. IEEE Information Theory Workshop, Dublin, Ireland, Sep. 2010.
38. I. Tal and A. Vardy, "How to construct polar codes," in IEEE Information Theory Workshop, Dublin, Ireland, Sep. 2010.
39. A. Thangaraj, S. Dihidar, A. R. Calderbank, S. W. McLaughlin, and J. Merolla, "Applications of LDPC codes to the wiretap channel," IEEE Trans. Inf. Theory, 53, no. 8, 2933-2945, Aug. 2007.
40. M. V. Dijk, "On a special class of broadcast channels with confidential messages," IEEE Trans. Inf. Theory, 43, no. 2, 712-714, Mar. 1997.
41. V. K. Wei, "Generalized Hamming weights for linear codes," IEEE Trans. Inf. Theory, 37, no. 5, 1412-1418, Sep. 1991.
42. A. D. Wyner, "The wire-tap channel," Bell Syst. Tech. J., 54, no. 8, 1355-1387, Oct. 1975.
43. D. Yellin, A. Vardy, and O. Amrani, "Joint equalization and coding for intersymbol interference channels," IEEE Trans. Inf. Theory, 43, no. 2, 409-425, Mar. 1997.