Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-09T05:37:23.853Z Has data issue: false hasContentIssue false

7 - MISO Wiretap Channel with Strictly Causal CSI: A Topological Viewpoint

from Part II - Secure Communication

Published online by Cambridge University Press:  28 June 2017

Z. H. Awan
Affiliation:
Lehrstuhl für Digitale Kommunikationssysteme, Ruhr-Universität Bochum
A. Sezgin
Affiliation:
Lehrstuhl für Digitale Kommunikationssysteme, Ruhr-Universität Bochum
Rafael F. Schaefer
Affiliation:
Technische Universität Berlin
Holger Boche
Affiliation:
Technische Universität München
Ashish Khisti
Affiliation:
University of Toronto
H. Vincent Poor
Affiliation:
Princeton University, New Jersey
Get access

Summary

Physical-layer security offers an alternative to cryptology, where instead of using the secrecy keys, randomness of the wireless channel is utilized to conceal information. In this chapter, we give an overview of different state-of-the-art multi-terminal information theoretic models to secure information with varying quality of channel state information at the transmitter. We first introduce the essential elements of information theoretic security, and later on discuss its application from a degrees of freedom viewpoint. In particular, we focus our attention on the models in which the topology of the network is known at the transmitter.

Introduction

Wireless communication has completely revolutionized the lives of common users. Modern communication systems provide high data rates, which allow users to perform different day-to-day tasks wirelessly. For example, users can access their bank account details and monitor their home security remotely. However, due to the broadcast nature of the medium, the information exchange between these communication nodes can be overheard by unintended users in the network. The leakage of information to unintended users may have serious consequences. In this chapter, we intend to answer this fundamental question of how to secure wireless communication.

State of the Art and Preliminaries

In conventional systems, cryptographic encryption is used to conceal information from adversaries. Figure 7.1 shows a simple example which sheds light on the problem of secret key sharing studied in cryptology. The source message at Alice is converted to ciphertext with the help of a secret key which is shared between Alice and the legitimate receiver, Bob. The ciphertext is then communicated over the wireless channel and is received by both Bob and Eve. Upon getting the ciphertext and having access to the secret key, Bob can easily recover Alice's message [1]. It is assumed that Eve, the eavesdropper, is of limited computational complexity or has limited resources. Thus, it is unable to generate all combinations of secret key, and consequently cannot recover Alice's message. In this framework, secrecy relies on the difficulty level of some hard mathematical problem which the eavesdropper is unable to solve due to limited computational resources.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2017

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] W., Stallings, Cryptography and Network Security: Principles and Practice, 2nd edn. Upper Saddle River, NJ: Prentice-Hall, Inc., 1999.
[2] A. D., Wyner, “The wire-tap channel,” Bell Syst. Tech. J., vol. 54, pp. 1355–1387, Oct. 1975.Google Scholar
[3] I., Csiszár and J., Körner, “Broadcast channels with confidential messages,” IEEE Trans. Inf. Theory, vol. 24, no. 3, pp. 339–348, May 1978.Google Scholar
[4] R., Liu, T., Liu, H. V., Poor, and S., Shamai (Shitz), “New results on multiple-input multiple-output broadcast channels with confidential messages,” IEEE Trans. Inf. Theory, vol. 59, no. 3, pp. 1346–1359, Mar. 2013.Google Scholar
[5] E., Tekin and A., Yener, “The Gaussian multiple access wire-tap channel,” IEEE Trans. Inf. Theory, vol. 54, no. 12, pp. 5747–5755, Dec. 2008.Google Scholar
[6] Y., Liang and H. V., Poor, “Multiple access channels with confidential messages,” IEEE Trans. Inf. Theory, vol. 54, no. 3, pp. 976–1002, Mar. 2008.Google Scholar
[7] E., Tekin and A., Yener, “The general Gaussian multiple-access and two-way wiretap channels: Achievable rates and cooperative jamming,” IEEE Trans. Inf. Theory, vol. 54, no. 6, pp. 2735–2751, Jun. 2008.Google Scholar
[8] Z. H., Awan, A., Zaidi, and L., Vandendorpe, “On multiaccess channel with unidirectional cooperation and security constraints,” in Proc. 50th Annual Allerton Conf. Commun., Control, Computing, Monticello, IL, USA, Sep. 2012, pp. 982–987.
[9] Z. H., Awan, A., Zaidi, and L., Vandendorpe, “Multiaccess channel with partially cooperating encoders and security constraints,” IEEE Trans. Inf. Forensics Security, vol. 8, no. 7, pp. 1243–1254, Jul. 2013.Google Scholar
[10] L., Lai and H. El, Gamal, “The relay eavesdropper channel: Cooperation for secrecy,” IEEE Trans. Inf. Theory, vol. 54, no. 9, pp. 4005–4019, Sep. 2008.Google Scholar
[11] Z. H., Awan, A., Zaidi, and L., Vandendorpe, “On secure transmission over parallel relay eavesdropper channel,” in Proc. 48th Annual Allerton Conf. Commun., Control, Computing, Monticello, IL, USA, Sep. 2010, pp. 859–866.
[12] Z. H. Awan, A., Zaidi, and L., Vandendorpe, “Secure communication over parallel relay channel,” IEEE Trans. Inf. Forensics Security, vol. 7, no. 2, pp. 359–371, Apr. 2012.Google Scholar
[13] O. O., Koyluoglu and H. E., Gamal, “Cooperative encoding for secrecy in interference channels,” IEEE Trans. Inf. Theory, vol. 57, no. 9, pp. 5682–5694, Sep. 2011.Google Scholar
[14] Z., Li, R., Yates, and W., Trappe, “Secrecy capacity of a class of one-sided interference channel,” in Proc. IEEE Int. Symp. Inf. Theory, Toronto, ON, Canada, Jul. 2008, pp. 379–383.
[15] A., Khisti and G. W., Wornell, “Secure transmission with multiple antennas–Part II: The MIMOME wiretap channel,” IEEE Trans. Inf. Theory, vol. 56, no. 11, pp. 5515–5532, Nov. 2010.Google Scholar
[16] F., Oggier and B., Hassibi, “The secrecy capacity of theMIMO wiretap channel,” IEEE Trans. Inf. Theory, vol. 57, no. 8, pp. 4961–4972, Aug. 2011.Google Scholar
[17] T., Liu and S., Shamai (Shitz), “A note on the secrecy capacity of the multiple-antenna wiretap channel,” IEEE Trans. Inf. Theory, vol. 55, no. 6, pp. 2547–2553, Jun. 2009.Google Scholar
[18] R., Bustin, R., Liu, H. V., Poor, and S., Shamai (Shitz), “An MMSE approach to the secrecy capacity of the MIMO Gaussian wiretap channel,” EURASIP J. Wireless Commun. Netw., p. 8, Nov. 2009.Google Scholar
[19] Y., Liang, H. V., Poor, and S., Shamai (Shitz), “Information theoretic security,” Foundations and Trends in Communications and Information Theory, vol. 5, no. 4–5, pp. 355–580, 2009.Google Scholar
[20] V. R., Cadambe and S. A., Jafar, “Interference alignment and the degrees of freedom of wireless X networks,” IEEE Trans. Inf. Theory, vol. 55, no. 9, pp. 3893–3908, Sep. 2009.Google Scholar
[21] S. A., Jafar, “Interference alignment – A new look at signal dimensions in a communication network,” Foundations and Trends in Communications and Information Theory, vol. 7, no. 1, pp. 1–134, 2010.Google Scholar
[22] M. A., Maddah-Ali and D., Tse, “Completely stale transmitter channel state information is still very useful,” IEEE Trans. Inf. Theory, vol. 58, no. 7, pp. 4418–4431, Jul. 2012.Google Scholar
[23] C. S., Vaze and M. K., Varanasi, “The degrees of freedom region of the two-user and certain three-user MIMO broadcast channel with delayed CSI,” Jan. 2011. [Online]. Available: http://arxiv.org/abs/1101.0306
[24] M. J., Abdoli, A., Ghasemi, and A. K., Khandani, “On the degrees of freedom of three-user MIMO broadcast channel with delayed CSIT,” in IEEE Int. Symp. Inf. Theory, St. Petersburg, Russia, Jul. 2011, pp. 209–213.
[25] G., Tiangao and S. A., Jafar, “Optimal use of current and outdated channel state information: Degrees of freedom of the MISO BC with mixed CSIT,” IEEE Commun. Letters, vol. 16, no. 7, pp. 1084–1087, Jul. 2012.Google Scholar
[26] S., Yang, M., Kobayashi, P., Piantanida, and S., Shamai (Shitz), “Secrecy degrees of freedom of MIMO broadcast channels with delayed CSIT,” IEEE Trans. Inf. Theory, vol. 59, no. 9, pp. 5244–5256, 2013.Google Scholar
[27] A., Zaidi, Z. H., Awan, S., Shamai (Shitz), and L., Vandendorpe, “Secure degrees of freedom of MIMO X-channels with output feedback and delayed CSIT,” IEEE Trans. Inf. Forensics Security, vol. 8, no. 11, pp. 1760–1774, Nov. 2013.Google Scholar
[28] R. H., Etkin, D. N. C., Tse, and H., Wang, “Gaussian interference channel capacity to within one bit,” IEEE Trans. Inf. Theory, vol. 54, no. 12, pp. 5534–5562, Dec. 2008.Google Scholar
[29] J., Chen, P., Elia, and S. A., Jafar, “On the vector broadcast channel with alternating CSIT: A topological perspective,” Feb. 2014. [Online]. Available: http://arxiv.org/abs/1402.5912
[30] R., Tandon, S. A., Jafar, S., Shamai (Shitz), and H. V., Poor, “On the synergistic benefits of alternating CSIT for the MISO broadcast channel,” IEEE Trans. Inf. Theory, vol. 59, no. 7, pp. 4106–4128, Jul. 2013.Google Scholar
[31] Z. H., Awan, A., Zaidi, and A., Sezgin, “Achievable secure degrees of freedom of MISO broadcast channel with alternating CSIT,” in IEEE Int. Symp. Inf. Theory, Honolulu, HI, USA, Jun. 2014, pp. 31–35.
[32] P., Mukherjee, R., Tandon, and S., Ulukus, “MISO broadcast channels with confidential messages and alternating CSIT,” in IEEE Int. Symp. Inf. Theory, Honolulu, HI, USA, Jun. 2014, pp. 216–220.
[33] T. M., Cover and J. A., Thomas, Elements of Information Theory, 2nd edn. Chichester: Wiley & Sons, 2006.
[34] Z. H., Awan and A., Sezgin, “On MISO wiretap channel with delayed CSIT and alternating topology,” in Proc. 10th Int. ITG Conf. Systems, Communications and Coding, Hamburg, Germany, Feb. 2015, pp. 1–6.

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×