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Register a new userNumerical Study on Secrecy Capacity and Code Length Dependence of the Performances in Optical Wiretap Channels
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Added by
Hiroyuki Endo
Publication date
2015
fields
Informatics Engineering
and research's language is
English
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Secrecy issues of free-space optical links realizing information theoretically secure communications as well as high transmission rates are discussed. We numerically study secrecy communication rates of optical wiretap channel based on on-off keying modulation under typical conditions met in satellite-ground links. It is shown that under reasonable degraded conditions on a wiretapper, information theoretically secure communications should be possible in a much wider distance range than a range limit of quantum key distribution, enabling secure optical links between geostationary earth orbit satellites and ground stations with currently available technologies. We also provide the upper bounds on the decoding error probability and the leaked information to estimate a necessary code length for given required levels of performances. This result ensures that a reasonable length wiretap channel code for our proposed scheme must exist.
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Recently, the secrecy capacity of the multi-antenna wiretap channel was characterized by Khisti and Wornell [1] using a Sato-like argument. This note presents an alternative characterization using a channel enhancement argument. This characterization relies on an extremal entropy inequality recently proved in the context of multi-antenna broadcast channels, and is directly built on the physical intuition regarding to the optimal transmission strategy in this communication scenario.
This paper employs equal-image-size source partitioning techniques to derive the capacities of the general discrete memoryless wiretap channel (DM-WTC) under four different secrecy criteria. These criteria respectively specify requirements on the expected values and tail probabilities of the differences, in absolute value and in exponent, between the joint probability of the secret message and the eavesdroppers observation and the corresponding probability if they were independent. Some of these criteria reduce back to the standard leakage and variation distance constraints that have been previously considered in the literature. The capacities under these secrecy criteria are found to be different when non-vanishing error and secrecy tolerances are allowed. Based on these new results, we are able to conclude that the strong converse property generally holds for the DM-WTC only under the two secrecy criteria based on constraining the tail probabilities. Under the secrecy criteria based on the expected values, an interesting phase change phenomenon is observed as the tolerance values vary.
We study the secrecy capacity of a helper-assisted Gaussian wiretap channel with a source, a legitimate receiver, an eavesdropper and an external helper, where each terminal is equipped with multiple antennas. Determining the secrecy capacity in this scenario generally requires solving a nonconvex secrecy rate maximization (SRM) problem. To deal with this issue, we first reformulate the original SRM problem into a sequence of convex subproblems. For the special case of single-antenna legitimate receiver, we obtain the secrecy capacity via a combination of convex optimization and one-dimensional search, while for the general case of multi-antenna legitimate receiver, we propose an iterative solution. To gain more insight into how the secrecy capacity of a helper-assisted Gaussian wiretap channel behaves, we examine the achievable secure degrees of freedom (s.d.o.f.) and obtain the maximal achievable s.d.o.f. in closed-form. We also derive a closed-form solution to the original SRM problem which achieves the maximal s.d.o.f.. Numerical results are presented to illustrate the efficacy of the proposed schemes.
The fading broadcast channel with confidential messages (BCC) is investigated, where a source node has common information for two receivers (receivers 1 and 2), and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The channel state information (CSI) is assumed to be known at both the transmitter and the receivers. The secrecy capacity region is first established for the parallel Gaussian BCC, and the optimal source power allocations that achieve the boundary of the secrecy capacity region are derived. In particular, the secrecy capacity region is established for the Gaussian case of the Csiszar-Korner BCC model. The secrecy capacity results are then applied to give the ergodic secrecy capacity region for the fading BCC.
In this paper we consider the secure transmission in fast Rayleigh fading channels with full knowledge of the main channel and only the statistics of the eavesdroppers channel state information at the transmitter. For the multiple-input, single-output, single-antenna eavesdropper systems, we generalize Goel and Negis celebrated artificial-noise (AN) assisted beamforming, which just selects the directions to transmit AN heuristically. Our scheme may inject AN to the direction of the message, which outperforms Goel and Negis scheme where AN is only injected in the directions orthogonal to the main channel. The ergodic secrecy rate of the proposed AN scheme can be represented by a highly simplified power allocation problem. To attain it, we prove that the optimal transmission scheme for the message bearing signal is a beamformer, which is aligned to the direction of the legitimate channel. After characterizing the optimal eigenvectors of the covariance matrices of signal and AN, we also provide the necessary condition for transmitting AN in the main channel to be optimal. Since the resulting secrecy rate is a non-convex power allocation problem, we develop an algorithm to efficiently solve it. Simulation results show that our generalized AN scheme outperforms Goel and Negis, especially when the quality of legitimate channel is much worse than that of eavesdroppers. In particular, the regime with non-zero secrecy rate is enlarged, which can significantly improve the connectivity of the secure network when the proposed AN assisted beamforming is applied.
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