Almost universal codes for fading wiretap channels

2016 IEEE Information Theory Workshop (ITW)

et al. 2016

Abstract-For many wiretap channel models asymptotically optimal coding schemes are known, but less effort has been put into actual realizations of wiretap codes for practical parameters. Bounds on the mutual information and error probability when using coset coding on a Rayleigh fading channel were recently established by Oggier and Belfiore, and the results in this paper build on their work. However, instead of using their ultimate inverse norm sum approximation, a more precise expression for the eavesdropper's probability of correct decision is used in order to determine a general class of good coset codes. The code constructions are based on well-rounded lattices arising from simple geometric criteria. In addition to new coset codes and simulation results, novel number-theoretic results on wellrounded ideal lattices are presented.

Section: B Correct Decoding Probabilitymentioning

confidence: 99%

Well-rounded lattices for reliability and security in Rayleigh fading SISO channels

Gnilke

Tran

2016 IEEE Information Theory Workshop (ITW)

et al. 2016

“…We studied the design of secure lattice coset codes in a general wireless model with any fading and Gaussian noise, and focused on the mod Λ s channel as well as on Gaussian coset coding. Recalling the eavesdropper's probability bounds [5], [6] and deriving a variant of the information bounds [7], [8] we saw that both are an increasing function of the average flatness factor, i.e., the theta series of the faded eavesdroppers lattice Λ e,h averaged over channel realizations h.…”

Section: Discussionmentioning

confidence: 99%

“…We will give a variant of the information bounds [7], [8] from which it is explicit that the bounds agree (up to constants) with this upper bound on the probability that Eve correctly decodes the message. Hence, to minimize this probability, it will be necessary to minimize the upper bound on the mutual information, and vice versa.…”

Section: Information and Probability Boundsmentioning

confidence: 94%

“…For fading channel models, probability and information bounds were derived in [5], [6], and [7], [8], respectively. Codes achieving security and reliability in the multiple-input multiple-output (MIMO) channel were given in [8]. In this paper, we recall the strategy of [5], [6] and give a variant of the information bounds.…”

Section: A Related Work and Contributionsmentioning

confidence: 99%

“…Our choice of setups can be roughly seen as removing such boundary effects by a modulo operation, and smoothing the boundary of the transmission region, respectively. The AWGN information bounds have been derived for these setups in [4], and the information-theoretic results for the fading channels in [7], [8] are for the Gaussian coset coding setup.…”

Section: System Model and Coset Codesmentioning

confidence: 99%

See 2 more Smart Citations

Information bounds and flatness factor approximation for fading wiretap MIMO channels

Barreal

2016 26th International Telecommunication Networks and Applications Conference (ITNAC)

Karpuk

et al. 2016

Abstract-In this article, the design of secure lattice coset codes for general wireless channels with fading and Gaussian noise is studied. Recalling the eavesdropper's probability and information bounds, a variant of the latter is given from which it is explicitly seen that both quantities are upper bounded by (increasing functions of) the expected flatness factor of the faded lattice related to the eavesdropper.By making use of a recently developed approximation of the theta series of a lattice, it is further shown how the average flatness factor can be approximated numerically. In particular, based on the numerical computations, the average flatness factor not only bounds but also orders correctly the performance of different lattices. I. INTRODUCTIONIn the wireless wiretap scheme two legitimate communication parties, Alice and Bob, exchange information in the presence of an eavesdropper, Eve. In this setting, the communication parties rely on physical layer security rather than cryptographic protocols. Hence, Eve is assumed to have no computational limitations and know the cryptographic key, if any, but to have a worse signal quality than Bob.The objective of code design in a wiretap channel is to maximize the data rate and Bob's correct decoding probability while minimizing Eve's information. It was shown in the seminal paper of Wyner [1] that the legitimate parties can design codes with asymptotically non-zero rate, zero error probability and zero information leakage. Today, this setup is particularly interesting in wireless channels that are open in nature but vulnerable to distortions As a practical construction of a wiretap code, [2] introduced the general technique of coset coding, where random bits are added to the message to confuse the eavesdropper. In the specific case of a wireless channel, where lattice codes are suitable, the code lattice Λ b is endowed with a sublattice Λ e ⊂ Λ b which carries the random bits [3].

Well-rounded lattices for coset coding in MIMO wiretap channels

Gnilke

Barreal

2016 26th International Telecommunication Networks and Applications Conference (ITNAC)

et al. 2016

The concept of well-rounded lattices has recently found important applications in the setting of a fading singleinput single-output (SISO) wiretap channel. It has been shown that, under this setup, the property of being well-rounded is critical for minimizing the eavesdropper's probability of correct decoding in lower SNR regimes. The superior performance of coset codes constructed from well-rounded lattices has been illustrated in several simulations.In the present article, this work is extended to fading multipleinput multiple-output (MIMO) wiretap channels, and similar design criteria as in the SISO case are derived. Further, explicit coset codes for Rayleigh fading MIMO wiretap channels are designed. In particular, it is shown through extensive simulations that sublattices of the well-known Alamouti code and Golden code which meet our design criteria perform better than scalar multiples of the code lattice for the same parameters.