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IEEE Information Theory Workshop (ITW)

Finite-Input Intersymbol Interference Wiretap Channels

Aria Nouri, Reza Asvadi, Jun Chen, Pascal O. Vontobel

Published Oct 17, 2021• 3 citations
Publisher

Abstract

We consider reliable and secure communication over intersymbol interference wiretap channels (ISI-WTCs). In particular, we first examine the setup where the source at the input of an ISI-WTC is unconstrained and then, based on a general achievability result for arbitrary wiretap channels, we derive an achievable secure rate for this ISI-WTC. Afterwards, we examine the setup where the source at the input of an ISI-WTC is constrained to be a finite-state machine source (FSMS) of a certain order and structure. optimizing the parameters of this FSMS toward maximizing the secure rate is a computationally intractable problem in general, and so, toward finding a local maximum, we propose an iterative algorithm that at every iteration replaces the secure rate function by a suitable surrogate function whose maximum can be found efficiently.

DOI
10.1109/itw48936.2021.9611416

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We consider reliable and secure communication over intersymbol interference wiretap channels (ISI-WTCs). In particular, we first examine the setup where the source at the input of an ISI-WTC is unconstrained and then, based on a general achievability result for arbitrary wiretap channels, we derive an achievable secure rate for this ISI-WTC. Afterwards, we examine the setup where the source at the input of an ISI-WTC is constrained to be a finite-state machine source (FSMS) of a certain order and structure. optimizing the parameters of this FSMS toward maximizing the secure rate is a computationally intractable problem in general, and so, toward finding a local maximum, we propose an iterative algorithm that at every iteration replaces the secure rate function by a suitable surrogate function whose maximum can be found efficiently.
We consider reliable and secure communication over intersymbol interference wiretap channels (ISI-WTCs). In particular, we first derive an achievable secure rate for ISI-WTCs without imposing any constraints on the input distribution. Afterwards, we focus on the setup where the input distribution of the ISI-WTC is constrained to be a time-invariant finite-order Markov chain. Optimizing the parameters of this Markov chain toward maximizing the achievable secure rates is a computationally intractable problem in general, and so, toward finding a local maximum, we propose an iterative algorithm that at every iteration replaces the secure rate function with a suitable surrogate function whose maximum can be found efficiently. Although the secure rates achieved in the unconstrained setup are potentially larger than the secure rates achieved in the constrained setup, the latter setup has the advantage of leading to efficient algorithms for estimating and optimizing the achievable secure rates, and also has the benefit of being the basis of efficient coding schemes.
We consider reliable and secure communication over partial-response wiretap channels (PR-WTCs). In particular, we first examine the setup where the source at the input of a PR-WTC is unconstrained and then, based on a general achievability result for arbitrary wiretap channels, we derive an achievable secure information rate for this PR-WTC. Afterwards, we examine the setup where the source at the input of a PR-WTC is constrained to be a finite-state machine source (FSMS) of a certain order and structure. Optimizing the parameters of this FSMS toward maximizing the secure information rate is a computationally intractable problem in general, and so, toward finding a local maximum, we propose an iterative algorithm that at every iteration replaces the secure information rate function by a suitable surrogate function whose maximum can be found efficiently. Although we expect the secure information rates achieved in the unconstrained setup to be larger than the secure information rates achieved in the constrained setup, the latter setup has the advantage of leading to efficient algorithms for estimating achievable secure rates and also has the benefit of being the basis of efficient encoding and decoding schemes.
We consider the multiple-input multiple-output (MIMO) wiretap channel with intersymbol interference (ISI) in which a transmitter (Alice) wishes to securely communicate with a receiver (Bob) in presence of an eavesdropper (Eve). We focus on the practically relevant setting in which there is no channel state information (CSI) at Alice about either of the channels to Bob or Eve, except statistical information about the ISI channels (i.e., Alice only knows the effective number of ISI taps). The key contribution of this work is to show that even with no CSI at Alice, positive secure degrees of freedom (SDoF) are achievable by carefully exploiting a) the heterogeneity of the ISI links to Bob and Eve, and b) the relative number of antennas at all the three terminals. To this end, we propose a novel achievable scheme that carefully mixes information and artificial noise symbols in order to exploit ISI heterogeneity to achieve positive SDoF. To the best of our knowledge, this is the first work to explore the idea of exploiting ISI channel length heterogeneity to achieve positive SDoF for the MIMO wiretap channel with no CSI at the legitimate transmitter.
Information-theoretic security offered by the wiretap channel model has been extensively studied for various scenarios recently. One scenario that has not received much attention is secrecy for systems with memory in the form of input constraints or inter-symbol interference (ISI). In this work, we consider finite state wiretap channels (FSWCs), which model the scenario of secrecy with memory. Using results on secrecy capacity for arbitrary wiretap channels, we first arrive at the secrecy capacity of a FSWC. Then, we develop a stochastic algorithm for computing tight lower bounds on the secrecy capacity of a less-noisy FSWC, and illustrate the computation through examples. Our results provide numerical comparisons between secrecy capacities with and without memory, and provide specific targets for code design.
In this paper, the problem of securely computing a function over the binary modulo-2 adder multiple-access wiretap channel is considered. The problem involves a legitimate receiver that wishes to reliably and efficiently compute a function of distributed binary sources while an eavesdropper has to be kept ignorant of them. In order to characterize the corresponding fundamental limit, the notion of secrecy computation-capacity is introduced. Although determining the secrecy computation-capacity is challenging for arbitrary functions, it surprisingly turns out that if the function perfectly matches the algebraic structure of the channel and the joint source distribution fulfills certain conditions, the secrecy computation-capacity equals the computation capacity, which is the supremum of all achievable computation rates without secrecy constraints. Unlike the case of securely transmitting messages, no additional randomness is needed at the encoders nor does the legitimate receiver need any advantage over the eavesdropper. The results therefore show that the problem of securely computing a function over a multiple-access wiretap channel may significantly differ from the one of securely communicating messages.
Secure signaling over multiple-input multiple-output (MIMO) wiretap channel (WTC) is studied under interference and transmit power constraints. The classical MIMO WTC model is extended to interference-limited scenarios, so that interference to other users does not exceed a given threshold while ensuring simultaneously no information leakage to an eavesdropper. The operational secrecy capacity of the Gaussian MIMO WTC under interference and transmit power constraints is rigorously established in two forms (a non-convex max problem and a convex-concave max-min problem), to which per-antenna power constraints can be added as well. Optimal signaling directions are characterized in the general case, from which (tight) upper bounds to the rank of optimal transmit covariance matrix are derived. A sufficient condition for the optimality of beamforming and a necessary condition for optimal full-rank signaling are given. Closed-form rank-1 and high-rank solutions are obtained in the case of zero interference constraints. Sufficient and necessary conditions for non-zero secrecy capacity are established. The results are extended to multi-user scenarios. A sufficient and necessary condition for the unbounded growth of the secrecy capacity with transmit power is obtained. The interplay between transmit and interference power constraints is studied, and its significant impact on optimal signaling is demonstrated (so that neither constraint can be absorbed into the other one in general, as was sometimes suggested in the literature). Overall, these results provide insights into fundamental information-theoretic limits and optimal signaling strategies for secure communications under interference constraints.