Hadi Aghaee, Bahareh Akhbari
In this paper, we want to derive achievable secrecy rate regions for quantum interference channel with classical inputs under one-shot setting. The main idea to this end is to use the combination of superposition and rate splitting for encoding scheme and constructing a decoding scheme based on simultaneous decoding.
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In this paper, the individual secrecy of two-way wiretap channel is investigated, where two legitimate users' messages are separately guaranteed secure against an external eavesdropper. For one thing, in some communication scenarios, the joint secrecy is impossible to achieve both positive secrecy rates of two users. For another, the individual secrecy satisfies the secrecy demand of many practical communication systems. Thus, firstly, an achievable secrecy rate region is derived for the general two-way wiretap channel with individual secrecy. In a deterministic channel, the region with indivi…
We establish Ahlswede dichotomy for arbitrarily varying classical-quantum wiretap channels. This means that either the deterministic secrecy capacity of an arbitrarily varying classical-quantum wiretap channel is zero or it equals its randomness-assisted secrecy capacity. We analyze the secrecy capacity of arbitrarily varying classical-quantum wiretap channels when the sender and the receiver use various resources. It turns out that having randomness, common randomness, and correlation as resources are very helpful for achieving a positive deterministic secrecy capacity of arbitrarily varying …
We determine the secrecy capacity of the compound channel with quantum wiretapper and channel state information at the transmitter. Moreover, we derive a lower bound on the secrecy capacity of this channel without channel state information and determine the secrecy capacity of the compound classical-quantum wiretap channel with channel state information at the transmitter. We use this result to derive a new proof for a lower bound on the entanglement generating capacity of compound quantum channel. We also derive a new proof for the entanglement generating capacity of compound quantum channel …
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 sa…
In this paper, the one-sided secrecy of two-way wiretap channel with feedback is investigated, where the confidential messages of one user through multiple transmissions is guaranteed secure against an external eavesdropper. For one thing, one-sided secrecy satisfies the secure demand of many practical scenarios. For another, the secrecy is measured over many blocks since the correlation between eavesdropper's observation and the confidential messages in successive blocks, instead of secrecy measurement of one block in previous works. Thus, firstly, an achievable secrecy rate region is derived…
A Gaussian multiple-input multiple-output (MIMO) wiretap channel model is considered. The input is a two-antenna transmitter, while the outputs are the legitimate receiver and an eavesdropper, both equipped with multiple antennas. All channels are assumed to be known. The problem of obtaining the optimal input covariance matrix that achieves secrecy capacity subject to a power constraint is addressed, and a closed-form expression for the secrecy capacity is obtained.
Finite-Length Analysis of Polar Secrecy Codes for Wiretap Channels
本文研究窃听信道下极化保密码的有限长度性能，给出归一化互信息安全泄漏的界，并用于刻画其有限长度缩放行为及实际块长度下的保密保证。
In this paper, we consider the achievable sum secrecy rate in full-duplex wiretap channel in the presence of an eavesdropper and imperfect channel state information (CSI). We assume that the users participating in full-duplex communication and the eavesdropper have single antenna each. The users have individual transmit power constraints. They also transmit jamming signals to improve the secrecy rates. We obtain the achievable perfect secrecy rate region by maximizing the sum secrecy rate. We also obtain the corresponding optimum powers of the message signals and the jamming signals. Numerical…
Finite-blocklength performance of polar wiretap codes under a total variation secrecy constraint
研究极化码在退化对称窃听信道下的性能，提出基于总变差距离的保密性约束方法，为有限块长下的窃听码 secrecy rate 下界计算提供新准则。
This paper is concerned with the general multiple access wiretap channel and the existence of codes that accomplish reliability and strong secrecy. Information leakage to the eavesdropper is assessed by the variational distance metric, whereas the average error probability is bounded by modifying Feinsteins Lemma. We derive an achievable strong secrecy rate region by utilizing the resolvability theory for the multiple-access channel in terms of information-spectrum methods.
A multiple-input single-output (MISO) wiretap channel model is considered, that includes a multi-antenna transmitter, a single-antenna legitimate receiver and a single-antenna eavesdropper. For the scenario in which spherical uncertainty for both the legitimate and the eavesdropper channels is included, the problem of finding the optimal input covariance that maximizes the worst-case secrecy rate subject to a power constraint, is considered, and an explicit expression for the maximum worst-case secrecy rate is provided.
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.
The wiretap channel model of Wyner is one of the first communication models with both reliability and security constraints. Capacity-achieving schemes for various models of the wiretap channel have received considerable attention in recent literature. In this paper, we show that capacity of the general (not necessarily degraded or symmetric) wiretap channel under a "strong secrecy constraint" can be achieved using a transmission scheme based on polar codes. We also extend our construction to the case of broadcast channels with confidential messages defined by Csisz{á}r and K{örner}, achieving …
We propose the notion of secrecy gain as a code design criterion for wiretap lattice codes to be used over an additive white Gaussian noise channel. Our analysis relies on the error probabilites of both the legitimate user and the eavesdropper. We focus on geometrical properties of lattices, described by their theta series, to characterize good wiretap codes.
We analyze the exact exponential decay rate of the expected amount of information leaked to the wiretapper in Wyner's wiretap channel setting using wiretap channel codes constructed from both i.i.d. and constant-composition random codes. Our analysis for those sampled from i.i.d. random coding ensemble shows that the previously-known achievable secrecy exponent using this ensemble is indeed the exact exponent for an average code in the ensemble. Furthermore, our analysis on wiretap channel codes constructed from the ensemble of constant-composition random codes leads to an exponent which, in a…
This work studies the secrecy-capacity of a scalar-Gaussian wiretap channel with an amplitude constraint on the input. It is known that for this channel, the secrecy-capacity-achieving distribution is discrete with finitely many points. This work improves such result by showing an upper bound of the order $\frac{\mathsf{A}}{σ_1^2}$ where $\mathsf{A}$ is the amplitude constraint and $σ_1^2$ is the variance of the Gaussian noise over the legitimate channel.
In this work, an explicit wiretap coding scheme based on polar lattices is proposed to achieve the secrecy capacity of the additive white Gaussian noise (AWGN) wiretap channel. Firstly, polar lattices are used to construct secrecy-good lattices for the mod-$Λ_s$ Gaussian wiretap channel. Then we propose an explicit shaping scheme to remove this mod-$Λ_s$ front end and extend polar lattices to the genuine Gaussian wiretap channel. The shaping technique is based on the lattice Gaussian distribution, which leads to a binary asymmetric channel at each level for the multilevel lattice codes. By emp…
In this paper, new two-user multiple access wiretap channel models are studied. First, the multiple access wiretap channel II with a discrete memoryless main channel, under three different wiretapping scenarios, is introduced. The wiretapper, as in the classical wiretap channel II model, chooses a fixed-length subset of the channel uses on which she obtains noise-free observations of one of the codewords, a superposition of the two codewords, or each of the two codewords. These thus extend the recently examined wiretap channel II with a noisy main channel to a multiple access setting with a va…
Polar lattices, which are constructed from polar codes, are provably good for the additive white Gaussian noise (AWGN) channel. In this work, we propose a new polar lattice construction that achieves the secrecy capacity under the strong secrecy criterion over the mod-$Λ$ Gaussian wiretap channel. This construction leads to an AWGN-good lattice and a secrecy-good lattice simultaneously. The design methodology is mainly based on the equivalence in terms of polarization between the $Λ/Λ'$ channel in lattice coding and the equivalent channel derived from the chain rule of mutual information in mu…
We derive a lower bound on the secrecy capacity of the compound wiretap channel with channel state information at the transmitter which matches the general upper bound on the secrecy capacity of general compound wiretap channels given by Liang et al. and thus establishing a full coding theorem in this case. We achieve this with a stronger secrecy criterion and the maximum error probability criterion, and with a decoder that is robust against the effect of randomisation in the encoding. This relieves us from the need of decoding the randomisation parameter which is in general not possible withi…
The growth of interest in massive MIMO systems is accompanied with hardware cost and computational complexity. Antenna selection is an efficient approach to overcome this cost-plus-complexity issue which also enhances the secrecy performance in wiretap settings. Optimal antenna selection requires exhaustive search which is computationally infeasible for settings with large dimensions. This paper develops an iterative algorithm for antenna selection in massive multiuser MIMO wiretap settings. The algorithm takes a stepwise approach to find a suitable subset of transmit antennas. Numerical inves…
The coding problem for wiretap channels with causal channel state information available at the encoder and/or the decoder is studied under the strong secrecy criterion. This problem consists of two aspects: one is due to naive wiretap channel coding and the other is due to one-time pad cipher based on the secret key agreement between Alice and Bob using the channel state information. These two aspects are closely related to each other and investigated in details from the viewpoint of achievable rates with strong secrecy. The general wiretap channel with various directions of channel state info…
In this paper, we consider the achievable sum secrecy rate in MISO (multiple-input-single-output) {\em full-duplex} wiretap channel in the presence of a passive eavesdropper and imperfect channel state information (CSI). We assume that the users participating in full-duplex communication have multiple transmit antennas, and that the users and the eavesdropper have single receive antenna each. The users have individual transmit power constraints. They also transmit jamming signals to improve the secrecy rates. We obtain the achievable perfect secrecy rate region by maximizing the worst case sum…
We consider lattice coding for the Gaussian wiretap channel, where the challenge is to ensure reliable communication between two authorized parties while preventing an eavesdropper from learning the transmitted messages. Recently, a measure called the secrecy function of a lattice coding scheme was proposed as a design criterion to characterize the eavesdropper's probability of correct decision. In this paper, the family of formally unimodular lattices is presented and shown to possess the same secrecy function behavior as unimodular and isodual lattices. Based on Construction A, we provide a …
We determine the secrecy capacities under common randomness assisted coding of arbitrarily varying classical-quantum wiretap channels.Furthermore, we determine the secrecy capacity of a mixed channel model which is compound from the sender to the legal receiver and varies arbitrarily from the sender to the eavesdropper. As an application we examine when the secrecy capacity is a continuous function of the system parameters and show that resources, i.e., having access to a perfect copy of the outcome of a random experiment. are helpful for channel stability.
In this paper, we consider the problem of power allocation in MIMO wiretap channel for secrecy in the presence of multiple eavesdroppers. Perfect knowledge of the destination channel state information (CSI) and only the statistical knowledge of the eavesdroppers CSI are assumed. We first consider the MIMO wiretap channel with Gaussian input. Using Jensen's inequality, we transform the secrecy rate max-min optimization problem to a single maximization problem. We use generalized singular value decomposition and transform the problem to a concave maximization problem which maximizes the sum secr…
In this paper we consider the problem of secure network coding where an adversary has access to an unknown subset of links chosen from a known collection of links subsets. We study the capacity region of such networks, commonly called "wiretap networks", subject to weak and strong secrecy constraints, and consider both zero-error and asymptotically zero-error communication. We prove that in general discrete memoryless networks modeled by discrete memoryless channels, the capacity region subject to strong secrecy requirement and the capacity region subject to weak secrecy requirement are equal.…
An alternative or supplementary approach named as physical layer security has been proposed to afford an extra security layer on top of the conventional cryptography technique. In this paper, an overview of secrecy performance investigations over the classic Alice-Bob-Eve wiretap fading channels is conducted. On the basis of the classic wiretap channel model, we have comprehensively listed and thereafter compared the existing works on physical layer secrecy analysis considering the small-scale, large-scale, composite, and cascaded fading channel models. Exact secrecy metrics expressions, inclu…
Achieving Optimal Short-Blocklength Secrecy Rate Using Multi-Kernel PAC Codes for the Binary Erasure Wiretap Channel
本文针对二进制擦除窃听信道，提出多核PAC码短分组编码方案，证明在特定保密泄漏约束下可在分组长度16至128实现理论最优保密速率。
In many information-theoretic channel coding problems, adding an input cost constraint to the operational setup amounts to restricting the optimization domain in the capacity formula. This paper shows that, in contrast to common belief, such a simple modification does not hold for the cost-constrained (CC) wiretap channel (WTC). The secrecy-capacity of the discrete memoryless (DM) WTC without cost constraints is described by a single auxiliary random variable. For the CC DM-WTC, however, we show that two auxiliaries are necessary to achieve capacity. Specifically, we first derive the secrecy-c…
We consider the MIMO wiretap channel, that is a MIMO broadcast channel where the transmitter sends some confidential information to one user which is a legitimate receiver, while the other user is an eavesdropper. Perfect secrecy is achieved when the the transmitter and the legitimate receiver can communicate at some positive rate, while insuring that the eavesdropper gets zero bits of information. In this paper, we compute the perfect secrecy capacity of the multiple antenna MIMO broadcast channel, where the number of antennas is arbitrary for both the transmitter and the two receivers.
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-dimensiona…
This paper presents a detailed secrecy outage performance analysis of correlated multi-antenna wiretap channels with three popular diversity combining schemes, namely maximal ratio combining, selection combining, and equal gain combining at the legitimate receiver. For single input multiple output wiretap channels, both exact and asymptotic expressions are derived for the secrecy outage probability (SOP) of these systems. The findings suggest that, compared with the scenario where all the channels are independent, correlation of the main channels alone increases the SOP by a factor of 1/ det(U…
This paper studies a scalar Gaussian wiretap channel where instead of an average input power constraint, we consider a peak amplitude constraint on the input. The goal is to obtain insights into the secrecy-capacity and the structure of the secrecy-capacity-achieving distribution. Capitalizing on the recent theoretical progress on the structure of the secrecy-capacity-achieving distribution, this paper develops a numerical procedure, based on the gradient ascent algorithm and a version of the Blahut-Arimoto algorithm, for computing the secrecy-capacity and the secrecy-capacity-achieving input …
This work investigates the effect of finite-alphabet source input on the secrecy rate of a multi-antenna wiretap system. Existing works have characterized maximum achievable secrecy rate or secrecy capacity for single and multiple antenna systems based on Gaussian source signals and secrecy code. Despite the impracticality of Gaussian sources, the compact closed-form expression of mutual information between linear channel Gaussian input and corresponding output has led to broad application of Gaussian input assumption in physical secrecy analysis. For practical considerations, we study the eff…
We derive a lower bound on the secrecy capacity of the compound wiretap channel with channel state information at the transmitter which matches the general upper bound on the secrecy capacity of general compound wiretap channels given by Liang et al. and thus establishing a full coding theorem in this case. We achieve this with a quite strong secrecy criterion and with a decoder that is robust against the effect of randomisation in the encoding. This relieves us from the need of decoding the randomisation parameter which is in general not possible within this model. Moreover we prove a lower b…
Incorporating the physical layer characteristics to secure communications has received considerable attention in recent years. Moreover, cooperation with some nodes of network can give benefits of multiple-antenna systems, increasing the secrecy capacity of such channels. In this paper, we consider cooperative wiretap channel with the help of an Amplify and Forward (AF) relay to transmit confidential messages from source to legitimate receiver in the presence of an eavesdropper. In this regard, the secrecy capacity of AF relying is derived, assuming the relay is subject to a peak power constra…
In this paper, a new wiretap channel model is proposed, where the legitimate transmitter and receiver communicate over a discrete memoryless channel. The wiretapper has perfect access to a fixed-length subset of the transmitted codeword symbols of her choosing. Additionally, she observes the remainder of the transmitted symbols through a discrete memoryless channel. This new model subsumes the classical wiretap channel and wiretap channel II with noisy main channel as its special cases. The strong secrecy capacity of the proposed channel model is identified. Achievability is established by sol…
In this paper, we consider a semi-deterministic wiretap channel where the main channel is noiseless and the eavesdropper's channel is a binary erasure channel (BEC). We provide a lower bound for the achievable secrecy rates of polar and Reed Muller codes and compare it to the second order coding rate for the semi-deterministic wiretap channel. To the best of our knowledge, this is the first work which demonstrates the secrecy performance of polar and Reed-Muller codes in short blocklengths. The results show that under a total variation secrecy metric, Reed Muller codes can achieve secrecy rate…
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 eavesdropper's 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 pre…
Shannon's secrecy system is studied in a setting, where both the legitimate decoder and the wiretapper have access to side information sequences correlated to the source, but the wiretapper receives both the coded information and the side information via channels that are more noisy than the respective channels of the legitmate decoder, which in turn, also shares a secret key with the encoder. A single--letter characterization is provided for the achievable region in the space of five figures of merit: the equivocation at the wiretapper, the key rate, the distortion of the source reconstructio…
This work investigates the secrecy capacity of the Wiretap Broadcast Channel (WBC) with an external eavesdropper where a source wishes to communicate two private messages over a Broadcast Channel (BC) while keeping them secret from the eavesdropper. We derive a non-trivial outer bound on the secrecy capacity region of this channel which, in absence of security constraints, reduces to the best known outer bound to the capacity of the standard BC. An inner bound is also derived which follows the behavior of both the best known inner bound for the BC and the Wiretap Channel. These bounds are show…
Adaptive Coding for Two-Way Wiretap Channel under Strong Secrecy
本文针对双向窃听信道的强保密需求，提出两种自适应编码方案，推导了不同保密约束下的保密容量域内界，并证明满足条件独立条件的信道在联合保密约束下仍可实现正传输速率。
We consider a two user multiple-access channel with an eavesdropper at the receiving end. We use previously transmitted messages as a key in the next slot till we achieve the capacity region of the usual Multiple Access Channel (MAC).
Identification Under the Semantic Effective Secrecy Constraint
本文在语义有效保密准则下研究离散无记忆窃听信道的识别问题，提出输出统计近似与传输结合的方法，推导容量定理并给出紧界及示例。
Finite-Length Empirical Comparison of Polar, PAC, and Invertible-Extractor Secrecy Codes over the Wiretap BSC
本文通过经验比较三种保密编码方案在有限块长下的性能，发现PAC码在不改变保密性的同时显著提升可靠性，且极码/PAC码在安全保证上优于可逆提取器框架。
We propose a secure transmission scheme for a relay wiretap channel, where a source communicates with a destination via a decode-and-forward relay in the presence of spatially random-distributed eavesdroppers. We assume that the source is equipped with multiple antennas, whereas the relay, the destination, and the eavesdroppers are equipped with a single antenna each. In the proposed scheme, in addition to information signals, the source transmits artificial noise signals in order to confuse the eavesdroppers. With the target of maximizing the secrecy throughput of the relay wiretap channel, w…
We consider the multi-antenna wiretap channel in which the transmitter wishes to send a confidential message to its receiver while keeping it secret to the eavesdropper. It has been known that the secrecy capacity of such a channel does not increase with signal-to-noise ratio when the transmitter has no channel state information (CSI) under mild conditions. Motivated by Jafar's robust interference alignment technique, we study the so-called staggered multi-antenna block-fading wiretap channel where the legitimate receiver and the eavesdropper have different temporal correlation structures. Ass…
This paper investigates the maximal secret communication rate over a wiretap channel subject to reliability and secrecy constraints at a given blocklength. New achievability and converse bounds are derived, which are uniformly tighter than existing bounds, and lead to the tightest bounds on the second-order coding rate for discrete memoryless and Gaussian wiretap channels. The exact second-order coding rate is established for semi-deterministic wiretap channels, which characterizes the optimal tradeoff between reliability and secrecy in the finite-blocklength regime. Underlying our achievabili…
One key metric for physical layer security is the secrecy capacity. This is the maximum rate that a system can transmit with perfect secrecy. For a Multiple Input Multiple Output (MIMO) system (a newer technology for 5G, 6G and beyond) the secrecy capacity is not fully understood. For a Gaussian MIMO channel, the secrecy capacity is a non-convex optimisation problem for which a general solution is not available. Previous work by the authors showed that the secrecy capacity of a MIMO system with a single eavesdrop antenna is concave to a cut off point. In this work, which extends the previous p…
We show that duals of certain low-density parity-check (LDPC) codes, when used in a standard coset coding scheme, provide strong secrecy over the binary erasure wiretap channel (BEWC). This result hinges on a stopping set analysis of ensembles of LDPC codes with block length $n$ and girth $\geq 2k$, for some $k \geq 2$. We show that if the minimum left degree of the ensemble is $l_\mathrm{min}$, the expected probability of block error is $\calO(\frac{1}{n^{\lceil l_\mathrm{min} k /2 \rceil - k}})$ when the erasure probability $ε< ε_\mathrm{ef}$, where $ε_\mathrm{ef}$ depends on the degree dist…
Secrecy Coding for the Binary Symmetric Wiretap Channel via Linear Programming
本文利用线性规划优化方法研究主信道无噪声、窃听信道为BSC的窃听信道，提出更紧的有限码长保密速率极限及优于随机装箱码的保密编码方案，并给出线性和非线性码的装箱技术。
The Gaussian wiretap channel with rate-limited help, available at the legitimate receiver (Rx) or/and transmitter (Tx), is studied under various channel configurations (degraded, reversely degraded and non-degraded). In the case of Rx help and all channel configurations, the rate-limited help results in a secrecy capacity boost equal to the help rate irrespective of whether the help is secure or not, so that the secrecy of help does not provide any capacity increase. The secrecy capacity is positive for the reversely-degraded channel (where the no-help secrecy capacity is zero) and no wiretap …
This paper shows determining the secrecy capacity of a unicast network with uniform wiretap sets is at least as difficult as the k-unicast problem. In particular, we show that a general k-unicast problem can be reduced to the problem of finding the secrecy capacity of a corresponding single unicast network with uniform link capacities and one arbitrary wiretap link.
The wiretap channel has been devised and studied first by Wyner, and subsequently extended to the case with non-degraded general wiretap channels by Csiszar and Korner. Focusing mainly on the Poisson wiretap channel with cost constraint, we newly introduce the notion of reliability and security functions as a fundamental tool to analyze and/or design the performance of an efficient wiretap channel system. Compact formulae for those functions are explicitly given for stationary memoryless wiretap channels. It is also demonstrated that, based on such a pair of reliability and security functions,…
Probabilistic Shaped Multilevel Polar Coding for Wiretap Channel
针对高斯窃听信道中离散星座输入与高斯保密容量之间的差距，提出概率成形多级极化编码方案，优化输入分布并集成多级极化码，证明可达保密容量并满足安全条件，仿真验证优于均匀输入。
This letter proposes a novel UAV-enabled mobile jamming scheme to improve the secrecy rate of ground wiretap channel. Specifically, a UAV is employed to transmit jamming signals to combat against eavesdropping. Such a mobile jamming scheme is particularly appealing since the UAV-enabled jammer can fly close to the eavesdropper and opportunistically jam it by leveraging the UAV's mobility. We aim to maximize the average secrecy rate by jointly optimizing the UAV's trajectory and jamming power over a given flight period. To make the problem more tractable, we drive a closed-form lower bound for …
This paper investigates the maximal secrecy rate over a wiretap channel subject to reliability and secrecy constraints at a given blocklength. New achievability and converse bounds are derived, which are shown to be tighter than existing bounds. The bounds also lead to the tightest second-order coding rate for discrete memoryless and Gaussian wiretap channels.
We consider a wiretap channel and use previously transmitted messages to generate a secret key which increases the secrecy capacity. This can be bootstrapped to increase the secrecy capacity to the Shannon capacity without using any feedback or extra channel while retaining the strong secrecy of the wiretap channel.
This paper considers a multiple-input multiple-output (MIMO) Gaussian wiretap channel model, where there exists a transmitter, a legitimate receiver and an eavesdropper, each equipped with multiple antennas. Perfect secrecy is achieved when the transmitter and the legitimate receiver can communicate at some positive rate, while ensuring that the eavesdropper gets zero bits of information. In this paper, the perfect secrecy capacity of the multiple antenna MIMO wiretap channel is found for aribtrary numbers of antennas under the assumption that the transmitter performs beamforming based on the …
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