We consider the problem of encoding a deterministic source sequence (a.k.a.\ individual sequence) for the degraded wiretap channel by means of an encoder and decoder that can both be implemented as finite--state machines. Our first main result is a necessary condition for both reliable and secure transmission in terms of the given source sequence, the bandwidth expansion factor, the secrecy capacity, the number of states of the encoder and the number of states of the decoder. Equivalently, this necessary condition can be presented as a converse bound (i.e., a lower bound) on the smallest achievable bandwidth expansion factor. The bound is asymptotically achievable by Lempel-Ziv compression followed by good channel coding for the wiretap channel. Given that the lower bound is saturated, we also derive a lower bound on the minimum necessary rate of purely random bits needed for local randomness at the encoder in order to meet the security constraint. This bound too is achieved by the same achievability scheme. Finally, we extend the main results to the case where the legitimate decoder has access to a side information sequence, which is another individual sequence that may be related to the source sequence, and a noisy version of the side information sequence leaks to the wiretapper.
A wiretap protocol is a pair of randomized encoding and decoding functions such that knowledge of a bounded fraction of the encoding of a message reveals essentially no information about the message, while knowledge of the entire encoding reveals the message using the decoder. In this paper we study the notion of efficiently invertible extractors and show that a wiretap protocol can be constructed from such an extractor. We will then construct invertible extractors for symbol-fixing, affine, and general sources and apply them to create wiretap protocols with asymptotically optimal trade-offs b…
The Gaussian multiple-input multiple-output (MIMO) multi-receiver wiretap channel is studied in this paper. The base station broadcasts confidential messages to K intended users while keeping the messages secret from an eavesdropper. The capacity of this channel has already been characterized by applying dirty-paper coding and stochastic encoding. However, K factorial encoding orders may need to be enumerated for that, which makes the problem intractable. We prove that there exists one optimal encoding order and reduced the K factorial times to a one-time encoding. The optimal encoding order i…
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…
A polar coding scheme is proposed for the Wiretap Broadcast Channel with two legitimate receivers and one eavesdropper. We consider a model in which the transmitter wishes to send different confidential (and non-confidential) information to each legitimate receiver. First, we compare two inner-bounds on the achievable region of this model from the literature, and then we design a polar coding scheme that achieves the stronger one. In the proposed scheme, the encoding uses polar-based Marton's coding, where one inner-layer must be reliably decoded by both legitimate receivers, and each receiver…
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…
We consider MIMO (Multiple Input Multiple Output) wiretap channels, where a legitimate transmitter Alice is communicating with a legitimate receiver Bob in the presence of an eavesdropper Eve, and communication is done via MIMO channels. We suppose that Alice's strategy is to use a codebook which has a lattice structure, which then allows her to perform coset encoding. We analyze Eve's probability of correctly decoding the message Alice meant to Bob, and from minimizing this probability, we derive a code design criterion for MIMO lattice wiretap codes. The case of block fading channels is trea…
We consider transmission over a wiretap channel where both the main channel and the wiretapper's channel are Binary Erasure Channels (BEC). We use convolutional LDPC ensembles based on the coset encoding scheme. More precisely, we consider regular two edge type convolutional LDPC ensembles. We show that such a construction achieves the whole rate-equivocation region of the BEC wiretap channel. Convolutional LDPC ensemble were introduced by Felström and Zigangirov and are known to have excellent thresholds. Recently, Kudekar, Richardson, and Urbanke proved that the phenomenon of "Spatial Coupli…
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…
We consider the Gaussian wiretap channel, where two legitimate players Alice and Bob communicate over an additive white Gaussian noise (AWGN) channel, while Eve is eavesdropping, also through an AWGN channel. We propose a coding strategy based on lattice coset encoding. We analyze Eve's probability of decoding, from which we define the secrecy gain as a design criterion for wiretap lattice codes, expressed in terms of the lattice theta series, which characterizes Eve's confusion as a function of the channel parameters. The secrecy gain is studied for even unimodular lattices, and an asymptotic…
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…
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.
In this paper, we propose a polar coding scheme for secure communication over the multiple-input, single-output, single-antenna eavesdropper (MISOSE) fading channel. We consider the case of block fading channels with known eavesdropper channel state information (CSI) and the case of fading channels with known eavesdropper channel distribution information (CDI). We use the artificial noise assisted secure precoding method to maximize the secrecy capacity in the first case, and to overcome the unawareness of the eavesdropper CSI in the second case. We show that our proposed scheme can provide bo…
Freie Universität Berlin（柏林自由大学）；Universität Siegen（锡根大学）
The use of deep learning-based techniques for approximating secure encoding functions has attracted considerable interest in wireless communications due to impressive results obtained for general coding and decoding tasks for wireless communication systems. Of particular importance is the development of model-free techniques that work without knowledge about the underlying channel. Such techniques utilize for example generative adversarial networks to estimate and model the conditional channel distribution, mutual information estimation as a reward function, or reinforcement learning. In this …
In this work we study encoding/decoding schemes for the transmission of a discrete time analog Gaussian source over a Gaussian wiretap channel. The intended receiver is assumed to have a certain minimum signal to noise ratio (SNR) and the eavesdropper is assumed to have a strictly lower SNR compared to the intended receiver. For a fixed information leakage to the eavesdropper, we are interested in minimizing the distortion in source reconstruction at the intended receiver, and we propose joint source channel coding (JSCC) schemes for this setup. For a fixed information leakage to the eavesdrop…
The coding problem for wiretap channels with causal channel state information (CSI) available at the encoder (Alice) and/or the decoder (Bob) is studied. We are concerned here particularily with the problem of achievable secret-message secret-key rate pairs under the semantic security criterion. Our main result extends all the previous results on achievable rates as given by Chia and El Gamal [10], Fujita [11], and Han and Sasaki [23]. In order to do this, we first derive a unifying theorem (Theorem 2) with causal CSI at Alice, which follows immediately by leveraging the unifying seminal theor…
End-to-end learning of communication systems with neural networks and particularly autoencoders is an emerging research direction which gained popularity in the last year. In this approach, neural networks learn to simultaneously optimize encoding and decoding functions to establish reliable message transmission. In this paper, this line of thinking is extended to communication scenarios in which an eavesdropper must further be kept ignorant about the communication. The secrecy of the transmission is achieved by utilizing a modified secure loss function based on cross-entropy which can be impl…
We study the problem of secure transmission over a Gaussian multi-input single-output (MISO) two receiver channel with an external eavesdropper, under the assumption that the state of the channel which is available to each receiver is conveyed either perfectly ($P$) or with delay ($D$) to the transmitter. Denoting by $S_1$, $S_2$, and $S_3$ the channel state information at the transmitter (CSIT) of user 1, user 2, and eavesdropper, respectively, the overall CSIT can then alternate between eight possible states, i.e., $(S_1,S_2,S_3) \in \{P,D\}^3$. We denote by $λ_{S_1 S_2 S_3}$ the fraction of…
In a point-to-point communication system which consists of a sender, a receiver and a set of noiseless channels, the sender wishes to transmit a private message to the receiver through the channels which may be eavesdropped by a wiretapper. The set of wiretap sets is arbitrary. The wiretapper can access any one but not more than one wiretap set. From each wiretap set, the wiretapper can obtain some partial information about the private message which is measured by the equivocation of the message given the symbols obtained by the wiretapper. The security strategy is to encode the message with s…
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…
We consider transmission over a wiretap channel where both the main channel and the wiretapper's channel are Binary Erasure Channels (BEC). We propose a code construction method using two edge type LDPC codes based on the coset encoding scheme. Using a standard LDPC ensemble with a given threshold over the BEC, we give a construction for a two edge type LDPC ensemble with the same threshold. If the given standard LDPC ensemble has degree two variable nodes, our construction gives rise to degree one variable nodes in the code used over the main channel. This results in zero threshold over the m…
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…
In this paper, we consider the Gaussian diamond-wiretap channel that consists of an orthogonal broadcast channel from a source to two relays and a Gaussian fast-fading multiple access-wiretap channel from the two relays to a legitimate destination and an eavesdropper. For the multiple access part, we consider both the case with full channel state information (CSI) and the case with no eavesdropper's CSI, at the relays and the legitimate destination. For both the cases, we establish the exact secure degrees of freedom and generalize the results for multiple relays. For the converse part, we int…
We consider the problem of private information retrieval through wiretap channel II (PIR-WTC-II). In PIR-WTC-II, a user wants to retrieve a single message (file) privately out of $M$ messages, which are stored in $N$ replicated and non-communicating databases. An external eavesdropper observes a fraction $μ_n$ (of its choice) of the traffic exchanged between the $n$th database and the user. In addition to the privacy constraint, the databases should encode the returned answer strings such that the eavesdropper learns absolutely nothing about the \emph{contents} of the databases. We aim at char…
Wyner's work on wiretap channels and the recent works on information theoretic security are based on random codes. Achieving information theoretical security with practical coding schemes is of definite interest. In this note, the attempt is to overcome this elusive task by employing the polar coding technique of Arıkan. It is shown that polar codes achieve non-trivial perfect secrecy rates for binary-input degraded wiretap channels while enjoying their low encoding-decoding complexity. In the special case of symmetric main and eavesdropper channels, this coding technique achieves the secrecy …
In this work we study the problem of secure communication over a fully quantum Gel'fand-Pinsker channel. The best known achievability rate for this channel model in the classical case was proven by Goldfeld, Cuff and Permuter in [Goldfeld, Cuff, Permuter, 2016]. We generalize the result of [Goldfeld, Cuff, Permuter, 2016]. One key feature of the results obtained in this work is that all the bounds obtained are in terms of error exponent. We obtain our achievability result via the technique of simultaneous pinching. This in turn allows us to show the existence of a simultaneous decoder. Further…
Suppose Alice wishes to send messages to Bob through a communication channel C_1, but her transmissions also reach an eavesdropper Eve through another channel C_2. The goal is to design a coding scheme that makes it possible for Alice to communicate both reliably and securely. Reliability is measured in terms of Bob's probability of error in recovering the message, while security is measured in terms of Eve's equivocation ratio. Wyner showed that the situation is characterized by a single constant C_s, called the secrecy capacity, which has the following meaning: for all $ε> 0$, there exist co…
Correlated sources are present in communication systems where protocols ensure that there is some predetermined information for sources. Here correlated sources across an eavesdropped channel that incorporate a heterogeneous encoding scheme and their effect on the information leakage when some channel information and a source have been wiretapped is investigated. The information leakage bounds for the Slepian-Wolf scenario are provided. Thereafter, the Shannon cipher system approach is presented. Further, an implementation method using a matrix partition approach is described.
Suppose Alice wishes to send messages to Bob through a communication channel C_1, but her transmissions also reach an eavesdropper Eve through another channel C_2. The goal is to design a coding scheme that makes it possible for Alice to communicate both reliably and securely. Reliability is measured in terms of Bob's probability of error in recovering the message, while security is measured in terms of the mutual information between the message and Eve's observations. Wyner showed that the situation is characterized by a single constant C_s, called the secrecy capacity, which has the followin…
In this paper, we investigate how constraints on the randomization in the encoding process affect the secrecy rates achievable over wiretap channels. In particular, we characterize the secrecy capacity with a rate-limited local source of randomness and a less capable eavesdropper's channel, which shows that limited rate incurs a secrecy rate penalty but does not preclude secrecy. We also discuss a more practical aspect of rate-limited randomization in the context of cooperative jamming. Finally, we show that secure communication is possible with a non-uniform source for randomness; this sugges…
Channel polarization is a phenomenon in which a particular recursive encoding induces a set of synthesized channels from many instances of a memoryless channel, such that a fraction of the synthesized channels becomes near perfect for data transmission and the other fraction becomes near useless for this task. Mahdavifar and Vardy have recently exploited this phenomenon to construct codes that achieve the symmetric private capacity for private data transmission over a degraded wiretap channel. In the current paper, we build on their work and demonstrate how to construct quantum wiretap polar c…
We present adaptive on-line schemes for lossy encoding of individual sequences under the conditions of the Wyner-Ziv (WZ) problem. In the first part of this article, a set of fixed-rate scalar source codes with zero delay is presented. We propose a randomized on-line coding scheme, which achieves asymptotically (and with high probability), the performance of the best source code in the set, uniformly over all source sequences. The scheme uses the same rate and has zero delay. We then present an efficient algorithm for implementing our on-line coding scheme in the case of a relatively small set…
We study the problem of secure transmission over a Gaussian two-user multi-input single-output (MISO) broadcast channel under the assumption that links connecting the transmitter to the two receivers may have unequal strength statistically. In addition to this, the state of the channel to each receiver is conveyed in a strictly causal manner to the transmitter. We focus on a two state topological setting of strong v.s. weak links. Under these assumptions, we first consider the MISO wiretap channel and establish bounds on generalized secure degrees of freedom (GSDoF). Next, we extend this model…
We consider the problem of secure and reliable communication over a noisy multipath network. Previous work considering a noiseless version of our problem proposed a hybrid universal network coding cryptosystem (HUNCC). By combining an information-theoretically secure encoder together with partial encryption, HUNCC is able to obtain security guarantees, even in the presence of an all-observing eavesdropper. In this paper, we propose a version of HUNCC for noisy channels (N-HUNCC). This modification requires four main novelties. First, we present a network coding construction which is jointly, i…
Besides the determined construction of polar codes in BEC channels, different construction techniques have been proposed for AWGN channels. The current state-of-the-art algorithm starts with a design-SNR (or an operating SNR) and then processing is carried out to approximate each individual bit channel. However, as found in this paper, for fading channels, an operating SNR can not be directly used in approximating the bit channels. To achieve a better BER performance, the input SNR for the polar code construction in fadding channels is derived. A selection of the design-SNR for both the AWGN a…
Motivated by video coding applications, the problem of sequential coding of correlated sources with encoding and/or decoding frame-delays is studied. The fundamental tradeoffs between individual frame rates, individual frame distortions, and encoding/decoding frame-delays are derived in terms of a single-letter information-theoretic characterization of the rate-distortion region for general inter-frame source correlations and certain types of potentially frame specific and coupled single-letter fidelity criteria. The sum-rate-distortion region is characterized in terms of generalized directed …
We propose two coding schemes combining decode-forward (DF) and noisy network coding (NNC) with different flavors. The first is a combined DF-NNC scheme for the one-way relay channel which includes both DF and NNC as special cases by performing rate splitting, partial block Markov encoding and NNC. The second combines two different DF strategies and layered NNC for the two-way relay channel. One DF strategy performs coherent block Markov encoding at the source at the cost of power splitting at the relay, the other performs independent source and relay encoding but with full relay power, and la…
We consider lossy compression of a binary symmetric source by means of a low-density generator-matrix code. We derive two lower bounds on the rate distortion function which are valid for any low-density generator-matrix code with a given node degree distribution L(x) on the set of generators and for any encoding algorithm. These bounds show that, due to the sparseness of the code, the performance is strictly bounded away from the Shannon rate-distortion function. In this sense, our bounds represent a natural generalization of Gallager's bound on the maximum rate at which low-density parity-che…
