In this work we consider the communication of information in the presence of a causal adversarial jammer. In the setting under study, a sender wishes to communicate a message to a receiver by transmitting a codeword x=(x_1,...,x_n) bit-by-bit over a communication channel. The adversarial jammer can view the transmitted bits x_i one at a time, and can change up to a p-fraction of them. However, the decisions of the jammer must be made in an online or causal manner. Namely, for each bit x_i the jammer's decision on whether to corrupt it or not (and on how to change it) must depend only on x_j for j <= i. This is in contrast to the "classical" adversarial jammer which may base its decisions on its complete knowledge of x. We present a non-trivial upper bound on the amount of information that can be communicated. We show that the achievable rate can be asymptotically no greater than min{1-H(p),(1-4p)^+}. Here H(.) is the binary entropy function, and (1-4p)^+ equals 1-4p for p < 0.25, and 0 otherwise.
We consider the problem of communication over a multi-path network in the presence of a causal adversary. The limited-view causal adversary is able to eavesdrop on a subset of links and also jam on a potentially overlapping subset of links based on the current and past information. To ensure that the communication takes place reliably and secretly, resilient network codes with necessary redundancy are needed. We study two adversarial models - additive and overwrite jamming and we optionally assume passive feedback from decoder to encoder, i.e., the encoder sees everything that the decoder sees…
Authentication over Arbitrarily Varying Channels with Causal Adversaries
Northern Arizona University（北亚利桑那大学）；Tata Institute of Fundamental Research（塔塔基础研究所）；Indian Institute of Technology Bombay（孟买印度理工学院）；Arizona State University（亚利桑那州立大学）
This paper considers an arbitrarily-varying fading channel consisting of one transmitter, one receiver and an arbitrarily varying adversary. The channel is assumed to have additive Gaussian noise and fast fading of the gain from the legitimate user to the receiver. We study four variants of the problem depending on whether the transmitter and/or adversary have access to the fading gains; we assume the receiver always knows the fading gains. In two variants the adversary does not have access to the gains, we show that the capacity corresponds to the capacity of a standard point-to-point fading …
In this paper, we take an arbitrarily varying channel (AVC) approach to examine the problem of writing on a dirty paper in the presence of an adversary. We consider an additive white Gaussian noise (AWGN) channel with an additive white Gaussian state, where the state is known non-causally to the encoder and the adversary, but not the decoder. We determine the randomized coding capacity of this AVC under the maximal probability of error criterion. Interestingly, it is shown that the jamming adversary disregards the state knowledge to choose a white Gaussian channel input which is independent of…
In this paper, we study a model of communication under adversarial noise. In this model, the adversary makes online decisions on whether to corrupt a transmitted bit based on only the value of that bit. Like the usual binary symmetric channel of information theory or the fully adversarial channel of combinatorial coding theory, the adversary can, with high probability, introduce at most a given fraction of error. It is shown that, the capacity (maximum rate of reliable information transfer) of such memoryless adversary is strictly below that of the binary symmetric channel. We give new upper b…
We study communication systems over state-dependent channels in the presence of a malicious state-aware jamming adversary. The channel has a memoryless state with an underlying distribution. The adversary introduces a jamming signal into the channel. The state sequence is known non-causally to both the encoder and the adversary. Taking an Arbitrarily Varying Channel (AVC) approach, we consider two setups, namely, the discrete memoryless Gel'fand-Pinsker (GP) AVC and the additive white Gaussian Dirty Paper (DP) AVC. We determine the randomized coding capacity of both the AVCs under a maximum pr…
Secure communication over a wiretap channel is investigated, in which an active adversary modifies the state of the channel and the legitimate transmitter has the opportunity to sense and learn the adversary's actions. The adversary has the ability to switch the channel state and observe the corresponding output at every channel use while the encoder has causal access to observations that depend on the adversary's actions. A joint learning/transmission scheme is developed in which the legitimate users learn and adapt to the adversary's actions. For some channel models, it is shown that the ach…
We characterize the capacity for the discrete-time arbitrarily varying channel with discrete inputs, outputs, and states when (a) the encoder and decoder do not share common randomness, (b) the input and state are subject to cost constraints, (c) the transition matrix of the channel is deterministic given the state, and (d) at each time step the adversary can only observe the current and past channel inputs when choosing the state at that time. The achievable strategy involves stochastic encoding together with list decoding and a disambiguation step. The converse uses a two-phase "babble-and-p…
Secrecy in communication systems is measured herein by the distortion that an adversary incurs. The transmitter and receiver share secret key, which they use to encrypt communication and ensure distortion at an adversary. A model is considered in which an adversary not only intercepts the communication from the transmitter to the receiver, but also potentially has side information. Specifically, the adversary may have causal or noncausal access to a signal that is correlated with the source sequence or the receiver's reconstruction sequence. The main contribution is the characterization of the…
We study the problem of communication over a discrete arbitrarily varying channel (AVC) when a noisy version of the state is known non-causally at the encoder. The state is chosen by an adversary which knows the coding scheme. A state-myopic encoder observes this state non-causally, though imperfectly, through a noisy discrete memoryless channel (DMC). We first characterize the capacity of this state-dependent channel when the encoder-decoder share randomness unknown to the adversary, i.e., the randomized coding capacity. Next, we show that when only the encoder is allowed to randomize, the ca…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；University of Pennsylvania（宾夕法尼亚大学）；University of California, Santa Barbara（加州大学圣巴巴拉分校）
Adversarial examples have recently drawn considerable attention in the field of machine learning due to the fact that small perturbations in the data can result in major performance degradation. This phenomenon is usually modeled by a malicious adversary that can apply perturbations to the data in a constrained fashion, such as being bounded in a certain norm. In this paper, we study this problem when the adversary is constrained by the $\ell_0$ norm; i.e., it can perturb a certain number of coordinates in the input, but has no limit on how much it can perturb those coordinates. Due to the com…
The growing need for reliable communication over untrusted networks has caused a renewed interest in adversarial channel models, which often behave much differently than traditional stochastic channel models. Of particular practical use is the assumption of a \textit{causal} or \textit{online} adversary who is limited to causal knowledge of the transmitted codeword. In this work, we consider stochastic-adversarial mixed noise models. In the set-up considered, a transmit node (Alice) attempts to communicate with a receive node (Bob) over a binary erasure channel (BEC) or binary symmetric channe…
This work establishes that the physical layer can be used to perform information-theoretic authentication in additive white Gaussian noise channels, as long as the adversary is not omniscient. The model considered consists of an encoder, decoder, and adversary, where the adversary has access to the message, a non-causal noisy observation of the encoder's transmission, and unlimited transmission power, while the decoder observes a noisy version of the sum of the encoder and adversary's outputs. A method to modify a generic existing channel code to enable authentication is presented. It is shown…
We introduce a game-theoretic framework to study the hypothesis testing problem, in the presence of an adversary aiming at preventing a correct decision. Specifically, the paper considers a scenario in which an analyst has to decide whether a test sequence has been drawn according to a probability mass function (pmf) P_X or not. In turn, the goal of the adversary is to take a sequence generated according to a different pmf and modify it in such a way to induce a decision error. P_X is known only through one or more training sequences. We derive the asymptotic equilibrium of the game under the …
We consider the problem of covert communication over a state-dependent channel when the channel state is available either non-causally, causally, or strictly causally, either at the transmitter alone or at both transmitter and receiver. Covert communication with respect to an adversary, called "warden," is one in which, despite communication over the channel, the warden's observation remains indistinguishable from an output induced by innocent channel-input symbols. Covert communication involves fooling an adversary in part by a proliferation of codebooks; for reliable decoding at the legitima…
New bounds on the semantic secrecy capacity of the binary adversarial wiretap channel are established . Against an adversary which reads a $ρ_r$ fraction of the transmitted codeword and modifies a $ρ_w$ fraction of the codeword, we show an achievable rate of $1-h(ρ_w)-ρ_r$, where $h(\cdot)$ is the binary entropy function. We also give an upper bound which is nearly matching when $ρ_r$ is small.
Traditional channel coding with feedback constructs and transmits a codeword only after all message bits are available at the transmitter. This paper joins Guo & Kostina and Lalitha et. al. in developing approaches for causal (or progressive) encoding, where the transmitter may begin transmitting codeword symbols as soon as the first message bit arrives. Building on the work of Horstein, Shayevitz and Feder, and Naghshvar et. al., this paper extends our previous computationally efficient systematic algorithm for traditional posterior matching to produce a four-phase encoder that progressively …
We consider the problem of communication over the binary symmetric channel with feedback, where the information sequence is made available in a causal, possibly random, fashion. We develop a real-time variant of the renowned Horstein scheme and provide analytical guarantees for its error-probability exponential decay rate. We further use the scheme to stabilize an unstable control plant over a binary symmetric channel and compare the analytical guarantees with its empirical performance as well as with those of anytime-reliable codes.
The problem of channel code design for the $M$-ary input AWGN channel with additive $Q$-ary interference where the sequence of i.i.d. interference symbols is known causally at the encoder is considered. The code design criterion at high SNR is derived by defining a new distance measure between the input symbols of the Shannon's \emph{associated} channel. For the case of binary-input channel, i.e., M=2, it is shown that it is sufficient to use only two (out of $2^Q$) input symbols of the \emph{associated} channel in the encoding as far as the distance spectrum of code is concerned. This reduces…
Secure communication in a potentially malicious environment becomes more and more important. The arbitrarily varying wiretap channel (AVWC) provides information theoretical bounds on how much information can be exchanged even in the presence of an active attacker. If the active attacker has non-causal side information, situations in which a legitimate communication system has been hacked, can be modeled. We investigate the AVWC with non-causal side information at the jammer for the case that there exists a best channel to the eavesdropper. Non-causal side information means that the transmitted…
Northern Arizona University（北亚利桑那大学）；University of Wisconsin-Eau Claire（威斯康星大学欧克莱尔分校）；Arizona State University（亚利桑那州立大学）；DEVCOM Army Research Laboratory（美国陆军研究开发中心陆军研究实验室）；New Jersey Institute of Technology（新泽西理工学院）
An error correcting code ($\mathsf{ECC}$) allows a sender to send a message to a receiver such that even if a constant fraction of the communicated bits are corrupted, the receiver can still learn the message correctly. Due to their importance and fundamental nature, $\mathsf{ECC}$s have been extensively studied, one of the main goals being to maximize the fraction of errors that the $\mathsf{ECC}$ is resilient to. For adversarial erasure errors (over a binary channel) the maximal error resilience of an $\mathsf{ECC}$ is $\frac12$ of the communicated bits. In this work, we break this $\frac12$…
In the binary online (or "causal") channel coding model, a sender wishes to communicate a message to a receiver by transmitting a codeword $\mathbf{x} =(x_1,\ldots,x_n) \in \{0,1\}^n$ bit by bit via a channel limited to at most $pn$ corruptions. The channel is "online" in the sense that at the $i$th step of communication the channel decides whether to corrupt the $i$th bit or not based on its view so far, i.e., its decision depends only on the transmitted bits $(x_1,\ldots,x_i)$. This is in contrast to the classical adversarial channel in which the error is chosen by a channel that has a full …
We consider the problem of communication over a channel with a causal jamming adversary subject to quadratic constraints. A sender Alice wishes to communicate a message to a receiver Bob by transmitting a real-valued length-$n$ codeword $\mathbf{x}=x_1,...,x_n$ through a communication channel. Alice and Bob do not share common randomness. Knowing Alice's encoding strategy, an adversarial jammer James chooses a real-valued length-n noise sequence $\mathbf{s}=s_1,..,s_n$ in a causal manner, i.e., each $s_t (1<=t<=n)$ can only depend on $x_1,...,x_t$. Bob receives $\mathbf{y}$, the sum of Alice's…
Berger's paper `The Source Coding Game', IEEE Trans. Inform. Theory, 1971, considers the problem of finding the rate-distortion function for an adversarial source comprised of multiple known IID sources. The adversary, called the `switcher', was allowed only causal access to the source realizations and the rate-distortion function was obtained through the use of a type covering lemma. In this paper, the rate-distortion function of the adversarial source is described, under the assumption that the switcher has non-causal access to all source realizations. The proof utilizes the type covering le…
This paper considers an extension of the linear non-Gaussian acyclic model (LiNGAM) that determines the causal order among variables from a dataset when the variables are expressed by a set of linear equations, including noise. In particular, we assume that the variables are binary. The existing LiNGAM assumes that no confounding is present, which is restrictive in practice. Based on the concept of independent component analysis (ICA), this paper proposes an extended framework in which the mutual information among the noises is minimized. Another significant contribution is to reduce the reali…
In this work we consider the communication of information in the presence of a causal adversarial jammer. In the setting under study, a sender wishes to communicate a message to a receiver by transmitting a codeword $(x_1,...,x_n)$ bit-by-bit over a communication channel. The sender and the receiver do not share common randomness. The adversarial jammer can view the transmitted bits $x_i$ one at a time, and can change up to a $p$-fraction of them. However, the decisions of the jammer must be made in a causal manner. Namely, for each bit $x_i$ the jammer's decision on whether to corrupt it or n…
We analyze a two-receiver binary-input discrete memoryless broadcast channel, in which the transmitter communicates a common message simultaneously to both receivers and a covert message to only one of them. The unintended recipient of the covert message is treated as an adversary who attempts to detect the covert transmission. This model captures the problem of embedding covert messages in an innocent codebook and generalizes previous covert communication models in which the innocent behavior corresponds to the absence of communication between legitimate users. We identify the exact asymptoti…
We propose an adversarial training procedure for learning a causal implicit generative model for a given causal graph. We show that adversarial training can be used to learn a generative model with true observational and interventional distributions if the generator architecture is consistent with the given causal graph. We consider the application of generating faces based on given binary labels where the dependency structure between the labels is preserved with a causal graph. This problem can be seen as learning a causal implicit generative model for the image and labels. We devise a two-st…
