arXiv subjects

Mayank Bakshi

Publications and source records attributed to Mayank Bakshi.

35 records · Page 2Linked to original sources

arXiv2020

Undetectable Radios: Covert Communication under Spectral Mask Constraints

We consider the problem of covert communication over continuous-time additive white Gaussian noise (AWGN) channels under spectral mask constraints, wherein two legitimate parties attempt to communicate reliably in the presence of an eavesdropper that should be unable to estimate if communication takes place. The spectral mask constraint is imposed to restrict excessive radiation beyond the bandwidth of interest. We develop a communication scheme with theoretical reliability and covertness guarantees based on pulse amplitude modulation (PAM) with Binary Phase Shift Keying (BPSK) and root raised cosine (RRC) carrier pulses. Given a fixed transmission duration T and a spectral mask with bandwidth parameter W, we show that one can reliably and covertly transmit $O(\sqrt{WT})$ bits of information. We characterize the constant behind the $O$ and show that it is tight under some conditions.

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arXiv2019

Byzantine Multiple Access

We study communication over multiple access channels (MAC) where one of the users is possibly adversarial. When all users are non-adversarial, we want their messages to be decoded reliably. When an adversary is present, we consider two different decoding guarantees. In part I, we require that the honest users' messages be decoded reliably. We study the 3-user MAC; 2-user MAC capacity follows from point-to-point AVC capacity. We characterize the capacity region for randomized codes. We also study the capacity region for deterministic codes. We obtain necessary conditions including a new non-symmetrizability condition for the capacity region to be non-trivial. We show that when none of the users are symmetrizable, the randomized coding capacity region is also achievable with deterministic codes. In part II, we consider the weaker goal of authenticated communication where we only require that an adversarial user must not be able to cause an undetected error on the honest users' messages. For the 2-user MAC, we show that the following 3-phase scheme is rate-optimal: a standard MAC code is first used to achieve unauthenticated communication followed by two authentication phases where each user authenticates their message treating the other user as a possible adversary. We show that the authentication phases can be very short since this form of authentication itself, when possible, can be achieved for message sets whose size grow doubly exponentially in blocklength. This leads to our result that the authenticated communication capacity region of a discrete memoryless MAC is either zero or the (unauthenticated) MAC capacity region itself. This also, arguably, explains the similar nature of authenticated communication capacity of a discrete memoryless point-to-point adversarial channel recently found by Kosut and Kliewer (ITW, 2018).

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arXiv2018

Computationally Efficient Covert Communication

In this paper, we design the first computationally efficient codes for simultaneously reliable and covert communication over Binary Symmetric Channels (BSCs). Our setting is as follows: a transmitter Alice wishes to potentially reliably transmit a message to a receiver Bob, while ensuring that the transmission taking place is covert with respect to an eavesdropper Willie (who hears Alice's transmission over a noisier BSC). Prior works show that Alice can reliably and covertly transmit O(\sqrt{n}) bits over n channel uses without any shared secret between Alice and Bob. One drawback of prior works is that the computational complexity of the codes designed scales as 2^{Θ(\sqrt{n})}. In this work we provide the first computationally tractable codes with provable guarantees on both reliability and covertness, while simultaneously achieving the best known throughput for the problem.

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arXiv2017

Plausible Deniability over Broadcast Channels

In this paper, we introduce the notion of Plausible Deniability in an information theoretic framework. We consider a scenario where an entity that eavesdrops through a broadcast channel summons one of the parties in a communication protocol to reveal their message (or signal vector). It is desirable that the summoned party have enough freedom to produce a fake output that is likely plausible given the eavesdropper's observation. We examine three variants of this problem -- Message Deniability, Transmitter Deniability, and Receiver Deniability. In the first setting, the message sender is summoned to produce the sent message. Similarly, in the second and third settings, the transmitter and the receiver are required to produce the transmitted codeword, and the received vector respectively. For each of these settings, we examine the maximum communication rate that allows a given minimum rate of plausible fake outputs. For the Message and Transmitter Deniability problems, we fully characterise the capacity region for general broadcast channels, while for the Receiver Deniability problem, we give an achievable rate region for physically degraded broadcast channels.

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arXiv2016

Reliable Deniable Communication: Hiding Messages in Noise

A transmitter Alice may wish to reliably transmit a message to a receiver Bob over a binary symmetric channel (BSC), while simultaneously ensuring that her transmission is deniable from an eavesdropper Willie. That is, if Willie listening to Alice's transmissions over a "significantly noisier" BSC than the one to Bob, he should be unable to estimate even whether Alice is transmitting. We consider two scenarios. In our first scenario, we assume that the channel transition probability from Alice to Bob and Willie is perfectly known to all parties. Here, even when Alice's (potential) communication scheme is publicly known to Willie (with no common randomness between Alice and Bob), we prove that over 'n' channel uses Alice can transmit a message of length O(sqrt{n}) bits to Bob, deniably from Willie. We also prove information-theoretic order-optimality of this result. In our second scenario, we allow uncertainty in the knowledge of the channel transition probability parameters. In particular, we assume that the channel transition probabilities for both Bob and Willie are uniformly drawn from a known interval. Here, we show that, in contrast to the previous setting, Alice can communicate O(n) bits of message reliably and deniably (again, with no common randomness). We give both an achievability result and a matching converse for this setting. Our work builds upon the work of Bash et al on AWGN channels (but with common randomness) and differs from other recent works (by Wang et al and Bloch) in two important ways - firstly our deniability metric is variational distance (as opposed to Kullback-Leibler divergence), and secondly, our techniques are significantly different from these works.

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arXiv2016

Arbitrarily Varying Networks: Capacity-achieving Computationally Efficient Codes

We consider the problem of communication over a network containing a hidden and malicious adversary that can control a subset of network resources, and aims to disrupt communications. We focus on omniscient node-based adversaries, i.e., the adversaries can control a subset of nodes, and know the message, network code and packets on all links. Characterizing information-theoretically optimal communication rates as a function of network parameters and bounds on the adversarially controlled network is in general open, even for unicast (single source, single destination) problems. In this work we characterize the information-theoretically optimal randomized capacity of such problems, i.e., under the assumption that the source node shares (an asymptotically negligible amount of) independent common randomness with each network node a priori (for instance, as part of network design). We propose a novel computationally-efficient communication scheme whose rate matches a natural information-theoretically "erasure outer bound" on the optimal rate. Our schemes require no prior knowledge of network topology, and can be implemented in a distributed manner as an overlay on top of classical distributed linear network coding.

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arXiv2015

Coding against a Limited-view Adversary: The Effect of Causality and Feedback

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. The problem assumes transmissions are in the large alphabet regime. For both jamming models, we find the capacity under four scenarios - reliability without feedback, reliability and secrecy without feedback, reliability with passive feedback, reliability and secrecy with passive feedback. We observe that, in comparison to the non-causal setting, the capacity with a causal adversary is strictly increased for a wide variety of parameter settings and present our intuition through several examples.

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arXiv2015

Energy-efficient Decoders for Compressive Sensing: Fundamental Limits and Implementations

The fundamental problem considered in this paper is "What is the \textit{energy} consumed for the implementation of a \emph{compressive sensing} decoding algorithm on a circuit?". Using the "information-friction" framework, we examine the smallest amount of \textit{bit-meters} as a measure for the energy consumed by a circuit. We derive a fundamental lower bound for the implementation of compressive sensing decoding algorithms on a circuit. In the setting where the number of measurements scales linearly with the sparsity and the sparsity is sub-linear with the length of the signal, we show that the \textit{bit-meters} consumption for these algorithms is order-tight, i.e., it matches the lower bound asymptotically up to a constant factor. Our implementations yield interesting insights into design of energy-efficient circuits that are not captured by the notion of computational efficiency alone.

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arXiv2014

Reliable, Deniable, and Hidable Communication over Multipath Networks

We consider the scenario wherein Alice wants to (potentially) communicate to the intended receiver Bob over a network consisting of multiple parallel links in the presence of a passive eavesdropper Willie, who observes an unknown subset of links. A primary goal of our communication protocol is to make the communication "deniable", {\it i.e.}, Willie should not be able to {\it reliably} estimate whether or not Alice is transmitting any {\it covert} information to Bob. Moreover, if Alice is indeed actively communicating, her covert messages should be information-theoretically "hidable" in the sense that Willie's observations should not {\it leak any information} about Alice's (potential) message to Bob -- our notion of hidability is slightly stronger than the notion of information-theoretic strong secrecy well-studied in the literature, and may be of independent interest. It can be shown that deniability does not imply either hidability or (weak or strong) information-theoretic secrecy; nor does any form of information-theoretic secrecy imply deniability. We present matching inner and outer bounds on the capacity for deniable and hidable communication over {\it multipath networks}.

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arXiv2014

SUPER: Sparse signals with Unknown Phases Efficiently Recovered

Suppose ${\bf x}$ is any exactly $k$-sparse vector in $\mathbb{C}^{n}$. We present a class of phase measurement matrix $A$ in $\mathbb{C}^{m\times n}$, and a corresponding algorithm, called SUPER, that can resolve ${\bf x}$ up to a global phase from intensity measurements $|A{\bf x}|$ with high probability over $A$. Here $|A{\bf x}|$ is a vector of component-wise magnitudes of $A{\bf x}$. The SUPER algorithm is the first to simultaneously have the following properties: (a) it requires only ${\cal O}(k)$ (order-optimal) measurements, (b) the computational complexity of decoding is ${\cal O}(k\log k)$ (near order-optimal) arithmetic operations.

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arXiv2013

FRANTIC: A Fast Reference-based Algorithm for Network Tomography via Compressive Sensing

We study the problem of link and node delay estimation in undirected networks when at most k out of n links or nodes in the network are congested. Our approach relies on end-to-end measurements of path delays across pre-specified paths in the network. We present a class of algorithms that we call FRANTIC. The FRANTIC algorithms are motivated by compressive sensing; however, unlike traditional compressive sensing, the measurement design here is constrained by the network topology and the matrix entries are constrained to be positive integers. A key component of our design is a new compressive sensing algorithm SHO-FA-INT that is related to the prior SHO-FA algorithm for compressive sensing, but unlike SHO-FA, the matrix entries here are drawn from the set of integers {0, 1, ..., M}. We show that O(k log n /log M) measurements suffice both for SHO-FA-INT and FRANTIC. Further, we show that the computational complexity of decoding is also O(k log n/log M) for each of these algorithms. Finally, we look at efficient constructions of the measurement operations through Steiner Trees.

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arXiv2013

GROTESQUE: Noisy Group Testing (Quick and Efficient)

Group-testing refers to the problem of identifying (with high probability) a (small) subset of $D$ defectives from a (large) set of $N$ items via a "small" number of "pooled" tests. For ease of presentation in this work we focus on the regime when $D = \cO{N^{1-\gap}}$ for some $\gap > 0$. The tests may be noiseless or noisy, and the testing procedure may be adaptive (the pool defining a test may depend on the outcome of a previous test), or non-adaptive (each test is performed independent of the outcome of other tests). A rich body of literature demonstrates that $Θ(D\log(N))$ tests are information-theoretically necessary and sufficient for the group-testing problem, and provides algorithms that achieve this performance. However, it is only recently that reconstruction algorithms with computational complexity that is sub-linear in $N$ have started being investigated (recent work by \cite{GurI:04,IndN:10, NgoP:11} gave some of the first such algorithms). In the scenario with adaptive tests with noisy outcomes, we present the first scheme that is simultaneously order-optimal (up to small constant factors) in both the number of tests and the decoding complexity ($\cO{D\log(N)}$ in both the performance metrics). The total number of stages of our adaptive algorithm is "small" ($\cO{\log(D)}$). Similarly, in the scenario with non-adaptive tests with noisy outcomes, we present the first scheme that is simultaneously near-optimal in both the number of tests and the decoding complexity (via an algorithm that requires $\cO{D\log(D)\log(N)}$ tests and has a decoding complexity of {${\cal O}(D(\log N+\log^{2}D))$}. Finally, we present an adaptive algorithm that only requires 2 stages, and for which both the number of tests and the decoding complexity scale as {${\cal O}(D(\log N+\log^{2}D))$}. For all three settings the probability of error of our algorithms scales as $\cO{1/(poly(D)}$.

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arXiv2013

Near-Optimal Stochastic Threshold Group Testing

We formulate and analyze a stochastic threshold group testing problem motivated by biological applications. Here a set of $n$ items contains a subset of $d \ll n$ defective items. Subsets (pools) of the $n$ items are tested -- the test outcomes are negative, positive, or stochastic (negative or positive with certain probabilities that might depend on the number of defectives being tested in the pool), depending on whether the number of defective items in the pool being tested are fewer than the {\it lower threshold} $l$, greater than the {\it upper threshold} $u$, or in between. The goal of a {\it stochastic threshold group testing} scheme is to identify the set of $d$ defective items via a "small" number of such tests. In the regime that $l = o(d)$ we present schemes that are computationally feasible to design and implement, and require near-optimal number of tests (significantly improving on existing schemes). Our schemes are robust to a variety of models for probabilistic threshold group testing.

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arXiv2013

On AVCs with Quadratic Constraints

In this work we study an Arbitrarily Varying Channel (AVC) with quadratic power constraints on the transmitter and a so-called "oblivious" jammer (along with additional AWGN) under a maximum probability of error criterion, and no private randomness between the transmitter and the receiver. This is in contrast to similar AVC models under the average probability of error criterion considered in [1], and models wherein common randomness is allowed [2] -- these distinctions are important in some communication scenarios outlined below. We consider the regime where the jammer's power constraint is smaller than the transmitter's power constraint (in the other regime it is known no positive rate is possible). For this regime we show the existence of stochastic codes (with no common randomness between the transmitter and receiver) that enables reliable communication at the same rate as when the jammer is replaced with AWGN with the same power constraint. This matches known information-theoretic outer bounds. In addition to being a stronger result than that in [1] (enabling recovery of the results therein), our proof techniques are also somewhat more direct, and hence may be of independent interest.

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arXiv2012

SHO-FA: Robust compressive sensing with order-optimal complexity, measurements, and bits

Suppose x is any exactly k-sparse vector in R^n. We present a class of sparse matrices A, and a corresponding algorithm that we call SHO-FA (for Short and Fast) that, with high probability over A, can reconstruct x from Ax. The SHO-FA algorithm is related to the Invertible Bloom Lookup Tables recently introduced by Goodrich et al., with two important distinctions - SHO-FA relies on linear measurements, and is robust to noise. The SHO-FA algorithm is the first to simultaneously have the following properties: (a) it requires only O(k) measurements, (b) the bit-precision of each measurement and each arithmetic operation is O (log(n) + P) (here 2^{-P} is the desired relative error in the reconstruction of x), (c) the decoding complexity is O(k) arithmetic operations and encoding complexity is O(n) arithmetic operations, and (d) if the reconstruction goal is simply to recover a single component of x instead of all of x, with significant probability over A this can be done in constant time. All constants above are independent of all problem parameters other than the desired success probability. For a wide range of parameters these properties are information-theoretically order-optimal. In addition, our SHO-FA algorithm works over fairly general ensembles of "sparse random matrices", is robust to random noise, and (random) approximate sparsity for a large range of k. In particular, suppose the measured vector equals A(x+z)+e, where z and e correspond respectively to the source tail and measurement noise. Under reasonable statistical assumptions on z and e our decoding algorithm reconstructs x with an estimation error of O(||z||_2 +||e||_2). The SHO-FA algorithm works with high probability over A, z, and e, and still requires only O(k) steps and O(k) measurements over O(log n)-bit numbers. This is in contrast to the worst-case z model, where it is known O(k log n/k) measurements are necessary.

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arXiv2010

Concatenated Polar Codes

Polar codes have attracted much recent attention as the first codes with low computational complexity that provably achieve optimal rate-regions for a large class of information-theoretic problems. One significant drawback, however, is that for current constructions the probability of error decays sub-exponentially in the block-length (more detailed designs improve the probability of error at the cost of significantly increased computational complexity \cite{KorUS09}). In this work we show how the the classical idea of code concatenation -- using "short" polar codes as inner codes and a "high-rate" Reed-Solomon code as the outer code -- results in substantially improved performance. In particular, code concatenation with a careful choice of parameters boosts the rate of decay of the probability of error to almost exponential in the block-length with essentially no loss in computational complexity. We demonstrate such performance improvements for three sets of information-theoretic problems -- a classical point-to-point channel coding problem, a class of multiple-input multiple output channel coding problems, and some network source coding problems.

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arXiv2010

On Zero-Error Source Coding with Feedback

We consider the problem of zero error source coding with limited feedback when side information is present at the receiver. First, we derive an achievable rate region for arbitrary joint distributions on the source and the side information. When all source pairs of source and side information symbols are observable with non-zero probability, we show that this characterization gives the entire rate region. Next, we demonstrate a class of sources for which asymptotically zero feedback suffices to achieve zero-error coding at the rate promised by the Slepian-Wolf bound for asymptotically lossless coding. Finally, we illustrate these results with the aid of three simple examples.

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