arXiv subjects

Bikash Kumar Dey

Publications and source records attributed to Bikash Kumar Dey.

At least 19 recordsLinked to original sources

arXiv2026

Authentication over Arbitrarily Varying Channels with Causal Adversaries

We study authentication over a discrete memoryless arbitrarily varying channel (AVC) in which the adversary selects the channel state causally based on past channel outputs. We prove that the authentication capacity is positive exactly when the channel is not distribution-overwritable under stochastic encoding, and not I-overwritable under deterministic encoding. In the stochastic case, whenever the authentication capacity is positive, it coincides with the no-adversary Shannon capacity. Both converses follow from a novel wait-and-overwrite attack: the adversary tracks the no-adversary posterior over the message via the posterior guessing probability, and once it concentrates past a threshold, it samples a guess and a decoy from the posterior and overwrites the channel to mimic a no-adversary transmission of the decoy. The positivity results are obtained by constructing positive-rate codes with controlled overlap between codewords, together with a martingale concentration argument that handles adaptive adversarial strategies. For stochastic encoding, the full-capacity achievability further combines a capacity-achieving channel code with an authentication tag. These characterizations separate the causal stochastic-code and causal deterministic-code settings from each other and from the oblivious-adversary setting studied by Kosut and Kliewer.

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arXiv2025

Sequential Adversarial Hypothesis Testing

We study the adversarial binary hypothesis testing problem in the sequential setting. Associated with each hypothesis is a closed, convex set of distributions. Given the hypothesis, each observation is generated according to a distribution chosen (from the set associated with the hypothesis) by an adversary who has access to past observations. In the sequential setting, the number of observations the detector uses to arrive at a decision is variable; this extra freedom improves the asymptotic performance of the test. We characterize the closure of the set of achievable pairs of error exponents. We also study the problem under constraints on the number of observations used and the probability of error incurred.

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arXiv2025

Hypothesis Testing for Adversarial Channels: Chernoff-Stein Exponents

We study the Chernoff-Stein exponent of the following binary hypothesis testing problem: Associated with each hypothesis is a set of channels. A transmitter, without knowledge of the hypothesis, chooses the vector of inputs to the channel. Given the hypothesis, from the set associated with the hypothesis, an adversary chooses channels, one for each element of the input vector. Based on the channel outputs, a detector attempts to distinguish between the hypotheses. We study the Chernoff-Stein exponent for the cases where the transmitter (i) is deterministic, (ii) may privately randomize, and (iii) shares randomness with the detector that is unavailable to the adversary. It turns out that while a memoryless transmission strategy is optimal under shared randomness, it may be strictly suboptimal when the transmitter only has private randomness.

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arXiv2025

Identification Over Noisy Permutation Channels

We study message identification over the noisy permutation channel. For discrete memoryless channels (DMCs), the number of identifiable messages grows doubly exponentially, and the maximum second-order exponent is same as the Shannon capacity of the DMC. We consider a $q$-ary noisy permutation channel where the transmitted vector is first permuted by a permutation chosen uniformly at random, and then passed through a DMC with strictly positive entries in its transition probability matrix $U$. In an earlier work, we showed that over $q$-ary noiseless permutation channel, $2^{c_n n^{q-1}}$ messages can be identified if $c_n\rightarrow 0$, and a strong converse holds for $2^{c_n n^{q-1}}$ messages if $c_n\rightarrow \infty$. For the $q$-ary noisy permutation channel, we show that message sizes growing as $2^{R_n \left( \frac{n}{\log n}\right)^{(r-1)/2}}$, where $r$ be the rank of $U$, are identifiable for any $R_n\rightarrow 0$. We also prove a strong converse result showing that for any sequence of identification codes with $$2^{\left(R_n n^{(q-1)/2}(\log n)^{1+\frac{(q-1)(q-2)}{2}}\right)},$$ messages, where $R_n \rightarrow \infty$, the sum of Type-I and Type-II error probabilities approaches at least $1$ as $n\rightarrow \infty$. Our converse proof uses the idea of channel resolvability. We propose a novel deterministic quantization scheme for quantization of a distribution over the set of all compositions/types by an $M$-type input distribution when the distortion is measured on the output distribution in total variation distance. This plays a key role in the converse proof. We have also studied identification with deterministic encoder and decoder, and proved tight achievability, weak converse, and strong converse.

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arXiv2025

Sliding Window Adversarial Channels

In an arbitrarily varying channel (AVC), the channel has a state which is under the control of an adversarial jammer and the corresponding capacities are often functions of the "power" constraints on the transmitter and jammer. In this paper we propose a model in which the constraints must hold almost surely over contiguous subsequences of the codeword and state, which we call a sliding window constraint. We study oblivious jammers and codes with stochastic encoding under maximum probability of error. We show that this extra limitation on the jammer is beneficial for the transmitter: in some cases, the capacity for unique decoding with a sliding window constraint is equal to the capacity for list decoding in the standard model without sliding windows, roughly implying that the addition of window constraints reduces list decoding to unique decoding. The list decoding capacity in the standard model can be strictly larger than the unique decoding capacity.

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arXiv2024

Byzantine Multiple Access Channels -- Part II: Communication With Adversary Identification

We introduce the problem of determining the identity of a byzantine user (internal adversary) in a communication system. We consider a two-user discrete memoryless multiple access channel where either user may deviate from the prescribed behaviour. Since small deviations may be indistinguishable from the effects of channel noise, it might be overly restrictive to attempt to detect all deviations. When neither user deviates, correct decoding is required. When one user deviates, the decoder must either output a pair of messages of which the message of the non-deviating user is correct or identify the deviating user. The users and the receiver do not share any randomness. The results include a characterization of the set of channels where communication is feasible, and an inner and outer bound on the capacity region. We also show that whenever the rate region has non-empty interior, the capacity region is same as the capacity region under randomized encoding, where each user shares independent randomness with the receiver. We also give an outer bound for this randomized coding capacity region.

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arXiv2024

Identification over Permutation Channels

We study message identification over a q-ary uniform permutation channel, where the transmitted vector is permuted by a permutation chosen uniformly at random. For discrete memoryless channels(DMCs), the number of identifiable messages grows doubly exponentially. Identification capacity, the maximum second-order exponent, is known to be the same as the Shannon capacity of the DMC. Permutation channels support reliable communication of only polynomially many messages. A simple achievability result shows that message sizes growing as 2^{ε_nn^{q-1}} are identifiable for any ε_n\rightarrow0. We prove two converse results. A ``soft'' converse shows that for any R>0, there is no sequence of identification codes with message size growing as 2^{Rn^{q-1}} with a power-law decay (n^{-μ}) of the error probability. We also prove a ``strong" converse showing that for any sequence of identification codes with message size 2^{R_n n^{q-1}}, where R_n\rightarrow\infty, the sum of type I and type II error probabilities approaches at least 1 as n\rightarrow\infty. To prove the soft converse, we use a sequence of steps to construct a new identification code with a simpler structure which relates to a set system, and then use a lower bound on the normalized maximum pairwise intersection of a set system. To prove the strong converse, we use results on approximation of distributions. The achievability and converse results are generalized to the case of coding over multiple blocks. We finally study message identification over a q-ary uniform permutation channel in the presence of causal block-wise feedback from the receiver, where the encoder receives an entire n-length received block after the transmission of the block is complete. We show that in the presence of feedback, the maximum number of identifiable messages grows doubly exponentially, and we present a two-phase achievability scheme.

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arXiv2023

Byzantine Multiple Access Channels -- Part I: Reliable Communication

We study communication over a Multiple Access Channel (MAC) where users can possibly be adversarial. The receiver is unaware of the identity of the adversarial users (if any). When all users are non-adversarial, we want their messages to be decoded reliably. When a user behaves adversarially, we require that the honest users' messages be decoded reliably. An adversarial user can mount an attack by sending any input into the channel rather than following the protocol. It turns out that the $2$-user MAC capacity region follows from the point-to-point Arbitrarily Varying Channel (AVC) capacity. For the $3$-user MAC in which at most one user may be malicious, we characterize the capacity region for deterministic codes and randomized codes (where each user shares an independent random secret key with the receiver). These results are then generalized for the $k$-user MAC where the adversary may control all users in one out of a collection of given subsets.

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arXiv2021

Communication With Adversary Identification in Byzantine Multiple Access Channels

We introduce the problem of determining the identity of a byzantine user (internal adversary) in a communication system. We consider a two-user discrete memoryless multiple access channel where either user may deviate from the prescribed behaviour. Owing to the noisy nature of the channel, it may be overly restrictive to attempt to detect all deviations. In our formulation, we only require detecting deviations which impede the decoding of the non-deviating user's message. When neither user deviates, correct decoding is required. When one user deviates, the decoder must either output a pair of messages of which the message of the non-deviating user is correct or identify the deviating user. The users and the receiver do not share any randomness. The results include a characterization of the set of channels where communication is feasible, and an inner and outer bound on the capacity region.

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arXiv2021

Compound Arbitrarily Varying Channels

We propose a communication model, that we call compound arbitrarily varying channels (CAVC), which unifies and generalizes compound channels and arbitrarily varying channels (AVC). A CAVC can be viewed as a noisy channel with a fixed, but unknown, compound-state and an AVC-state which may vary with every channel use. The AVC-state is controlled by an adversary who is aware of the compound-state. We study three problems in this setting: 'communication', 'communication and compound-state identification', and 'communication or compound-state identification'. For these problems, we study conditions for feasibility and capacity under deterministic coding and random coding.

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arXiv2021

Fundamental Limits of Demand-Private Coded Caching

We consider the coded caching problem with an additional privacy constraint that a user should not get any information about the demands of the other users. We first show that a demand-private scheme for $N$ files and $K$ users can be obtained from a non-private scheme that serves only a subset of the demands for the $N$ files and $NK$ users problem. We further use this fact to construct a demand-private scheme for $N$ files and $K$ users from a particular known non-private scheme for $N$ files and $NK-K+1$ users. It is then demonstrated that, the memory-rate pair $(M,\min \{N,K\}(1-M/N))$, which is achievable for non-private schemes with uncoded transmissions, is also achievable under demand privacy. We further propose a scheme that improves on these ideas by removing some redundant transmissions. The memory-rate trade-off achieved using our schemes is shown to be within a multiplicative factor of 3 from the optimal when $K < N$ and of 8 when $N\leq K$. Finally, we give the exact memory-rate trade-off for demand-private coded caching problems with $N\geq K=2$.

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arXiv2020

Private Index Coding

We study the fundamental problem of index coding under an additional privacy constraint that requires each receiver to learn nothing more about the collection of messages beyond its demanded messages from the server and what is available to it as side information. To enable such private communication, we allow the use of a collection of independent secret keys, each of which is shared amongst a subset of users and is known to the server. The goal is to study properties of the key access structures which make the problem feasible and then design encoding and decoding schemes efficient in the size of the server transmission as well as the sizes of the secret keys. We call this the private index coding problem. We begin by characterizing the key access structures that make private index coding feasible. We also give conditions to check if a given linear scheme is a valid private index code. For up to three users, we characterize the rate region of feasible server transmission and key rates, and show that all feasible rates can be achieved using scalar linear coding and time sharing; we also show that scalar linear codes are sub-optimal for four receivers. The outer bounds used in the case of three users are extended to arbitrary number of users and seen as a generalized version of the well-known polymatroidal bounds for the standard non-private index coding. We also show that the presence of common randomness and private randomness does not change the rate region. Furthermore, we study the case where no keys are shared among the users and provide some necessary and sufficient conditions for feasibility in this setting under a weaker notion of privacy. If the server has the ability to multicast to any subset of users, we demonstrate how this flexibility can be used to provide privacy and characterize the minimum number of server multicasts required.

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arXiv2020

Demand-Private Coded Caching and the Exact Trade-off for N=K=2

The distributed coded caching problem has been studied extensively in the recent past. While the known coded caching schemes achieve an improved transmission rate, they violate the privacy of the users since in these schemes the demand of one user is revealed to others in the delivery phase. In this paper, we consider the coded caching problem under the constraint that the demands of the other users remain information theoretically secret from each user. We first show that the memory-rate pair $(M,\min \{N,K\}(1-M/N))$ is achievable under information theoretic demand privacy, while using broadcast transmissions. We then show that a demand-private scheme for $N$ files and $K$ users can be obtained from a non-private scheme that satisfies only a restricted subset of demands of $NK$ users for $N$ files. We then focus on the demand-private coded caching problem for $K=2$ users, $N=2$ files. We characterize the exact memory-rate trade-off for this case. To show the achievability, we use our first result to construct a demand-private scheme from a non-private scheme satisfying a restricted demand subset that is known from an earlier work by Tian. Further, by giving a converse based on the extra requirement of privacy, we show that the obtained achievable region is the exact memory-rate trade-off.

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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

Function Computation through a Bidirectional Relay

We consider a function computation problem in a three node wireless network. Nodes A and B observe two correlated sources $X$ and $Y$ respectively, and want to compute a function $f(X,Y)$. To achieve this, nodes A and B send messages to a relay node C at rates $R_A$ and $R_B$ respectively. The relay C then broadcasts a message to A and B at rate $R_C$. We allow block coding, and study the achievable region of rate triples under both zero-error and $ε$-error. As a preparation, we first consider a broadcast network from the relay to A and B. A and B have side information $X$ and $Y$ respectively. The relay node C observes both $X$ and $Y$ and broadcasts an encoded message to A and B. We want to obtain the optimal broadcast rate such that A and B can recover the function $f(X,Y)$ from the received message and their individual side information $X$ and $Y$ respectively. For this problem, we show equivalence between $ε$-error and zero-error computations-- this gives a rate characterization for zero-error computation. As a corollary, this also gives a rate characterization for the relay network under zero-error for a class of functions called {\em component-wise one-to-one functions} when the support set of $p_{XY}$ is full. For the relay network, the zero-error rate region for arbitrary functions is characterized in terms of graph coloring of some suitably defined probabilistic graphs. We then give a single-letter inner bound to this rate region. Further, we extend the graph theoretic ideas to address the $ε$-error problem and obtain a single-letter inner bound.

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arXiv2018

Arbitrarily Varying Remote Sources

We study a lossy source coding problem for an arbitrarily varying remote source (AVRS) which was proposed in a prior work. An AVRS transmits symbols, each generated in an independent and identically distributed manner, which are sought to be estimated at the decoder. These symbols are remotely generated, and the encoder and decoder observe noise corrupted versions received through a two-output noisy channel. This channel is an arbitrarily varying channel controlled by a jamming adversary. We assume that the adversary knows the coding scheme as well as the source data non-causally, and hence, can employ malicious jamming strategies correlated to them. Our interest lies in studying the rate distortion function for codes with a stochastic encoder, i.e, when the encoder can privately randomize while the decoder is deterministic. We provide upper and lower bounds on this rate distortion function.

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arXiv2018

Quadratically Constrained Channels with Causal Adversaries

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 transmission $\mathbf{x}$ and James' jamming vector $\mathbf{s}$, and is required to reliably estimate Alice's message from this sum. In addition, Alice and James's transmission powers are restricted by quadratic constraints $P>0$ and $N>0$. In this work, we characterize the channel capacity for such a channel as the limit superior of the optimal values of a series of optimizations. Upper and lower bounds on the optimal values are provided both analytically and numerically. Interestingly, unlike many communication problems, in this causal setting Alice's optimal codebook may not have a uniform power allocation - for certain SNR, a codebook with a two-level uniform power allocation results in a strictly higher rate than a codebook with a uniform power allocation would.

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arXiv2017

Communication in the Presence of a State-Aware Adversary

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 probability of error criterion. Similar to other randomized coding setups, we show that the capacity is the same even under the average probability of error criterion. Even with non-causal knowledge of the state, we prove that the state-aware adversary cannot affect the rate any worse than when it employs a memoryless strategy which depends only on the instantaneous state. Thus, the AVC capacity characterization is given in terms of the capacity of the worst memoryless channels with state, induced by the adversary employing such memoryless jamming strategies. For the DP-AVC, it is further shown that among memoryless jamming strategies, none impact the communication more than a memoryless Gaussian jamming strategy which completely disregards the knowledge of the state. Thus, the capacity of the DP-AVC equals that of a standard AWGN channel with two independent sources of additive white Gaussian noise, i.e., the channel noise and the jamming noise.

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