arXiv subjects

Bikash Kumar Dey

Publications and source records attributed to Bikash Kumar Dey.

At least 37 records · Page 2Linked to original sources

arXiv2017

Coding for Arbitrarily Varying Remote Sources

We study a lossy source coding problem for a memoryless remote source. The source data is broadcast over an arbitrarily varying channel (AVC) controlled by an adversary. One output of the AVC is received as input at the encoder, and another output is received as side information at the decoder. The adversary is assumed to know the source data non-causally, and can employ randomized jamming strategies arbitrarily correlated to the source data. The decoder reconstructs the source data from the encoded message and the side information. We prove upper and lower bounds on the adversarial rate distortion function for the source under randomized coding. Furthermore, we present some interesting special cases of our general setup where the above bounds coincide, and thus, provide their complete rate distortion function characterization.

cs.IT↗

arXiv2016

Sufficiently Myopic Adversaries are Blind

In this work we consider a communication problem in which a sender, Alice, wishes to communicate with a receiver, Bob, over a channel controlled by an adversarial jammer, James, who is {\em myopic}. Roughly speaking, for blocklength $n$, the codeword $X^n$ transmitted by Alice is corrupted by James who must base his adversarial decisions (of which locations of $X^n$ to corrupt and how to corrupt them) not on the codeword $X^n$ but on $Z^n$, an image of $X^n$ through a noisy memoryless channel. More specifically, our communication model may be described by two channels. A memoryless channel $p(z|x)$ from Alice to James, and an {\it Arbitrarily Varying Channel} from Alice to Bob, $p(y|x,s)$ governed by a state $X^n$ determined by James. In standard adversarial channels the states $S^n$ may depend on the codeword $X^n$, but in our setting $S^n$ depends only on James's view $Z^n$. The myopic channel captures a broad range of channels and bridges between the standard models of memoryless and adversarial (zero-error) channels. In this work we present upper and lower bounds on the capacity of myopic channels. For a number of special cases of interest we show that our bounds are tight. We extend our results to the setting of {\em secure} communication in which we require that the transmitted message remain secret from James. For example, we show that if (i) James may flip at most a $p$ fraction of the bits communicated between Alice and Bob, and (ii) James views $X^n$ through a binary symmetric channel with parameter $q$, then once James is "sufficiently myopic" (in this case, when $q>p$), then the optimal communication rate is that of an adversary who is "blind" (that is, an adversary that does not see $X^n$ at all), which is $1-H(p)$ for standard communication, and $H(q)-H(p)$ for secure communication. A similar phenomenon exists for our general model of communication.

cs.IT↗

arXiv2016

Broadcast Function Computation with Complementary Side Information

We consider the function computation problem in a three node network with one encoder and two decoders. The encoder has access to two correlated sources $X$ and $Y$. The encoder encodes $X^n$ and $Y^n$ into a message which is given to two decoders. Decoder 1 and decoder 2 have access to $X$ and $Y$ respectively, and they want to compute two functions $f(X,Y)$ and $g(X,Y)$ respectively using the encoded message and their respective side information. We want to find the optimum (minimum) encoding rate under the zero error and $ε$-error (i.e. vanishing error) criteria. For the special case of this problem with $f(X,Y) = Y$ and $g(X,Y) = X$, we show that the $ε$-error optimum rate is also achievable with zero error. This result extends to a more general `complementary delivery index coding' problem with arbitrary number of messages and decoders. For other functions, we show that the cut-set bound is achievable under $ε$-error if $X$ and $Y$ are binary, or if the functions are from a special class of `compatible' functions which includes the case $f=g$.

cs.IT↗

arXiv2016

Wiretapped Oblivious Transfer

In this paper, we study the problem of obtaining $1$-of-$2$ string oblivious transfer (OT) between users Alice and Bob, in the presence of a passive eavesdropper Eve. The resource enabling OT in our setup is a noisy broadcast channel from Alice to Bob and Eve. Apart from the OT requirements between the users, Eve is not allowed to learn anything about the users' inputs. When Alice and Bob are honest-but-curious and the noisy broadcast channel is made up of two independent binary erasure channels (connecting Alice-Bob and Alice-Eve), we derive the $1$-of-$2$ string OT capacity for both $2$-privacy (when Eve can collude with either Alice or Bob) and $1$-privacy (when no such collusion is allowed). We generalize these capacity results to $1$-of-$N$ string OT and study other variants of this problem. When Alice and/or Bob are malicious, we present a different scheme based on interactive hashing. This scheme is shown to be optimal for certain parameter regimes. We present a new formulation of multiple, simultaneous OTs between Alice-Bob and Alice-Cathy. For this new setup, we present schemes and outer bounds that match in all but one regime of parameters. Finally, we consider the setup where the broadcast channel is made up of a cascade of two independent binary erasure channels (connecting Alice-Bob and Bob-Eve) and $1$-of-$2$ string OT is desired between Alice and Bob with $1$-privacy. For this setup, we derive an upper and lower bound on the $1$-of-$2$ string OT capacity which match in one of two possible parameter regimes.

cs.CR↗

arXiv2016

The benefit of a 1-bit jump-start, and the necessity of stochastic encoding, in jamming channels

We consider the problem of communicating a message $m$ in the presence of a malicious jamming adversary (Calvin), who can erase an arbitrary set of up to $pn$ bits, out of $n$ transmitted bits $(x_1,\ldots,x_n)$. The capacity of such a channel when Calvin is exactly causal, i.e. Calvin's decision of whether or not to erase bit $x_i$ depends on his observations $(x_1,\ldots,x_i)$ was recently characterized to be $1-2p$. In this work we show two (perhaps) surprising phenomena. Firstly, we demonstrate via a novel code construction that if Calvin is delayed by even a single bit, i.e. Calvin's decision of whether or not to erase bit $x_i$ depends only on $(x_1,\ldots,x_{i-1})$ (and is independent of the "current bit" $x_i$) then the capacity increases to $1-p$ when the encoder is allowed to be stochastic. Secondly, we show via a novel jamming strategy for Calvin that, in the single-bit-delay setting, if the encoding is deterministic (i.e. the transmitted codeword is a deterministic function of the message $m$) then no rate asymptotically larger than $1-2p$ is possible with vanishing probability of error, hence stochastic encoding (using private randomness at the encoder) is essential to achieve the capacity of $1-p$ against a one-bit-delayed Calvin.

cs.IT↗

arXiv2015

Oblivious Transfer over Wireless Channels

We consider the problem of oblivious transfer (OT) over OFDM and MIMO wireless communication systems where only the receiver knows the channel state information. The sender and receiver also have unlimited access to a noise-free real channel. Using a physical layer approach, based on the properties of the noisy fading channel, we propose a scheme that enables the transmitter to send obliviously one-of-two files, i.e., without knowing which one has been actually requested by the receiver, while also ensuring that the receiver does not get any information about the other file.

cs.IT↗

arXiv2015

On the Oblivious Transfer Capacity of the Degraded Wiretapped Binary Erasure Channel

We study oblivious transfer (OT) between Alice and Bob in the presence of an eavesdropper Eve over a degraded wiretapped binary erasure channel from Alice to Bob and Eve. In addition to the privacy goals of oblivious transfer between Alice and Bob, we require privacy of Alice and Bob's private data from Eve. In previous work we derived the OT capacity (in the honest-but-curious model) of the wiretapped binary independent erasure channel where the erasure processes of Bob and Eve are independent. Here we derive a lower bound on the OT capacity in the same secrecy model when the wiretapped binary erasure channel is degraded in favour of Bob.

cs.IT↗

arXiv2015

Dirty Paper Arbitrarily Varying Channel with a State-Aware Adversary

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 the state.

cs.IT↗

arXiv2014

Zero-Error Function Computation through a Bidirectional Relay

We consider zero error function computation in a three node wireless network. Nodes A and B observe $X$ and $Y$ respectively, and want to compute a function $f(X,Y)$ with zero error. 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 $R_C$ to help them compute $f(X,Y)$ with zero error. We allow block coding, and study the region of rate-triples $(R_A,R_B,R_C)$ that are feasible. The rate region is characterized in terms of graph coloring of some suitably defined probabilistic graphs. We give single letter inner and outer bounds which meet for some simple examples. We provide a sufficient condition on the joint distribution $p_{XY}$ under which the relay can also compute $f(X,Y)$ if A and B can compute it with zero error.

cs.IT↗

arXiv2014

How to Securely Compute the Modulo-Two Sum of Binary Sources

In secure multiparty computation, mutually distrusting users in a network want to collaborate to compute functions of data which is distributed among the users. The users should not learn any additional information about the data of others than what they may infer from their own data and the functions they are computing. Previous works have mostly considered the worst case context (i.e., without assuming any distribution for the data); Lee and Abbe (2014) is a notable exception. Here, we study the average case (i.e., we work with a distribution on the data) where correctness and privacy is only desired asymptotically. For concreteness and simplicity, we consider a secure version of the function computation problem of Körner and Marton (1979) where two users observe a doubly symmetric binary source with parameter p and the third user wants to compute the XOR. We show that the amount of communication and randomness resources required depends on the level of correctness desired. When zero-error and perfect privacy are required, the results of Data et al. (2014) show that it can be achieved if and only if a total rate of 1 bit is communicated between every pair of users and private randomness at the rate of 1 is used up. In contrast, we show here that, if we only want the probability of error to vanish asymptotically in block length, it can be achieved by a lower rate (binary entropy of p) for all the links and for private randomness; this also guarantees perfect privacy. We also show that no smaller rates are possible even if privacy is only required asymptotically.

cs.IT↗

arXiv2014

The Oblivious Transfer Capacity of the Wiretapped Binary Erasure Channel

We consider oblivious transfer between Alice and Bob in the presence of an eavesdropper Eve when there is a broadcast channel from Alice to Bob and Eve. In addition to the secrecy constraints of Alice and Bob, Eve should not learn the private data of Alice and Bob. When the broadcast channel consists of two independent binary erasure channels, we derive the oblivious transfer capacity for both 2-privacy (where the eavesdropper may collude with either party) and 1-privacy (where there are no collusions).

cs.IT↗

arXiv2014

Correlated Jamming in a Joint Source Channel Communication System

We study correlated jamming in joint source-channel communication systems. An i.i.d. source is to be communicated over a memoryless channel in the presence of a correlated jammer with non-causal knowledge of user transmission. This user-jammer interaction is modeled as a zero sum game. A set of conditions on the source and the channel is provided for the existence of a Nash equilibrium for this game, where the user strategy is uncoded transmission and the jammer strategy is i.i.d jamming. This generalizes a well-known example of uncoded communication of a Gaussian sources over Gaussian channels with additive jamming. Another example, of a Binary Symmetric source over a Binary Symmetric channel with jamming, is provided as a validation of this result.

cs.IT↗

arXiv2014

Writing on a Dirty Paper in the presence of Jamming

In this paper, the problem of writing on a dirty paper in the presence of jamming is examined. We consider an AWGN channel with an additive white Gaussian state and an additive adversarial jammer. The state is assumed to be known non-causally to the encoder and the jammer but not to the decoder. The capacity of the channel in the presence of a jammer is determined. A surprising result that this capacity is equal to the capacity of a relaxed version of the problem, where the state is also known non-causally to the decoder, is proved.

cs.IT↗

arXiv2012

Upper Bounds on the Capacity of Binary Channels with Causal Adversaries

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 not must depend only on $x_j$ for $j \leq i$. This is in contrast to the "classical" adversarial jamming situations in which the jammer has no knowledge of $(x_1,...,x_n)$, or knows $(x_1,...,x_n)$ completely. In this work, we present upper bounds (that hold under both the average and maximal probability of error criteria) on the capacity which hold for both deterministic and stochastic encoding schemes.

cs.IT↗

arXiv2011

On network coding for sum-networks

A directed acyclic network is considered where all the terminals need to recover the sum of the symbols generated at all the sources. We call such a network a sum-network. It is shown that there exists a solvably (and linear solvably) equivalent sum-network for any multiple-unicast network, and thus for any directed acyclic communication network. It is also shown that there exists a linear solvably equivalent multiple-unicast network for every sum-network. It is shown that for any set of polynomials having integer coefficients, there exists a sum-network which is scalar linear solvable over a finite field F if and only if the polynomials have a common root in F. For any finite or cofinite set of prime numbers, a network is constructed which has a vector linear solution of any length if and only if the characteristic of the alphabet field is in the given set. The insufficiency of linear network coding and unachievability of the network coding capacity are proved for sum-networks by using similar known results for communication networks. Under fractional vector linear network coding, a sum-network and its reverse network are shown to be equivalent. However, under non-linear coding, it is shown that there exists a solvable sum-network whose reverse network is not solvable.

cs.IT↗

arXiv2010

Network Flows for Functions

We consider in-network computation of an arbitrary function over an arbitrary communication network. A network with capacity constraints on the links is given. Some nodes in the network generate data, e.g., like sensor nodes in a sensor network. An arbitrary function of this distributed data is to be obtained at a terminal node. The structure of the function is described by a given computation schema, which in turn is represented by a directed tree. We design computing and communicating schemes to obtain the function at the terminal at the maximum rate. For this, we formulate linear programs to determine network flows that maximize the computation rate. We then develop fast combinatorial primal-dual algorithm to obtain $ε$-approximate solutions to these linear programs. We then briefly describe extensions of our techniques to the cases of multiple terminals wanting different functions, multiple computation schemas for a function, computation with a given desired precision, and to networks with energy constraints at nodes.

cs.NI↗

arXiv2010

On the solvability of 3-source 3-terminal sum-networks

We consider a directed acyclic network with three sources and three terminals such that each source independently generates one symbol from a given field $F$ and each terminal wants to receive the sum (over $F$) of the source symbols. Each link in the network is considered to be error-free and delay-free and can carry one symbol from the field in each use. We call such a network a 3-source 3-terminal {\it $(3s/3t)$ sum-network}. In this paper, we give a necessary and sufficient condition for a $3s/3t$ sum-network to allow all the terminals to receive the sum of the source symbols over \textit{any} field. Some lemmas provide interesting simpler sufficient conditions for the same. We show that linear codes are sufficient for this problem for $3s/3t$ though they are known to be insufficient for arbitrary number of sources and terminals. We further show that in most cases, such networks are solvable by simple XOR coding. We also prove a recent conjecture that if fractional coding is allowed, then the coding capacity of a $3s/3t$ sum-network is either $0,2/3$ or $\geq 1$.

cs.IT↗

arXiv2010

A Simple Necessary and Sufficient Condition for the Double Unicast Problem

We consider a directed acyclic network where there are two source-terminal pairs and the terminals need to receive the symbols generated at the respective sources. Each source independently generates an i.i.d. random process over the same alphabet. Each edge in the network is error-free, delay-free, and can carry one symbol from the alphabet per use. We give a simple necessary and sufficient condition for being able to simultaneously satisfy the unicast requirements of the two source-terminal pairs at rate-pair $(1,1)$ using vector network coding. The condition is also sufficient for doing this using only "XOR" network coding and is much simpler compared to the necessary and sufficient conditions known from previous work. Our condition also yields a simple characterization of the capacity region of a double-unicast network which does not support the rate-pair $(1,1)$.

cs.IT↗