arXiv subjects

Si-Hyeon Lee

Publications and source records attributed to Si-Hyeon Lee.

At least 37 records · Page 2Linked to original sources

arXiv2023

Achieving the Exactly Optimal Privacy-Utility Trade-Off with Low Communication Cost via Shared Randomness

We consider a discrete distribution estimation problem under a local differential privacy (LDP) constraint in the presence of shared randomness. By exploiting the shared randomness, we suggest a new method for constructing LDP schemes which achieve the exactly optimal privacy-utility trade-off (PUT) with the communication cost of less than or equal to the input data size for any privacy regime. The main idea is to decompose a block design scheme by Park et al. (2023), based on the combinatorial concept called resolution. The LDP scheme decomposed from a block design scheme is called a resolution of the block design scheme, and it achieves the same PUT as the original block design scheme while requiring a less communication cost. We provide two resolutions of an exactly PUT-optimal block design scheme, called the Baranyai's resolution and the cyclic shift resolution, both requiring the communication cost of less than or equal to the input data size. In particular, we show that the Baranyai's resolution achieves the minimum communication cost among all the PUT-optimal resolutions of block design schemes. One drawback of the Baranyai's resolution is that it can be obtained through a recursive algorithm in general. In contrast, the cyclic shift resolution has an explicit structure, but its communication cost can be larger than that of Baranyai's resolution. To complement this, we also suggest resolutions of other block design schemes achieving the optimal PUT for some privacy budgets, which require the minimum communication cost as the Baranyai's resolution and have explicit structures as the cyclic shift resolution.

cs.IT↗

arXiv2023

Multi-User Cooperation for Covert Communication Under Quasi-Static Fading

This work studies a covert communication scheme for an uplink multi-user scenario in which some users are opportunistically selected to help a covert user. In particular, the selected users emit interfering signals via an orthogonal resource dedicated to the covert user together with signals for their own communications using orthogonal resources allocated to the selected users, which helps the covert user hide the presence of the covert communication. For the covert communication scheme, we carry out extensive analysis and find system parameters in closed forms. The analytic derivation for the system parameters allow one to find the optimal combination of system parameters by performing a simple one-dimensional search. In addition, the analytic results elucidate relations among the system parameters. In particular, it will be proved that the optimal strategy for the non-covert users is an on-off scheme with equal transmit power. The theoretical results derived in this work are confirmed by comparing them with numerical results obtained with exhaustive searches. Finally, we demonstrate that the results of work can be utilized in versatile ways by demonstrating a design of covert communication with energy efficiency into account.

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arXiv2022

Anti-Jamming Games in Multi-Band Wireless Ad Hoc Networks

For multi-band wireless ad hoc networks of multiple users, an anti-jamming game between the users and a jammer is studied. In this game, the users (resp. jammer) want to maximize (resp. minimize) the expected rewards of the users taking into account various factors such as communication rate, hopping cost, and jamming loss. We analyze the arms race of the game and derive an optimal frequency hopping policy at each stage of the arms race based on the Markov decision process (MDP). It is analytically shown that the arms race reaches an equilibrium after a few rounds, and a frequency hopping policy and a jamming strategy at the equilibrium are characterized. We propose two kinds of collision avoidance protocols to ensure that at most one user communicates in each frequency band, and provide various numerical results that show the effects of the reward parameters and collision avoidance protocols on the optimal frequency hopping policy and the expected rewards at the equilibrium. Moreover, we discuss about equilibria for the case where the jammer adopts some unpredictable jamming strategies.

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arXiv2021

Some results on r-truncated degenerate Poisson Random Variables

The zero-truncated Poisson distributions are certain discrete probability distributions whose supports are the set of positive integers, which are also known as the conditional Poisson distributions or the positive Poisson distributions. In this paper, we introduce the r-truncated degenerate Poisson random variable with parameter a and investigate various properties of this random variable

math.PR↗

arXiv2020

Secrecy Capacity of a Gaussian Wiretap Channel With ADCs is Always Positive

We consider a complex Gaussian wiretap channel with finite-resolution analog-to-digital converters (ADCs) at both the legitimate receiver and the eavesdropper. For this channel, we show that a positive secrecy rate is always achievable as long as the channel gains at the legitimate receiver and at the eavesdropper are different, regardless of the quantization levels of the ADCs. For the achievability, we first consider the case of one-bit ADCs at the legitimate receiver and apply a binary input distribution where the two input points have the same phase when the channel gain at the legitimate receiver is less than that at the eavesdropper, and otherwise the opposite phase. Then the result is generalized for the case of arbitrary finite-resolution ADCs at the legitimate receiver by translating the input distribution appropriately. For the special case of the real Gaussian wiretap channel with one-bit ADCs at both the legitimate receiver and the eavesdropper, we show that our choice of input distribution satisfies a necessary condition of optimal distributions for Wyner codes.

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arXiv2020

Mobility-Assisted Covert Communication over Wireless Ad Hoc Networks

We study the effect of node mobility on the throughput scaling of the covert communication over a wireless adhoc network. It is assumed that $n$ mobile nodes want to communicate each other in a unit disk while keeping the presence of the communication secret from each of $Θ(n^s)$ non-colluding wardens ($s>0$). Our results show that the node mobility greatly improves the throughput scaling, compared to the case of fixed node location. In particular, for $0<s<1$, the aggregate throughput scaling is shown to be linear in $n$ when the number of channel uses that each warden uses to judge the presence of communication is not too large compared to $n$. For the achievability, we modify the two-hop based scheme by Grossglauser and Tse (2002), which was proposed for a wireless ad hoc network without a covertness constraint, by introducing a preservation region around each warden in which the senders are not allowed to transmit and by carefully analyzing the effect of covertness constraint on the transmit power and the resultant transmission rates. This scheme is shown to be optimal for $0<s<1$ under an assumption that each node outside preservation regions around wardens uses the same transmit power.

cs.IT↗

arXiv2020

Treating Interference as Noise is Optimal for Covert Communication over Interference Channels

We study the covert communication over K-user discrete memoryless interference channels (DM-ICs) with a warden. It is assumed that the warden's channel output distribution induced by K "off" input symbols, which are sent when no communication occurs, is not a convex combination of those induced by any other combination of input symbols (otherwise, the square-root law does not hold). We derive the exact covert capacity region and show that a simple point-to-point based scheme with treating interference as noise is optimal. In addition, we analyze the secret key length required for the reliable and covert communication with the desired rates, and present a channel condition where a secret key between each user pair is unnecessary. The results are extended to the Gaussian case and the case with multiple wardens.

cs.IT↗

arXiv2019

Throughput Scaling of Covert Communication over Wireless Adhoc Networks

We consider the problem of covert communication over wireless adhoc networks in which (roughly) $n$ legitimate nodes (LNs) and $n^κ$ for $0<κ<1$ non-communicating warden nodes (WNs) are randomly distributed in a square of unit area. Each legitimate source wants to communicate with its intended destination node while ensuring that every WN is unable to detect the presence of the communication. In this scenario, we study the throughput scaling law. Due the covert communication constraint, the transmit powers are necessarily limited. Under this condition, we introduce a preservation region around each WN. This region serves to prevent transmission from the LNs and to increase the transmit power of the LNs outside the preservation regions. For the achievability results, multi-hop (MH), hierarchical cooperation (HC), and hybrid HC-MH schemes are utilized with some appropriate modifications. In the proposed MH and hybrid schemes, because the preservation regions may impede communication along direct data paths, the data paths are suitably modified by taking a detour around each preservation region. To avoid the concentration of detours resulting extra relaying burdens, we distribute the detours evenly over a wide region. In the proposed HC scheme, we control the symbol power and the scheduling of distributed multiple-input multiple-output transmission. We also present matching upper bounds on the throughput scaling under the assumption that every active LN consumes the same average transmit power over the time period in which the WNs observe the channel outputs.

cs.IT↗

arXiv2018

Time-Division is Optimal for Covert Communication over Some Broadcast Channels

We consider a covert communication scenario where a transmitter wishes to communicate simultaneously to two legitimate receivers while ensuring that the communication is not detected by an adversary, the warden. The legitimate receivers and the adversary observe the transmission from the transmitter via a three-user discrete or Gaussian memoryless broadcast channel. We focus on the case where the "no-input" symbol is not redundant, i.e., the output distribution at the warden induced by the no-input symbol is not a mixture of the output distributions induced by other input symbols, so that the covert communication is governed by the square root law, i.e., at most $Θ(\sqrt{n})$ bits can be transmitted over $n$ channel uses. We show that for such a setting, a simple time-division strategy achieves the optimal throughputs for a non-trivial class of broadcast channels; this is not true for communicating over broadcast channels without the covert communication constraint. Our result implies that a code that uses two separate optimal point-to-point codes each designed for the constituent channels and each used for a fraction of the time is optimal in the sense that it achieves the best constants of the $\sqrt{n}$-scaling for the throughputs. Our proof strategy combines several elements in the network information theory literature, including concave envelope representations of the capacity regions of broadcast channels and El Gamal's outer bound for more capable broadcast channels.

cs.IT↗

arXiv2017

Covert Communication with Channel-State Information at the Transmitter

We consider the problem of covert communication over a state-dependent channel, where the transmitter has causal or noncausal knowledge of the channel states. Here, "covert" means that a warden on the channel should observe similar statistics when the transmitter is sending a message and when it is not. When a sufficiently long secret key is shared between the transmitter and the receiver, we derive closed-form formulas for the maximum achievable covert communication rate ("covert capacity") for discrete memoryless channels and, when the transmitter's channel-state information (CSI) is noncausal, for additive white Gaussian noise (AWGN) channels. For certain channel models, including the AWGN channel, we show that the covert capacity is positive with CSI at the transmitter, but is zero without CSI. We also derive lower bounds on the rate of the secret key that is needed for the transmitter and the receiver to achieve the covert capacity.

cs.IT↗

arXiv2016

The Wiretapped Diamond-Relay Channel

In this paper, we study a diamond-relay channel where the source is connected to $M$ relays through orthogonal links and the relays transmit to the destination over a wireless multiple-access channel in the presence of an eavesdropper. The eavesdropper not only observes the relay transmissions through another multiple-access channel, but also observes a certain number of source-relay links. The legitimate terminals know neither the eavesdropper's channel state information nor the location of source-relay links revealed to the eavesdropper except the total number of such links. For this wiretapped diamond-relay channel, we establish the optimal secure degrees of freedom. In the achievability part, our proposed scheme uses the source-relay links to transmit a judiciously constructed combination of message symbols, artificial noise symbols as well as fictitious message symbols associated with secure network coding. The relays use a combination of beamforming and interference alignment in their transmission scheme. For the converse part, we take a genie-aided approach assuming that the location of wiretapped links is known.

cs.IT↗

arXiv2016

Exact Moderate Deviation Asymptotics in Streaming Data Transmission

In this paper, a streaming transmission setup is considered where an encoder observes a new message in the beginning of each block and a decoder sequentially decodes each message after a delay of $T$ blocks. In this streaming setup, the fundamental interplay between the coding rate, the error probability, and the blocklength in the moderate deviations regime is studied. For output symmetric channels, the moderate deviations constant is shown to improve over the block coding or non-streaming setup by exactly a factor of $T$ for a certain range of moderate deviations scalings. For the converse proof, a more powerful decoder to which some extra information is fedforward is assumed. The error probability is bounded first for an auxiliary channel and this result is translated back to the original channel by using a newly developed change-of-measure lemma, where the speed of decay of the remainder term in the exponent is carefully characterized. For the achievability proof, a known coding technique that involves a joint encoding and decoding of fresh and past messages is applied with some manipulations in the error analysis.

cs.IT↗

arXiv2015

Secure Degrees of Freedom of the Gaussian Diamond-Wiretap Channel

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 introduce a new technique of capturing the trade-off between the message rate and the amount of individual randomness injected at each relay. In the achievability part, we show (i) how to strike a balance between sending message symbols and common noise symbols from the source to the relays in the broadcast component and (ii) how to combine artificial noise-beamforming and noise-alignment techniques at the relays in the multiple access component. In the case with full CSI, we propose a scheme where the relays simultaneously beamform common noise signals in the null space of the legitimate destination's channel, and align them with the message signals at the eavesdropper. In the case with no eavesdropper's CSI, we present a scheme that efficiently utilizes the broadcast links by incorporating computation between the message and common noise symbols at the source. Finally, most of our achievability and converse techniques can also be adapted to the Gaussian (non-fading) channel model.

cs.IT↗

arXiv2015

Streaming Data Transmission in the Moderate Deviations and Central Limit Regimes

We consider streaming data transmission over a discrete memoryless channel. A new message is given to the encoder at the beginning of each block and the decoder decodes each message sequentially, after a delay of $T$ blocks. In this streaming setup, we study the fundamental interplay between the rate and error probability in the central limit and moderate deviations regimes and show that i) in the moderate deviations regime, the moderate deviations constant improves over the block coding or non-streaming setup by a factor of $T$ and ii) in the central limit regime, the second-order coding rate improves by a factor of approximately $\sqrt{T}$ for a wide range of channel parameters. For both regimes, we propose coding techniques that incorporate a joint encoding of fresh and previous messages. In particular, for the central limit regime, we propose a coding technique with truncated memory to ensure that a summation of constants, which arises as a result of applications of the central limit theorem, does not diverge in the error analysis. Furthermore, we explore interesting variants of the basic streaming setup in the moderate deviations regime. We first consider a scenario with an erasure option at the decoder and show that both the exponents of the total error and the undetected error probabilities improve by factors of $T$. Next, by utilizing the erasure option, we show that the exponent of the total error probability can be improved to that of the undetected error probability (in the order sense) at the expense of a variable decoding delay. Finally, we also extend our results to the case where the message rate is not fixed but alternates between two values.

cs.IT↗

arXiv2015

A Unified Approach for Network Information Theory

In this paper, we take a unified approach for network information theory and prove a coding theorem, which can recover most of the achievability results in network information theory that are based on random coding. The final single-letter expression has a very simple form, which was made possible by many novel elements such as a unified framework that represents various network problems in a simple and unified way, a unified coding strategy that consists of a few basic ingredients but can emulate many known coding techniques if needed, and new proof techniques beyond the use of standard covering and packing lemmas. For example, in our framework, sources, channels, states and side information are treated in a unified way and various constraints such as cost and distortion constraints are unified as a single joint-typicality constraint. Our theorem can be useful in proving many new achievability results easily and in some cases gives simpler rate expressions than those obtained using conventional approaches. Furthermore, our unified coding can strictly outperform existing schemes. For example, we obtain a generalized decode-compress-amplify-and-forward bound as a simple corollary of our main theorem and show it strictly outperforms previously known coding schemes. Using our unified framework, we formally define and characterize three types of network duality based on channel input-output reversal and network flow reversal combined with packing-covering duality.

cs.IT↗

arXiv2015

Noisy Network Coding with Partial DF

In this paper, we propose a noisy network coding integrated with partial decode-and-forward relaying for single-source multicast discrete memoryless networks (DMN's). Our coding scheme generalizes the partial-decode-compress-and-forward scheme (Theorem 7) by Cover and El Gamal. This is the first time the theorem is generalized for DMN's such that each relay performs both partial decode-and-forward and compress-and-forward simultaneously. Our coding scheme simultaneously generalizes both noisy network coding by Lim, Kim, El Gamal, and Chung and distributed decode-and-forward by Lim, Kim, and Kim. It is not trivial to combine the two schemes because of inherent incompatibility in their encoding and decoding strategies. We solve this problem by sending the same long message over multiple blocks at the source and at the same time by letting the source find the auxiliary covering indices that carry information about the message simultaneously over all blocks.

cs.IT↗

arXiv2015

The Degraded Gaussian Diamond-Wiretap Channel

In this paper, we present nontrivial upper and lower bounds on the secrecy capacity of the degraded Gaussian diamond-wiretap channel and identify several ranges of channel parameters where these bounds coincide with useful intuitions. Furthermore, we investigate the effect of the presence of an eavesdropper on the capacity. We consider the following two scenarios regarding the availability of randomness: 1) a common randomness is available at the source and the two relays and 2) a randomness is available only at the source and there is no available randomness at the relays. We obtain the upper bound by taking into account the correlation between the two relay signals and the availability of randomness at each encoder. For the lower bound, we propose two types of coding schemes: 1) a decode-and-forward scheme where the relays cooperatively transmit the message and the fictitious message and 2) a partial DF scheme incorporated with multicoding in which each relay sends an independent partial message and the whole or partial fictitious message using dependent codewords.

cs.IT↗

arXiv2013

A New Achievable Scheme for Interference Relay Channels

We establish an achievable rate region for discrete memoryless interference relay channels that consist of two source-destination pairs and one or more relays. We develop an achievable scheme combining Han-Kobayashi and noisy network coding schemes. We apply our achievability to two cases. First, we characterize the capacity region of a class of discrete memoryless interference relay channels. This class naturally generalizes the injective deterministic discrete memoryless interference channel by El Gamal and Costa and the deterministic discrete memoryless relay channel with orthogonal receiver components by Kim. Moreover, for the Gaussian interference relay channel with orthogonal receiver components, we show that our scheme achieves a better sum rate than that of noisy network coding.

cs.IT↗