arXiv subjects

Sadaf Salehkalaibar

Publications and source records attributed to Sadaf Salehkalaibar.

18 recordsLinked to original sources

arXiv2025

Rate-Distortion-Perception Tradeoff Based on the Conditional-Distribution Perception Measure

This paper studies the rate-distortion-perception (RDP) tradeoff for a memoryless source model in the asymptotic limit of large block-lengths. The perception measure is based on a divergence between the distributions of the source and reconstruction sequences \emph{conditioned} on the encoder output, first proposed by Mentzer et al. We consider the case when there is no shared randomness between the encoder and the decoder and derive a single-letter characterization of the RDP function for the case of discrete memoryless sources. This is in contrast to the marginal-distribution metric case (introduced by Blau and Michaeli), whose RDP characterization remains open when there is no shared randomness. The achievability scheme is based on lossy source coding with a posterior reference map. For the case of continuous valued sources under the squared error distortion measure and the squared quadratic Wasserstein perception measure, we also derive a single-letter characterization and show that the decoder can be restricted to a noise-adding mechanism. Interestingly, the RDP function characterized for the case of zero perception loss coincides with that of the marginal metric, and further zero perception loss can be achieved with a 3-dB penalty in minimum distortion. Finally we specialize to the case of Gaussian sources, and derive the RDP function for Gaussian vector case and propose a reverse water-filling type solution. We also partially characterize the RDP function for a mixture of Gaussian vector sources.

cs.IT↗

arXiv2025

Rate-Distortion-Perception Tradeoff for Gaussian Vector Sources

This paper studies the rate-distortion-perception (RDP) tradeoff for a Gaussian vector source coding problem where the goal is to compress the multi-component source subject to distortion and perception constraints. Specifically, the RDP setting with either the Kullback-Leibler (KL) divergence or Wasserstein-2 metric as the perception loss function is examined, and it is shown that for Gaussian vector sources, jointly Gaussian reconstructions are optimal. We further demonstrate that the optimal tradeoff can be expressed as an optimization problem, which can be explicitly solved. An interesting property of the optimal solution is as follows. Without the perception constraint, the traditional reverse water-filling solution for characterizing the rate-distortion (RD) tradeoff of a Gaussian vector source states that the optimal rate allocated to each component depends on a constant, called the water level. If the variance of a specific component is below the water level, it is assigned a zero compression rate. However, with active distortion and perception constraints, we show that the optimal rates allocated to the different components are always positive. Moreover, the water levels that determine the optimal rate allocation for different components are unequal. We further treat the special case of perceptually perfect reconstruction and study its RDP function in the high-distortion and low-distortion regimes to obtain insight to the structure of the optimal solution.

cs.IT↗

arXiv2025

On Self-Adaptive Perception Loss Function for Sequential Lossy Compression

We consider causal, low-latency, sequential lossy compression, with mean squared-error (MSE) as the distortion loss, and a perception loss function (PLF) to enhance the realism of reconstructions. As the main contribution, we propose and analyze a new PLF that considers the joint distribution between the current source frame and the previous reconstructions. We establish the theoretical rate-distortion-perception function for first-order Markov sources and analyze the Gaussian model in detail. From a qualitative perspective, the proposed metric can simultaneously avoid the error-permanence phenomenon and also better exploit the temporal correlation between high-quality reconstructions. The proposed metric is referred to as self-adaptive perception loss function (PLF-SA), as its behavior adapts to the quality of reconstructed frames. We provide a detailed comparison of the proposed perception loss function with previous approaches through both information theoretic analysis as well as experiments involving moving MNIST and UVG datasets.

cs.LG↗

arXiv2023

On the Choice of Perception Loss Function for Learned Video Compression

We study causal, low-latency, sequential video compression when the output is subjected to both a mean squared-error (MSE) distortion loss as well as a perception loss to target realism. Motivated by prior approaches, we consider two different perception loss functions (PLFs). The first, PLF-JD, considers the joint distribution (JD) of all the video frames up to the current one, while the second metric, PLF-FMD, considers the framewise marginal distributions (FMD) between the source and reconstruction. Using information theoretic analysis and deep-learning based experiments, we demonstrate that the choice of PLF can have a significant effect on the reconstruction, especially at low-bit rates. In particular, while the reconstruction based on PLF-JD can better preserve the temporal correlation across frames, it also imposes a significant penalty in distortion compared to PLF-FMD and further makes it more difficult to recover from errors made in the earlier output frames. Although the choice of PLF decisively affects reconstruction quality, we also demonstrate that it may not be essential to commit to a particular PLF during encoding and the choice of PLF can be delegated to the decoder. In particular, encoded representations generated by training a system to minimize the MSE (without requiring either PLF) can be {\em near universal} and can generate close to optimal reconstructions for either choice of PLF at the decoder. We validate our results using (one-shot) information-theoretic analysis, detailed study of the rate-distortion-perception tradeoff of the Gauss-Markov source model as well as deep-learning based experiments on moving MNIST and KTH datasets.

eess.IV↗

arXiv2023

M22: A Communication-Efficient Algorithm for Federated Learning Inspired by Rate-Distortion

In federated learning (FL), the communication constraint between the remote learners and the Parameter Server (PS) is a crucial bottleneck. For this reason, model updates must be compressed so as to minimize the loss in accuracy resulting from the communication constraint. This paper proposes ``\emph{${\bf M}$-magnitude weighted $L_{\bf 2}$ distortion + $\bf 2$ degrees of freedom''} (M22) algorithm, a rate-distortion inspired approach to gradient compression for federated training of deep neural networks (DNNs). In particular, we propose a family of distortion measures between the original gradient and the reconstruction we referred to as ``$M$-magnitude weighted $L_2$'' distortion, and we assume that gradient updates follow an i.i.d. distribution -- generalized normal or Weibull, which have two degrees of freedom. In both the distortion measure and the gradient, there is one free parameter for each that can be fitted as a function of the iteration number. Given a choice of gradient distribution and distortion measure, we design the quantizer minimizing the expected distortion in gradient reconstruction. To measure the gradient compression performance under a communication constraint, we define the \emph{per-bit accuracy} as the optimal improvement in accuracy that one bit of communication brings to the centralized model over the training period. Using this performance measure, we systematically benchmark the choice of gradient distribution and distortion measure. We provide substantial insights on the role of these choices and argue that significant performance improvements can be attained using such a rate-distortion inspired compressor.

cs.LG↗

arXiv2022

On Distributed Lossy Coding of Symmetrically Correlated Gaussian Sources

A distributed lossy compression network with $L$ encoders and a decoder is considered. Each encoder observes a source and sends a compressed version to the decoder. The decoder produces a joint reconstruction of target signals with the mean squared error distortion below a given threshold. It is assumed that the observed sources can be expressed as the sum of target signals and corruptive noises which are independently generated from two symmetric multivariate Gaussian distributions. The minimum compression rate of this network versus the distortion threshold is referred to as the rate-distortion function, for which an explicit lower bound is established by solving a minimization problem. Our lower bound matches the well-known Berger-Tung upper bound for some values of the distortion threshold. The asymptotic gap between the upper and lower bounds is characterized in the large $L$ limit.

cs.IT↗

arXiv2022

Lossy Gradient Compression: How Much Accuracy Can One Bit Buy?

In federated learning (FL), a global model is trained at a Parameter Server (PS) by aggregating model updates obtained from multiple remote learners. Generally, the communication between the remote users and the PS is rate-limited, while the transmission from the PS to the remote users are unconstrained. The FL setting gives rise to the distributed learning scenario in which the updates from the remote learners have to be compressed so as to meet communication rate constraints in the uplink transmission toward the PS. For this problem, one wishes to compress the model updates so as to minimize the loss in accuracy resulting from the compression error. In this paper, we take a rate-distortion approach to address the compressor design problem for the distributed training of deep neural networks (DNNs). In particular, we define a measure of the compression performance under communication-rate constraints -- the \emph{per-bit accuracy} -- which addresses the ultimate improvement of accuracy that a bit of communication brings to the centralized model. In order to maximize the per-bit accuracy, we consider modeling the DNN gradient updates at remote learners as a generalized normal distribution. Under this assumption on the DNN gradient distribution, we propose a class of distortion measures to aid the design of quantizers for the compression of the model updates. We argue that this family of distortion measures, which we refer to as "$M$-magnitude weighted $L_2$" norm, captures the practitioner's intuition in the choice of gradient compressor. Numerical simulations are provided to validate the proposed approach for the CIFAR-10 dataset.

cs.LG↗

arXiv2021

Distributed Sequential Hypothesis Testing With Zero-Rate Compression

In this paper, we consider sequential testing over a single-sensor, a single-decision center setup. At each time instant $t$, the sensor gets $k$ samples $(k>0)$ and describes the observed sequence until time $t$ to the decision center over a zero-rate noiseless link. The decision center sends a single bit of feedback to the sensor to request for more samples for compression/testing or to stop the transmission. We have characterized the optimal exponent of type-II error probability under the constraint that type-I error probability does not exceed a given threshold $ε\in (0,1)$ and also when the expectation of the number of requests from decision center is smaller than $n$ which tends to infinity. Interestingly, the optimal exponent coincides with that for fixed-length hypothesis testing with zero-rate communication constraints.

cs.IT↗

arXiv2020

State Masking Over a Two-State Compound Channel

We consider fundamental limits for communicating over a compound channel when the state of the channel needs to be masked. Our model is closely related to an area of study known as covert communication that is a setting in which the transmitter wishes to communicate to legitimate receiver(s) while ensuring that the communication is not detected by an adversary. The main contribution in our two-state masking setup is the establishment of bounds on the throughput-key region when the constraint that quantifies how much the states are masked is defined to be the total variation distance between the two channel-induced distributions. For the scenario in which the key length is infinite, we provide sufficient conditions for when the bounds to coincide for the throughput, which follows the square-root law. Numerical examples, including that of a Gaussian channel, are provided to illustrate our results.

cs.IT↗

arXiv2020

On Sum Secure Degrees of Freedom for K-User MISO Broadcast Channel With Alternating CSIT

In this paper, the sum secure degrees of freedom (SDoF) of the $K$-user Multiple Input/Single Output (MISO) Broadcast Channel with Confidential Messages (BCCM) and alternating Channel State Information at the Transmitter (CSIT) is investigated. In the MISO BCCM, a $K$-antenna transmitter (TX) communicates toward $K$ single-antenna receivers (RXs), so that message for RX $k$ is kept secret from RX $j$ with $j<k$. For this model, we consider the scenario in which the CSI of the RXs from $2$ to $K$ is instantaneously known at the transmitter while CSI of RX $1$ is known at the transmitter (i) instantaneously for half of the time and (ii) with a unit delay for the remainder of the time. We refer to this CSIT availability as \emph{alternating} CSIT. Alternating CIST has been shown to provide synergistic gains in terms of SDoF and is thus of a viable strategy to ensure secure communication by simply relying on the CSI feedback strategy. Our main contribution is the characterization of sum SDoF for this model as $SDoF_{\rm sum}= (2K-1)/2$. Interestingly, this $SDoF_{\rm sum}$ is attained by a rather simple achievability in which the TX uses artificial noise to prevent the decoding of the message of the unintended receivers at RX $1$. For simplicity first, the proof for the case $K=3$ is discussed in detail and after that, we have presented the results for any number of RXs.

cs.IT↗

arXiv2020

Distributed Hypothesis Testing with Variable-Length Coding

The problem of distributed testing against independence with variable-length coding is considered when the \emph{average} and not the \emph{maximum} communication load is constrained as in previous works. The paper characterizes the optimum type-II error exponent of a single sensor single decision center system given a maximum type-I error probability when communication is either over a noise-free rate-$R$ link or over a noisy discrete memoryless channel (DMC) with stop-feedback. Specifically, let $ε$ denote the maximum allowed type-I error probability. Then the optimum exponent of the system with a rate-$R$ link under a constraint on the average communication load coincides with the optimum exponent of such a system with a rate $R/(1-ε)$ link under a maximum communication load constraint. A strong converse thus does not hold under an average communication load constraint. A similar observation holds also for testing against independence over DMCs. With variable-length coding and stop-feedback and under an average communication load constraint, the optimum type-II error exponent over a DMC of capacity $C$ equals the optimum exponent under fixed-length coding and a maximum communication load constraint when communication is over a DMC of capacity $C(1-ε)^{-1}$. In particular, under variable-length coding over a DMC with stop feedback a strong converse result does not hold and the optimum error exponent depends on the transition law of the DMC only through its capacity.

cs.IT↗

arXiv2020

On Hypothesis Testing Against Independence with Multiple Decision Centers

A distributed binary hypothesis testing problem is studied with one observer and two decision centers. Achievable type-II error exponents are derived for testing against conditional independence when the observer communicates with the two decision centers over one common and two individual noise-free bit pipes and when it communicates with them over a noisy broadcast channel (BC). The results are based on a coding and testing scheme that splits the observations into subblocks, so that transmitter and receivers can independently apply to each subblock either Gray-Wyner coordination coding with side-information or hybrid joint source-channel coding with side-information, followed by a Neyman-Pearson test over the subblocks at the receivers. This approach allows to avoid introducing further error exponents that one would expect from the receivers' decoding operations related to binning or the noisy transmission channel. The derived exponents are shown to be optimal in some special cases when communication is over noise-free links. The results reveal a tradeoff between the type-II error exponents at the two decision centers.

cs.IT↗

arXiv2020

Hypothesis Testing Over the Two-hop Relay Network

Coding and testing schemes and the corresponding achievable type-II error exponents are presented for binary hypothesis testing over two-hop relay networks. The schemes are based on cascade source coding techniques and {unanimous decision-forwarding}, the latter meaning that a terminal decides on the null hypothesis only if all previous terminals have decided on the null hypothesis. If the observations at the transmitter, the relay, and the receiver form a Markov chain in this order, then, without loss in performance, the proposed cascade source code can be replaced by two independent point-to-point source codes, one for each hop. The decoupled scheme (combined with decision-forwarding) is shown to attain the optimal type-II error exponents for various instances of "testing against conditional independence." The same decoupling is shown to be optimal also for some instances of "testing against independence," when the observations at the transmitter, the receiver, and the relay form a Markov chain in this order, and when the relay-to-receiver link is of sufficiently high rate. For completeness, the paper also presents an analysis of the Shimokawa-Han-Amari binning scheme for the point-to-point hypothesis testing setup.

cs.IT↗

arXiv2019

Distributed Hypothesis Testing with Variable-Length Coding

This paper characterizes the optimal type-II error exponent for a distributed hypothesis testing-against-independence problem when the \emph{expected} rate of the sensor-detector link is constrained. Unlike for the well-known Ahlswede-Csiszar result that holds under a \emph{maximum} rate constraint and where a strong converse holds, here the optimal exponent depends on the allowed type-I error exponent. Specifically, if the type-I error probability is limited by $ε$, then the optimal type-II error exponent under an \emph{expected} rate constraint $R$ coincides with the optimal type-II error exponent under a \emph{maximum} rate constraint of $(1-ε)R$.

cs.IT↗

arXiv2019

Covert Communication Over a Compound Channel

In this paper, we consider fundamental communication limits over a compound channel. Covert communication in the information-theoretic context has been primarily concerned with fundamental limits when the transmitter wishes to communicate to legitimate receiver(s) while ensuring that the communication is not detected by an adversary. This paper, however, considers an alternative, and no less important, setting in which the object to be masked is the state of the compound channel. Such a communication model has applications in the prevention of malicious parties seeking to jam the communication signal when, for example, the signal-to-noise ratio of a wireless channel is found to be low. Our main contribution is the establishment of bounds on the throughput-key region when the covertness constraint is defined in terms of the total variation distance. In addition, for the scenario in which the key length is infinite, we provide a sufficient condition for when the bounds coincide for the scaling of the throughput, which follows the square-root law. Numerical examples, including that of a Gaussian channel, are provided to illustrate our results.

cs.IT↗

arXiv2018

Distributed Hypothesis Testing based on Unequal-Error Protection Codes

Coding and testing schemes for binary hypothesis testing over noisy networks are proposed and their corresponding type-II error exponents are derived. When communication is over a discrete memoryless channel (DMC), our scheme combines Shimokawa-Han-Amari's hypothesis testing scheme with Borade's unequal error protection (UEP) for channel coding. A separate source channel coding architecture is employed. The resulting exponent is optimal for the newly introduced class of \emph{generalized testing against conditional independence}. When communication is over a MAC or a BC, our scheme combines hybrid coding with UEP. The resulting error exponent over the MAC is optimal in the case of generalized testing against conditional independence with independent observations at the two sensors, when the MAC decomposes into two individual DMCs. In this case, separate source-channel coding is sufficient; this same conclusion holds also under arbitrarily correlated sensor observations when testing is against independence. For the BC, the error exponents region of hybrid coding with UEP exhibits a tradeoff between the exponents attained at the two decision centers. When both receivers aim at maximizing the error exponents under different hypotheses and the marginal distributions of the sensors' observations are different under these hypotheses, then this tradeoff can be mitigated with the following strategy. The sensor makes a tentative guess on the hypothesis, submits this guess, and applies our coding and testing scheme for the DMC only for the decision center that is not interested in maximizing the exponent under the guessed hypothesis.

cs.IT↗

arXiv2018

Distributed Hypothesis Testing with Privacy Constraints

We revisit the distributed hypothesis testing (or hypothesis testing with communication constraints) problem from the viewpoint of privacy. Instead of observing the raw data directly, the transmitter observes a sanitized or randomized version of it. We impose an upper bound on the mutual information between the raw and randomized data. Under this scenario, the receiver, which is also provided with side information, is required to make a decision on whether the null or alternative hypothesis is in effect. We first provide a general lower bound on the type-II exponent for an arbitrary pair of hypotheses. Next, we show that if the distribution under the alternative hypothesis is the product of the marginals of the distribution under the null (i.e., testing against independence), then the exponent is known exactly. Moreover, we show that the strong converse property holds. Using ideas from Euclidean information theory, we also provide an approximate expression for the exponent when the communication rate is low and the privacy level is high. Finally, we illustrate our results with a binary and a Gaussian example.

cs.IT↗

arXiv2013

Key agreement over a 3-receiver broadcast channel

In this paper, we consider the problem of secret key agreement in state-dependent 3-receiver broadcast channels. In the proposed model, there are two legitimate receivers, an eavesdropper and a transmitter where the channel state information is non-causally available at the transmitter. We consider two setups. In the first setup, the transmitter tries to agree on a common key with the legitimate receivers while keeping it concealed from the eavesdropper. Simultaneously, the transmitter agrees on a private key with each of the legitimate receivers that needs to be kept secret from the other legitimate receiver and the eavesdropper. For this setup, we derive inner and outer bounds on the secret key capacity region. In the second setup, we assume that a backward public channel is available among the receivers and the transmitter. Each legitimate receiver wishes to share a private key with the transmitter. For this setup, an inner bound on the private key capacity region is found. Furthermore, the capacity region of the secret key in the state-dependent wiretap channel can be deduced from our inner and outer bounds.

cs.CR↗