A rate-distortion-perception (RDP) tradeoff has recently been proposed by Blau and Michaeli and also Matsumoto. Focusing on the case of perfect realism, which coincides with the problem of distribution-preserving lossy compression studied by Li et al., a coding theorem for the RDP tradeoff that allows for a specified amount of common randomness between the encoder and decoder is provided. The existing RDP tradeoff is recovered by allowing for the amount of common randomness to be infinite. The quadratic Gaussian case is examined in detail.
Blau and Michaeli recently introduced a novel concept for inverse problems of signal processing, that is, the perception-distortion tradeoff. We introduce their tradeoff into the rate distortion theory of lossy source coding in information theory, and clarify the tradeoff among information rate, distortion and perception for general information sources.
Blau and Michaeli recently introduced a novel concept for inverse problems of signal processing, that is, the perception-distortion tradeoff. We introduce their tradeoff into the rate distortion theory of variable-length lossy source coding in information theory, and clarify the tradeoff among information rate, distortion and perception for general information sources. We also discuss the fixed-length coding with average distortion criterion that was missing in the previous letter.
Asymptotic energy-distortion performance of zero-delay communication scenarios under additive white Gaussian noise is investigated. Using high-resolution analysis for quantizer design, the higher-order term in the logarithm of the distortion (termed the {\em energy-distortion dispersion}) is optimized while keeping the leading term (i.e., {\em energy-distortion exponent}) at its optimal value. For uniform and Gaussian sources, significant gains are observed compared to naïvely performed quantization, i.e., aimed at optimizing the source coding performance instead of the end-to-end distortion i…
University of Science and Technology of China（中国科学技术大学）
Signal degradation is ubiquitous and computational restoration of degraded signal has been investigated for many years. Recently, it is reported that the capability of signal restoration is fundamentally limited by the perception-distortion tradeoff, i.e. the distortion and the perceptual difference between the restored signal and the ideal `original' signal cannot be made both minimal simultaneously. Distortion corresponds to signal fidelity and perceptual difference corresponds to perceptual naturalness, both of which are important metrics in practice. Besides, there is another dimension wor…
Lossy compression algorithms are typically designed and analyzed through the lens of Shannon's rate-distortion theory, where the goal is to achieve the lowest possible distortion (e.g., low MSE or high SSIM) at any given bit rate. However, in recent years, it has become increasingly accepted that "low distortion" is not a synonym for "high perceptual quality", and in fact optimization of one often comes at the expense of the other. In light of this understanding, it is natural to seek for a generalization of rate-distortion theory which takes perceptual quality into account. In this paper, we …
We study the role of interaction in the Common Randomness Generation (CRG) and Secret Key Generation (SKG) problems. In the CRG problem, two players, Alice and Bob, respectively get samples $X_1,X_2,\dots$ and $Y_1,Y_2,\dots$ with the pairs $(X_1,Y_1)$, $(X_2, Y_2)$, $\dots$ being drawn independently from some known probability distribution $μ$. They wish to communicate so as to agree on $L$ bits of randomness. The SKG problem is the restriction of the CRG problem to the case where the key is required to be close to random even to an eavesdropper who can listen to their communication (but does…
In this paper, we analyze the fundamental stealthiness-distortion tradeoffs of linear Gaussian dynamical systems under data injection attacks using a power spectral analysis, whereas the Kullback-Leibler (KL) divergence is employed as the stealthiness measure. Particularly, we obtain explicit formulas in terms of power spectra that characterize analytically the stealthiness-distortion tradeoffs as well as the properties of the worst-case attacks. Furthermore, it is seen in general that the attacker only needs to know the input-output behaviors of the systems in order to carry out the worst-cas…
We investigate the rate distortion tradeoff in private read update write (PRUW) in relation to federated submodel learning (FSL). In FSL a machine learning (ML) model is divided into multiple submodels based on different types of data used for training. Each user only downloads and updates the submodel relevant to its local data. The process of downloading and updating the required submodel while guaranteeing privacy of the submodel index and the values of updates is known as PRUW. In this work, we study how the communication cost of PRUW can be reduced when a pre-determined amount of distorti…
University of Toronto（多伦多大学）；McMaster University（麦克马斯特大学）
In the context of lossy compression, Blau & Michaeli (2019) adopt a mathematical notion of perceptual quality and define the information rate-distortion-perception function, generalizing the classical rate-distortion tradeoff. We consider the notion of universal representations in which one may fix an encoder and vary the decoder to achieve any point within a collection of distortion and perception constraints. We prove that the corresponding information-theoretic universal rate-distortion-perception function is operationally achievable in an approximate sense. Under MSE distortion, we show th…
Most methods for publishing data with privacy guarantees introduce randomness into datasets which reduces the utility of the published data. In this paper, we study the privacy-utility tradeoff by taking maximal leakage as the privacy measure and the expected Hamming distortion as the utility measure. We study three different but related problems. First, we assume that the data-generating distribution (i.e., the prior) is known, and we find the optimal privacy mechanism that achieves the smallest distortion subject to a constraint on maximal leakage. Then, we assume that the prior belongs to s…
Integrated sensing and communications (ISAC) is recognized as a key enabling technology for future wireless networks. To shed light on the fundamental performance limits of ISAC systems, this paper studies the deterministic-random tradeoff between sensing and communications (S&C) from a rate-distortion perspective under vector Gaussian channels. We model the ISAC signal as a random matrix that carries information, whose realization is perfectly known to the sensing receiver, but is unknown to the communication receiver. We characterize the sensing mutual information conditioned on the random I…
Rateless DeepJSCC for Broadcast Channels: a Rate-Distortion-Complexity Tradeoff
Department of Electrical and Computer Engineering, University of Hong Kong（香港大学电子与计算机工程系）；School of Information and Electronics, Beijing Institute of Technology（北京理工大学信息与电子学院）；School of Cyberspace Science and Technology, Beijing Institute of Technology（北京理工大学网络空间科学与技术学院）
The Rate-Distortion-Perception-Classification Tradeoff: Joint Source Coding and Modulation via Inverse-Domain GANs
School of Informatics, Xiamen University（厦门大学信息学院）；School of Electronics and Information Engineering, Guangxi Normal University（广西师范大学电子与信息工程学院）；School of Engineering & Physical Sciences, Heriot-Watt University（赫瑞瓦特大学工程与物理科学学院）
Private information retrieval protocols guarantee that a user can privately and losslessly retrieve a single file from a database stored across multiple servers. In this work, we propose to simultaneously relax the conditions of perfect retrievability and privacy in order to obtain improved download rates when all files are stored uncoded on a single server. Information leakage is measured in terms of the average success probability for the server of correctly guessing the identity of the desired file. The main findings are: i) The derivation of the optimal tradeoff between download rate, dist…
Training-Free Rate-Distortion-Perception Traversal With Diffusion
Department of Information Engineering, The Chinese University of Hong Kong, Hong Kong（信息工程系，香港中文大学，香港）；College of Electronic and Information Engineering, Shenzhen University, Shenzhen（电子与信息工程学院，深圳大学，深圳）
A privacy-utility tradeoff is developed for an arbitrary set of finite-alphabet source distributions. Privacy is quantified using differential privacy (DP), and utility is quantified using expected Hamming distortion maximized over the set of distributions. The family of source distribution sets (source sets) is categorized into three classes, based on different levels of prior knowledge they capture. For source sets whose convex hull includes the uniform distribution, symmetric DP mechanisms are optimal. For source sets whose probability values have a fixed monotonic ordering, asymmetric DP m…
Rate-Distortion-Perception Tradeoff for the Gray-Wyner Problem
School of Automation and Intelligent Manufacturing, Southern University of Science and Technology（南方科技大学自动化与智能制造学院）；School of Cyber Science and Technology, Beihang University（北京航空航天大学网络空间科学学院）
A Synonymous Variational Perspective on the Rate-Distortion-Perception Tradeoff
Key Laboratory of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications（信息与通信技术联合实验室，教育部，北京邮电大学）；State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications（网络与交换技术国家重点实验室，北京邮电大学）
A communication setup is considered where a transmitter wishes to simultaneously sense its channel state and convey a message to a receiver. The state is estimated at the transmitter by means of generalized feedback, i.e. a strictly causal channel output that is observed at the transmitter. The scenario is motivated by a joint radar and communication system where the radar and data applications share the same frequency band. For the case of a memoryless channel with i.i.d. state sequences, we characterize the capacity-distortion tradeoff, defined as the best achievable rate below which a messa…
We study a discrete-time model where each packet has a cost of not being sent -- this cost might depend on the packet content. We study the tradeoff between the age and the cost where the sender is confined to packet-based strategies. The optimal tradeoff is found by an appropriate formulation of the problem as a Markov Decision Process (MDP). We show that the optimal tradeoff can be attained with finite-memory policies and we devise an efficient policy iteration algorithm to find these optimal policies. We further study a related problem where the transmitted packets are subject to erasures. …
A communication setup is considered where a transmitter wishes to convey a message to a receiver and simultaneously estimates the state of that receiver through a common waveform. The state is estimated at the transmitter by means of generalized feedback, i.e., a strictly causal channel output, and the known waveform. The scenario at hand is motivated by joint radar and communication, which aims to co-design radar sensing and communication over a shared spectrum and hardware. For the case of memoryless single receiver channels with i.i.d. time-varying state sequences, we fully characterize the…
We introduce a tunable measure for information leakage called maximal alpha-leakage. This measure quantifies the maximal gain of an adversary in inferring any (potentially random) function of a dataset from a release of the data. The inferential capability of the adversary is, in turn, quantified by a class of adversarial loss functions that we introduce as $α$-loss, $α\in[1,\infty]$. The choice of $α$ determines the specific adversarial action and ranges from refining a belief (about any function of the data) for $α=1$ to guessing the most likely value for $α=\infty$ while refining the $α^{th…
Mitsubishi Electric Research Laboratories（三菱电机研究实验室）；Tufts University（塔夫茨大学）；Arizona State University（亚利桑那州立大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Robust machine learning formulations have emerged to address the prevalent vulnerability of deep neural networks to adversarial examples. Our work draws the connection between optimal robust learning and the privacy-utility tradeoff problem, which is a generalization of the rate-distortion problem. The saddle point of the game between a robust classifier and an adversarial perturbation can be found via the solution of a maximum conditional entropy problem. This information-theoretic perspective sheds light on the fundamental tradeoff between robustness and clean data performance, which ultimat…
We consider information leakage to the user in private information retrieval (PIR) systems. Information leakage can be measured in terms of individual message leakage or total leakage. Individual message leakage, or simply individual leakage, is defined as the amount of information that the user can obtain on any individual message that is not being requested, and the total leakage is defined as the amount of information that the user can obtain about all the other messages except the one being requested. In this work, we characterize the tradeoff between the minimum download cost and the indi…
We consider the task of faithfully simulating a distributed quantum measurement, wherein we provide a protocol for the three parties, Alice, Bob and Eve, to simulate a repeated action of a distributed quantum measurement using a pair of non-product approximating measurements by Alice and Bob, followed by a stochastic mapping at Eve. The objective of the protocol is to utilize minimum resources, in terms of classical bits needed by Alice and Bob to communicate their measurement outcomes to Eve, and the common randomness shared among the three parties, while faithfully simulating independent rep…
