This work investigates functional source coding problems with maximal distortion, motivated by approximate function computation in many modern applications. The maximal distortion treats imprecise reconstruction of a function value as good as perfect computation if it deviates less than a tolerance level, while treating reconstruction that differs by more than that level as a failure.
Motivated by control with communication constraints, in this work we develop a time-invariant data compression architecture for linear-quadratic-Gaussian (LQG) control with minimum bitrate prefix-free feedback. For any fixed control performance, the approach we propose nearly achieves known directed information (DI) lower bounds on the time-average expected codeword length. We refine the analysis of a classical achievability approach, which required quantized plant measurements to be encoded via a time-varying lossless source code.
A number of engineering and scientific problems require representing and manipulating probability distributions over large alphabets, which we may think of as long vectors of reals summing to 1. In some cases it is required to represent such a vector with only $b$ bits per entry. A natural choice is to partition the interval $[{0,1}]$ into $2^{b}$ uniform bins and quantize entries to each bin independently.
We present a self-supervised and self-calibrating multi-shot approach to imaging through atmospheric turbulence, called TurbuGAN. Our approach requires no paired training data, adapts itself to the distribution of the turbulence, leverages domain-specific data priors, and can generalize from tens to thousands of measurements. We achieve such functionality through an adversarial sensing framework adapted from CryoGAN (Gupta et al. 2021), which uses a discriminator network to match the distributions of captured and simulated measurements.
Index coding can be viewed as a compression problem with multiple decoders with side information. In such a setup, an encoder compresses a number of messages into a common codeword such that every decoder can decode its requested messages with the help of knowing some other messages as side information. In this paper, we study how much information is leaked to a guessing adversary observing the codeword in index coding, where some messages in the system are sensitive and others are not.
Many modern applications involve accessing and processing graphical data, i.e., data that is naturally indexed by graphs. Examples come from Internet graphs, social networks, genomics and proteomics, and other sources. The typically large size of such data motivates seeking efficient ways for its compression and decompression. The current compression methods are usually tailored to specific models, or do not provide theoretical guarantees.
In recent years, there have been significant advances in the use of deep learning methods in inverse problems such as denoising, compressive sensing, inpainting, and super-resolution. While this line of works has predominantly been driven by practical algorithms and experiments, it has also given rise to a variety of intriguing theoretical problems. In this paper, we survey some of the prominent theoretical developments in this line of works, focusing in particular on generative priors, untrained neural network priors, and unfolding algorithms.
A recent result says that the lossless compression of a single source $X^{n}$ is achievable with a strong locality property; any $X_{i}$ can be decoded from a constant number of compressed bits, with a vanishing in $n$ probability of error. By contrast, we show that for two separately encoded sources $(X^{n},Y^{n})$ , lossless compression and strong locality is generally not possible. Specifically, we show that for the class of 鈥渃onfusable鈥 sources, strong locality cannot be achieved whenever one of the sources is compressed below its entropy.
We formalize the tail redundancy of a collection ${\mathcal{ P}}$ of distributions over a countably infinite alphabet, and show that this fundamental quantity characterizes the asymptotic per-symbol minimax redundancy of universally compressing sequences generated i.i.d. from ${\mathcal{ P}}$ . Contrary to the worst case formulations of universal compression, finite single letter minimax (average case) redundancy of ${\mathcal{ P}}$ does not automatically imply that the expected minimax redundancy of describing length- $n$ strings sampled i.i.d.
Current methods which compress multisets at an optimal rate have computational complexity that scales linearly with alphabet size, making them too slow to be practical in many real-world settings. We show how to convert a compression algorithm for sequences into one for multisets, in exchange for an additional complexity term that is quasi-linear in sequence length. This allows us to compress multisets of exchangeable symbols at an optimal rate, with computational complexity decoupled from the alphabet size.