Related papers: Linear code-based vector quantization for independ…
This paper deals with rate distortion or source coding with fidelity criterion, in measure spaces, for a class of source distributions. The class of source distributions is described by a relative entropy constraint set between the true and…
We address the task of higher-order derivative evaluation of computer programs that contain QR decompositions and real symmetric eigenvalue decompositions. The approach is a combination of univariate Taylor polynomial arithmetic and matrix…
We present a novel systematic theoretical framework to analyze the rate-distortion (R-D) limits of learned image compression. While recent neural codecs have achieved remarkable empirical results, their distance from the…
We consider a novel variant of $d$-semifaithful lossy coding in which the distortion measure is revealed only to the encoder and only at run-time, as well as an extension of it in which the distortion constraint $d$ is also revealed at…
Rate-Distortion Optimized Quantization (RDOQ) has played an important role in the coding performance of recent video compression standards such as H.264/AVC, H.265/HEVC, VP9 and AV1. This scheme yields significant reductions in bit-rate at…
We introduce the new concept of computation coding. Similar to how rate-distortion theory is concerned with the lossy compression of data, computation coding deals with the lossy computation of functions. Particularizing to linear…
Linear block transform coding remains a fundamental component of image and video compression. Although the Discrete Cosine Transform (DCT) is widely employed in all current compression standards, its sub-optimality has sparked ongoing…
Berger's paper `The Source Coding Game', IEEE Trans. Inform. Theory, 1971, considers the problem of finding the rate-distortion function for an adversarial source comprised of multiple known IID sources. The adversary, called the…
In this paper, we consider the rate-distortion-perception (RDP) trade-off for the lossy compression of a Bernoulli vector source, which is a finite collection of independent binary random variables. The RDP function quantifies in a way the…
Following the approach by R. K\"otter and F. R. Kschischang, we study network codes as families of k-dimensional linear subspaces of a vector space F_q^n, q being a prime power and F_q the finite field with q elements. In particular,…
Transformers achieve superior performance on many tasks, but impose heavy compute and memory requirements during inference. This inference can be made more efficient by partitioning the process across multiple devices, which, in turn,…
Linear computation coding is concerned with the compression of multidimensional linear functions, i.e. with reducing the computational effort of multiplying an arbitrary vector to an arbitrary, but known, constant matrix. This paper…
This paper studies the performance of sparse regression codes for lossy compression with the squared-error distortion criterion. In a sparse regression code, codewords are linear combinations of subsets of columns of a design matrix. It is…
We show the existence of variable-rate rate-distortion codes that meet the disortion constraint almost surely and are minimax, i.e., strongly, universal with respect to an unknown source distribution and a distortion measure that is…
We consider a distributed source coding problem of $L$ correlated Gaussian observations $Y_i, i=1,2,...,L$. We assume that the random vector $Y^{L}={}^{\rm t} (Y_1,Y_2,$ $...,Y_L)$ is an observation of the Gaussian random vector…
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…
We initiate the study of what we term ``fast good codes'' with ``fast good duals.'' Specifically, we consider the task of constructing a rate 1/2 binary linear code such that both it and its dual are asymptotically good (in fact, have…
We formulate quantum rate-distortion theory in the most general setting where classical side information is included in the tradeoff. Using a natural distortion measure based on entanglement fidelity and specializing to the case of an…
For a Gaussian source under mean-squared error (MSE), classical transform coding is rate--distortion (RD) optimal: the Karhunen--Loeve transform (KLT) diagonalizes the covariance, reverse waterfilling allocates the bits, and scalar…
Rate distortion theory treats the problem of encoding a source with minimum codebook size while at the same time allowing for a certain amount of errors in the reconstruction measured by a fidelity criterion and distortion level. Similar to…