Related papers: On the rate distortion function of Bernoulli Gauss…
Motivated by questions in lossy data compression and by theoretical considerations, we examine the problem of estimating the rate-distortion function of an unknown (not necessarily discrete-valued) source from empirical data. Our focus is…
We begin by presenting a simple lossy compressor operating at near-zero rate: The encoder merely describes the indices of the few maximal source components, while the decoder's reconstruction is a natural estimate of the source components…
In this paper, we consider a distributed remote source coding problem, where a sequence of observations of source vectors is available at the encoder. The problem is to specify the optimal rate for encoding the observations subject to a…
We consider the rate-distortion function for lossy source compression, as well as the channel capacity for error correction, through the lens of distributional robustness. We assume that the distribution of the source or of the additive…
In this paper we study the problem of recovering sparse or compressible signals from uniformly quantized measurements. We present a new class of convex optimization programs, or decoders, coined Basis Pursuit DeQuantizer of moment $p$…
We consider the problem of multiple description scalar quantizers and describing the achievable rate-distortion tuples in that setting. We formulate it as a combinatorial optimization problem of arranging numbers in a matrix to minimize the…
Results on two different settings of asymptotic behavior of approximation characteristics of individual functions are presented. First, we discuss the following classical question for sparse approximation. Is it true that for any individual…
In this paper, the optimal sampling strategies (uniform or nonuniform) and distortion tradeoffs for Gaussian bandlimited periodic signals with additive white Gaussian noise are studied. Our emphasis is on characterizing the optimal sampling…
Rate-distortion-perception theory generalizes Shannon's rate-distortion theory by introducing a constraint on the perceptual quality of the output. The perception constraint complements the conventional distortion constraint and aims to…
The rate-distortion saddle-point problem considered by Lapidoth (1997) consists in finding the minimum rate to compress an arbitrary ergodic source when one is constrained to use a random Gaussian codebook and minimum (Euclidean) distance…
We propose computationally efficient encoders and decoders for lossy compression using a Sparse Regression Code. The codebook is defined by a design matrix and codewords are structured linear combinations of columns of this matrix. The…
In this paper, we introduce new lower bounds on the distortion of scalar fixed-rate codes for lossy compression with side information available at the receiver. These bounds are derived by presenting the relevant random variables as a…
Inter-symbol interference (ISI) channels with data dependent Gauss Markov noise have been used to model read channels in magnetic recording and other data storage systems. The Viterbi algorithm can be adapted for performing maximum…
We study the problem of detection of a p-dimensional sparse vector of parameters in the linear regression model with Gaussian noise. We establish the detection boundary, i.e., the necessary and sufficient conditions for the possibility of…
In this paper we study the diameter of the random graph $G(n,p)$, i.e., the the largest finite distance between two vertices, for a wide range of functions $p=p(n)$. For $p=\la/n$ with $\la>1$ constant, we give a simple proof of an…
We present a general method to obtain the exact rate function $\Psi_{[a,b]}(k)$ controlling the large deviation probability $\text{Prob}[\mathcal{I}_N[a,b]=kN] \asymp e^{-N\Psi_{[a,b]}(k)}$ that a $N \times N$ sparse random matrix has…
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…
In the successive refinement problem, a fixed-length sequence emitted from an information source is encoded into two codewords by two encoders in order to give two reconstructions of the sequence. One of two reconstructions is obtained by…
There has been a great deal of work establishing that random linear codes are as list-decodable as uniformly random codes, in the sense that a random linear binary code of rate $1 - H(p) - \epsilon$ is $(p,O(1/\epsilon))$-list-decodable…
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,…