Related papers: Rate-distortion function via minimum mean square e…
A fundamental question in designing lossy data compression schemes is how well one can do in comparison with the rate-distortion function, which describes the known theoretical limits of lossy compression. Motivated by the empirical success…
We consider the semantic rate-distortion problem motivated by task-oriented video compression. The semantic information corresponding to the task, which is not observable to the encoder, shows impacts on the observations through a joint…
A receiver wants to compute a function of two correlated sources separately observed by two transmitters. One of the transmitters may send a possibly private message to the other transmitter in a cooperation phase before both transmitters…
In this paper, we propose a novel function named Rate Distortion-in-Distortion (RDD) function as an extension of the classical rate-distortion (RD) function, where the expected distortion constraint is replaced by a Gromov-type distortion.…
Let $X^n\in\mathcal{X}^n$ be a sequence drawn from a discrete memoryless source, and let $Y^n\in\mathcal{Y}^n$ be the corresponding reconstruction sequence that is output by a good rate-distortion code. This paper establishes a property of…
The problem of estimating the information rate distortion perception function (RDPF), which is a relevant information-theoretic quantity in goal-oriented lossy compression and semantic information reconstruction, is investigated here.…
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…
We consider the classic joint source-channel coding problem of transmitting a memoryless source over a memoryless channel. The focus of this work is on the long-standing open problem of finding the rate of convergence of the smallest…
I introduce rate-distortion theory for quantum coding, and derive a lower bound, involving the coherent information, on the rate at which qubits must be used to encode a quantum source with a given maximum level of distortion per source…
For the HB problem with the CR constraint, the rate-distortion function is derived under the assumption that the side information sequences are (stochastically) degraded. The rate-distortion function is also calculated explicitly for three…
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…
This paper is concerned with a rate-distortion theory for sequences of i.i.d. random variables with general distribution supported on general sets including manifolds and fractal sets. Manifold structures are prevalent in data science,…
We examine the structure of families of distortion balls from the perspective of Kolmogorov complexity. Special attention is paid to the canonical rate-distortion function of a source word which returns the minimal Kolmogorov complexity of…
In this paper we invoke a nonanticipative information Rate Distortion Function (RDF) for sources with memory, and we analyze its importance in probabilistic matching of the source to the channel so that transmission of a symbol-by-symbol…
The distortion-rate function of output-constrained lossy source coding with limited common randomness is analyzed for the special case of squared error distortion measure. An explicit expression is obtained when both source and…
In this paper, we study the rate distortion function of the i.i.d sequence of multiplications of a Bernoulli $p$ random variable and a gaussian random variable $\sim N(0,1)$. We use a new technique in the derivation of the lower bound in…
Around the mean dimensions and rate-distortion functions, using some tools from local entropy theory this paper establishes the following main results: $(1)$ We prove that for non-ergodic measures associated with almost sure processes, the…
We study lossy compression of a finite statement source generated in a fixed deductive environment. The source symbols are statements in a knowledge base endowed with a shared proof system, and reconstruction fidelity is measured by…
We consider correlated and distributed sources without cooperation at the encoder. For these sources, we derive the best achievable performance in the rate-distortion sense of any distributed compressed sensing scheme, under the constraint…
A Causal rate distortion function with a general fidelity criterion is formulated on abstract alphabets and the optimal reconstruction kernel is derived, which consists of a product of causal kernels. In the process, general abstract spaces…