Related papers: Pragmatic lossless compression: Fundamental limits…
This paper provides an extensive study of the behavior of the best achievable rate (and other related fundamental limits) in variable-length lossless compression. In the non-asymptotic regime, the fundamental limits of fixed-to-variable…
The problem of lossless data compression with side information available to both the encoder and the decoder is considered. The finite-blocklength fundamental limits of the best achievable performance are defined, in two different versions…
A new framework is introduced for examining and evaluating the fundamental limits of lossless data compression, that emphasizes genuinely non-asymptotic results. The {\em sample complexity} of compressing a given source is defined as the…
This paper investigates the problem of variable-length lossy source coding allowing a positive excess distortion probability and an overflow probability of codeword lengths. Novel one-shot achievability and converse bounds of the optimal…
Variable-length compression without prefix-free constraints and with side-information available at both encoder and decoder is considered. Instead of requiring the code to be error-free, we allow for it to have a non-vanishing error…
This paper studies the fundamental limits of the minimum average length of lossless and lossy variable-length compression, allowing a nonzero error probability $\epsilon$, for lossless compression. We give non-asymptotic bounds on the…
We present new lower and upper bounds for the compression rate of binary prefix codes optimized over memoryless sources according to two related exponential codeword length objectives. The objectives explored here are exponential-average…
We consider universal variable-to-fixed length compression of memoryless sources with a fidelity criterion. We design a dictionary codebook over the reproduction alphabet which is used to parse the source stream. Once a source subsequence…
Error probabilities of random codes for memoryless channels are considered in this paper. In the area of communication systems, admissible error probability is very small and it is sometimes more important to discuss the relative gap…
We describe a method for lossless quantum compression if the output of the information source is not known. We compute the best possible compression rate, minimizing the expected base length of the output quantum bit string (the base length…
This study investigates the fundamental limits of variable-length compression in which prefix-free constraints are not imposed (i.e., one-to-one codes are studied) and non-vanishing error probabilities are permitted. Due in part to a…
Universal fixed-to-variable lossless source coding for memoryless sources is studied in the finite blocklength and higher-order asymptotics regimes. Optimal third-order coding rates are derived for general fixed-to-variable codes and for…
The problem of determining the best achievable performance of arbitrary lossless compression algorithms is examined, when correlated side information is available at both the encoder and decoder. For arbitrary source-side information pairs,…
We examine the coordinated and universal rate-efficient sampling of a subset of correlated discrete memoryless sources followed by lossy compression of the sampled sources. The goal is to reconstruct a predesignated subset of sources within…
This paper studies the minimum achievable source coding rate as a function of blocklength $n$ and probability $\epsilon$ that the distortion exceeds a given level $d$. Tight general achievability and converse bounds are derived that hold at…
We consider the lossless compression bound of any individual data sequence. If we fit the data by a parametric model, the entropy quantity $nH({\hat \theta}_n)$ obtained by plugging in the maximum likelihood estimate is an underestimate of…
We study the problem of compression for the purpose of similarity identification, where similarity is measured by the mean square Euclidean distance between vectors. While the asymptotical fundamental limits of the problem - the minimal…
This paper considers lossy source coding of $n$-dimensional memoryless sources and shows an explicit approximation to the minimum source coding rate required to sustain the probability of exceeding distortion $d$ no greater than $\epsilon$,…
This paper establishes the exact strong converse exponent of the soft covering problem in the classical setting. This exponent characterizes the slowest achievable convergence speed of the total variation to one when a code of rate below…
We formalize the problem of prompt compression for large language models (LLMs) and present a framework to unify token-level prompt compression methods which create hard prompts for black-box models. We derive the distortion-rate function…