Related papers: Finite-State Dimension and Lossy Decompressors
This paper develops multihead finite-state compression, a generalization of finite-state compression, complementary to the multihead finite-state dimensions of Huang, Li, Lutz, and Lutz (2025). In this model, an infinite sequence of symbols…
We extend Ziv and Lempel's model of finite-state encoders to the realm of lossy compression of individual sequences. In particular, the model of the encoder includes a finite-state reconstruction codebook followed by an information lossless…
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…
Finite-state complexity is a variant of algorithmic information theory obtained by replacing Turing machines with finite transducers. We consider the state-size of transducers needed for minimal descriptions of arbitrary strings and, as our…
Traditionally, data compression deals with the problem of concisely representing a data source, e.g. a sequence of letters, for the purpose of eventual reproduction (either exact or approximate). In this work we are interested in the case…
We present a new similarity measure based on information theoretic measures which is superior than Normalized Compression Distance for clustering problems and inherits the useful properties of conditional Kolmogorov complexity. We show that…
We provide a rate distortion interpretation of the problem of quantum data compression of ensembles of mixed states with commuting density operators. There are two versions of this problem. In the visible case the sequence of states is…
We consider the most general (finite-dimensional) quantum mechanical information source, which is given by a quantum system $A$ that is correlated with a reference system $R$. The task is to compress $A$ in such a way as to reproduce the…
In analogy to the well-known notion of finite--state compressibility of individual sequences, due to Lempel and Ziv, we define a similar notion of "finite-state encryptability" of an individual plaintext sequence, as the minimum asymptotic…
In 2004, Dai, Lathrop, Lutz, and Mayordomo defined and investigated the finite-state dimension (a finite-state version of algorithmic dimension) of a sequence $S \in \Sigma^\infty$ and, in 2018, Case and Lutz defined and investigated the…
Lossy compressors are increasingly adopted in scientific research, tackling volumes of data from experiments or parallel numerical simulations and facilitating data storage and movement. In contrast with the notion of entropy in lossless…
Modern data compression methods are slowly reaching their limits after 80 years of research, millions of papers, and wide range of applications. Yet, the extravagant 6G communication speed requirement raises a major open question for…
This paper introduces matrix product state (MPS) decomposition as a new and systematic method to compress multidimensional data represented by higher-order tensors. It solves two major bottlenecks in tensor compression: computation and…
Finite-state dimension (Dai, Lathrop, Lutz, and Mayordomo (2004)) quantifies the information rate in an infinite sequence as measured by finite-state automata. In this paper, we define a relative version of finite-state dimension. The…
Error-bounded lossy compression has been effective in significantly reducing the data storage/transfer burden while preserving the reconstructed data fidelity very well. Many error-bounded lossy compressors have been developed for a wide…
Finite abstractions are discrete approximations of dynamical systems, such that the set of abstraction trajectories contains all system trajectories. There is a consensus that abstractions suffer from the curse of dimensionality: for the…
Image compression has been a frequent topic of presentations at ADASS. Compression is often viewed as just a technique to fit more data into a smaller space. Rather, the packing of data - its "density" - affects every facet of local data…
Increasing data volumes from scientific simulations and instruments (supercomputers, accelerators, telescopes) often exceed network, storage, and analysis capabilities. The scientific community's response to this challenge is scientific…
Data compression techniques are characterized by four key performance indices which are (i) associated accuracy, (ii) compression ratio, (iii) computational work, and (iv) degree of freedom. The method of data compression developed in this…
Lossy Image compression is necessary for efficient storage and transfer of data. Typically the trade-off between bit-rate and quality determines the optimal compression level. This makes the image quality metric an integral part of any…