Related papers: Entropy bounds for grammar compression

The basic problem of semantic compression is to minimize the length of a message while preserving its meaning. This differs from classical notions of compression in that the distortion is not measured directly at the level of bits, but…

Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be…

We consider an abstraction of computational security in password protected systems where a user draws a secret string of given length with i.i.d. characters from a finite alphabet, and an adversary would like to identify the secret string…

This paper investigates the size in bits of the LZ77 encoding, which is the most popular and efficient variant of the Lempel-Ziv encodings used in data compression. We prove that, for a wide natural class of variable-length encoders for…

Tandem duplication is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain et al. (2017) proposed the study of codes that correct tandem…

Dynamic dictionary-based compression schemes are the most daily used data compression schemes since they appeared in the foundational papers of Ziv and Lempel in 1977, commonly referred to as LZ77. Their work is the base of Deflate, gZip,…

Consider communication over a binary-input memoryless output-symmetric channel with low density parity check (LDPC) codes and maximum a posteriori (MAP) decoding. The replica method of spin glass theory allows to conjecture an analytic…

We describe a simple and general neural network weight compression approach, in which the network parameters (weights and biases) are represented in a "latent" space, amounting to a reparameterization. This space is equipped with a learned…

We propose a new proof technique that aims to be applied to the same problems as the Lov\'asz Local Lemma or the entropy-compression method. We present this approach in the context of non-repetitive colorings and we use it to improve…

The modern data compression is mainly based on two approaches to entropy coding: Huffman (HC) and arithmetic/range coding (AC). The former is much faster, but approximates probabilities with powers of 2, usually leading to relatively low…

In the Shortest Common Superstring problem (SCS), one needs to find the shortest superstring for a set of strings. While SCS is NP-hard and MAX-SNP-hard, the Greedy Algorithm "choose two strings with the largest overlap; merge them; repeat"…

The context transformation and generalized context transformation methods, we introduced recently, were able to reduce zero order entropy by exchanging digrams, and as a consequence, they were removing mutual information between consecutive…

In this paper, a fully compressed pattern matching problem is studied. The compression is represented by straight-line programs (SLPs), i.e. a context-free grammars generating exactly one string; the term fully means that both the pattern…

Unlike in statistical compression, where Shannon's entropy is a definitive lower bound, no such clear measure exists for the compressibility of repetitive sequences. Since statistical entropy does not capture repetitiveness, ad-hoc measures…

We consider the problem of constructing prefix-free codes in which a designated symbol, a space, can only appear at the end of codewords. We provide a linear-time algorithm to construct almost-optimal codes with this property, meaning that…

Even though fine-grained pruning techniques achieve a high compression ratio, conventional sparsity representations (such as CSR) associated with irregular sparsity degrade parallelism significantly. Practical pruning methods, thus, usually…

A range of recent works addresses the problem of compression of sequence of tokens into a shorter sequence of real-valued vectors to be used as inputs instead of token embeddings or key-value cache. These approaches are focused on reduction…

Large Language Models (LLMs) achieve strong performance across tasks, but face storage and compute challenges on edge devices. We propose EntroLLM, a compression framework combining mixed quantization and entropy coding to reduce storage…

This paper describes a new set of block source codes well suited for data compression. These codes are defined by sets of productions rules of the form a.l->b, where a in A represents a value from the source alphabet A and l, b are -small-…

Sparse coding techniques for image processing traditionally rely on a processing of small overlapping patches separately followed by averaging. This has the disadvantage that the reconstructed image no longer obeys the sparsity prior used…