Related papers: Optimal alphabet for single text compression
In grammar-based compression a string is represented by a context-free grammar, also called a straight-line program (SLP), that generates only that string. We refine a recent balancing result stating that one can transform an SLP of size…
A prescription to calculate the minimum number of bits needed for binary strip detector readout is presented. This permits a systematic analysis of the readout efficiency relative to this theoretical minimum number of bits. Different level…
Huffman Codes are optimal Instantaneous Fixed-to-Variable (FV) codes in which every source symbol can only be encoded by one codeword. Relaxing these constraints permits constructing better FV codes. More specifically, recent work has shown…
A $k$-bit delay decodable code-tuple is a lossless source code that can achieve a smaller average codeword length than Huffman codes by using a finite number of code tables and allowing at most $k$-bit delay for decoding. It is known that…
Gottesman-Kitaev-Preskill (GKP) encoding holds promise for continuous-variable fault-tolerant quantum computing. While an ideal GKP encoding is abstract and impractical due to its nonphysical nature, approximate versions provide viable…
In a distributed information application an encoder compresses an arbitrary vector while a similar reference vector is available to the decoder as side information. For the Hamming-distance similarity measure, and when guaranteed perfect…
Molecular communication (MC) enables information transfer through molecules at the nano-scale. This paper presents new and optimized source coding (data compression) methods for MC. In a recent paper, prefix source coding was introduced…
Traditional image compression methods aim to reconstruct images for human perception, prioritizing visual fidelity over task relevance. In contrast, Coding for Machines focuses on preserving information essential for automated…
Grammar-based compression is a popular and powerful approach to compressing repetitive texts but until recently its relatively poor time-space trade-offs during real-life construction made it impractical for truly massive datasets such as…
We consider the problem of computing the q-gram profile of a string \str of size $N$ compressed by a context-free grammar with $n$ production rules. We present an algorithm that runs in $O(N-\alpha)$ expected time and uses $O(n+q+\kq)$…
We study a binary distributed hypothesis testing problem where two agents observe correlated binary vectors and communicate compressed information at the same rate to a central decision maker. In particular, we study linear compression…
The Kolmogorov complexity of x, denoted C(x), is the length of the shortest program that generates x. For such a simple definition, Kolmogorov complexity has a rich and deep theory, as well as applications to a wide variety of topics…
We revisit the problem of deciding whether a given string is uniquely decodable from its bigram counts by means of a finite automaton. An efficient algorithm for constructing a polynomial-size nondeterministic finite automaton that decides…
We propose a new approach for universal lossless text compression, based on grammar compression. In the literature, a target string $T$ has been compressed as a context-free grammar $G$ in Chomsky normal form satisfying $L(G) = \{T\}$. Such…
This paper presents new lower and upper bounds for the optimal compression of binary prefix codes in terms of the most probable input symbol, where compression efficiency is determined by the nonlinear codeword length objective of…
To any infinite word w over a finite alphabet A we can associate two infinite words min(w) and max(w) such that any prefix of min(w) (resp. max(w)) is the lexicographically smallest (resp. greatest) amongst the factors of w of the same…
Errors are inevitable during all kinds quantum informational tasks and quantum error-correcting codes (QECCs) are powerful tools to fight various quantum noises. For standard QECCs physical systems have the same number of energy levels.…
Satisfiability of word equations is an important problem in the intersection of formal languages and algebra: Given two sequences consisting of letters and variables we are to decide whether there is a substitution for the variables that…
Best and Brouwer [Discrete Math. 17 (1977), 235-245] proved that triply-shortened and doubly-shortened binary Hamming codes (which have length $2^m-4$ and $2^m-3$, respectively) are optimal. Properties of such codes are here studied,…
Bitmap indexes must be compressed to reduce input/output costs and minimize CPU usage. To accelerate logical operations (AND, OR, XOR) over bitmaps, we use techniques based on run-length encoding (RLE), such as Word-Aligned Hybrid (WAH)…