Related papers: Variable-Length Codes Independent or Closed with r…

Given an alphabet A and a binary relation $\tau$ $\subseteq$ A * x A * , a language X $\subseteq$ A * is $\tau$-independent if $\tau$ (X) $\cap$ X = $\emptyset$; X is $\tau$-closed if $\tau$ (X) $\subseteq$ X. The language X is complete if…

Given a finite alphabet $A$ and a binary relation $\tau\subseteq A^*\times A^*$, a set $X$ is $\tau$-{\it independent} if $ \tau(X)\cap X=\emptyset$. Given a quasi-metric $d$ over $A^*$ (in the meaning of \cite{W31}) and $k\ge 1$, we…

A code is called solid if, roughly speaking, any correctly-transmitted codeword in an arbitrarily corrupted string of codewords can still be decoded correctly and unambiguously. So-called variable-length solid codes, in which codewords may…

This paper explores the design of convolutional codes for varying constraint lengths, focusing on their role in error correction in digital communication systems. Convolutional codes are essential in achieving reliable data transmission…

For discrete memoryless multiple-access channels, we propose a general definition of variable length codes with a measure of the transmission rates at the receiver side. This gives a receiver perspective on the multiple-access channel…

We consider the embedding problem in coding theory: given an independence (a code-related property) and an independent language $L$, find a maximal independent language containing $L$. We consider the case where the code-related property is…

Variable-length splittable codes are derived from encoding sequences of ordered integer pairs, where one of the pair's components is upper bounded by some constant, and the other one is any positive integer. Each pair is encoded by the…

We define a variable-length code having the property that no (non-empty) prefix of each its codeword is a suffix of any other one, and vice versa. This kind of code can be seen as an extension of two well-known codes in literature, called…

Variable-to-variable length (VV) codes are a class of lossless source coding. As their name implies, VV codes encode a variable-length sequence of source symbols into a variable-length codeword. This paper will give a complete proof of an…

Vision-language models (VLMs) are increasingly used to make visual content accessible via text-based descriptions. In current systems, however, description specificity is often conflated with their length. We argue that these two concepts…

We introduce a new class of non-standard variable-length codes, called adaptive codes. This class of codes associates a variable-length codeword to the symbol being encoded depending on the previous symbols in the input data string. An…

We consider the issue of direct access to any letter of a sequence encoded with a variable length code and stored in the computer's memory, which is a special case of the random access problem to compressed memory. The characteristics…

Explicit characterization of the capacity region of communication networks is a long standing problem. While it is known that network coding can outperform routing and replication, the set of feasible rates is not known in general.…

We study the new problem of Huffman-like codes subject to individual restrictions on the code-word lengths of a subset of the source words. These are prefix codes with minimal expected code-word length for a random source where additionally…

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…

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…

Variable-length feedback coding has the potential to significantly enhance communication reliability in finite block length scenarios by adapting coding strategies based on real-time receiver feedback. Designing such codes, however, is…

Lossless variable-length source coding with codeword cost is considered for general sources. The problem setting, where we impose on unequal costs on code symbols, is called the variable-length coding with codeword cost. In this problem,…

Set and multiset variables in constraint programming have typically been represented using subset bounds. However, this is a weak representation that neglects potentially useful information about a set such as its cardinality. For set…

We use large language models (LLMs) to uncover long-ranged structure in English texts from a variety of sources. The conditional entropy or code length in many cases continues to decrease with context length at least to $N\sim 10^4$…