Related papers: Reserved-Length Prefix Coding
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…
We introduce a new variant of variable-length source coding for sending a source over two parallel channels, one of which is costly and the other free. We give a complete solution to this problem. Next, we relate the problem to the number…
Although real-world text datasets, such as DNA sequences, are far from being uniformly random, average-case string searching algorithms perform significantly better than worst-case ones in most applications of interest. In this paper, we…
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 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…
Data compression has become a necessity not only the in the field of communication but also in various scientific experiments. The data that is being received is more and the processing time required has also become more. A significant…
A variable-length code is a fix-free code if no codeword is a prefix or a suffix of any other codeword. In a fix-free code any finite sequence of codewords can be decoded in both directions, which can improve the robustness to channel noise…
Prefix parsing asks whether an input prefix can be extended to a complete string generated by a given grammar. In the weighted setting, it also provides prefix probabilities, which are central to context-free language modeling,…
We give the first algorithm for adaptive alphabetic prefix-free coding that is worst-case optimal in terms of time and compression when $\sigma \in o \left( \frac{n^{1 / 2}}{\log n} \right)$, where $\sigma$ is the size of the alphabet and…
Large Language Models (LLMs) have been widely adopted in commercial code completion engines, significantly enhancing coding efficiency and productivity. However, LLMs may generate code with quality issues that violate coding standards and…
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…
Location data are widely used in mobile apps, ranging from location-based recommendations, to social media and navigation. A specific type of interaction is that of location-based alerts, where mobile users subscribe to a service provider…
We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and…
This article shows that any type of binary data can be defined as a collection from codewords of variable length. This feature helps us to define an Injective and surjective function from the suggested codewords to the required codewords.…
A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most…
A text written using symbols from a given alphabet can be compressed using the Huffman code, which minimizes the length of the encoded text. It is necessary, however, to employ a text-specific codebook, i.e. the symbol-codeword dictionary,…
Multiple algorithms are known for efficiently calculating the prefix probability of a string under a probabilistic context-free grammar (PCFG). Good algorithms for the problem have a runtime cubic in the length of the input string. However,…
We introduce a binary embedding framework, called Proximity Preserving Code (PPC), which learns similarity and dissimilarity between data points to create a compact and affinity-preserving binary code. This code can be used to apply fast…
The problem of storing permutations in a distributed manner arises in several common scenarios, such as efficient updates of a large, encrypted, or compressed data set. This problem may be addressed in either a combinatorial or a coding…
We investigate two source coding problems with secrecy constraints. In the first problem we consider real--time fully secure transmission of a memoryless source. We show that although classical variable--rate coding is not an option since…