Related papers: Quantum-inspired Huffman Coding
We analyze a generalization of Huffman coding to the quantum case. In particular, we notice various difficulties in using instantaneous codes for quantum communication. Nevertheless, for the storage of quantum information, we have succeeded…
Huffman compression is a statistical, lossless, data compression algorithm that compresses data by assigning variable length codes to symbols, with the more frequently appearing symbols given shorter codes than the less. This work is a…
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…
Training and serving Large Language Models (LLMs) relies heavily on parallelization and collective operations, which are frequently bottlenecked by network bandwidth. Lossless compression using e.g., Huffman codes can alleviate the issue,…
Canonical Huffman code is an optimal prefix-free compression code whose codewords enumerated in the lexicographical order form a list of binary words in non-decreasing lengths. Gagie et al. (2015) gave a representation of this coding…
Huffman coding is known to be optimal, yet its dynamic version may be even more efficient in practice. A new variant of Huffman encoding has been proposed recently, that provably always performs better than static Huffman coding by at least…
Efficient optimal prefix coding has long been accomplished via the Huffman algorithm. However, there is still room for improvement and exploration regarding variants of the Huffman problem. Length-limited Huffman coding, useful for many…
The Huffman coding algorithm is interpreted in the lattice of partitions of the source alphabet. Maximal chains in the partition lattice correspond to linear extensions of tree orders, and those among the chains that exhibit a simple greedy…
Today's high-performance computing (HPC) applications are producing vast volumes of data, which are challenging to store and transfer efficiently during the execution, such that data compression is becoming a critical technique to mitigate…
A loss-less compression technique is proposed which uses a variable length Region formation technique to divide the input file into a number of variable length regions. Huffman codes are obtained for entire file after formation of regions.…
The general scheme of data compression using the quantum noiseless coding theorem of Schumacher is dicussed for general quantum sources. When the Hilbert space of the quantum source is decomposable into orthogonal subspaces, one can first…
Data compression has been widely applied in many data processing areas. Compression methods use variable-size codes with the shorter codes assigned to symbols or groups of symbols that appear in the data frequently. Fibonacci coding, as a…
In this paper, source coding or data compression is viewed as a measurement problem. Given a measurement device with fewer states than the observable of a stochastic source, how can one capture the essential information? We propose modeling…
Many data compressors regularly encode probability distributions for entropy coding - requiring minimal description length type of optimizations. Canonical prefix/Huffman coding usually just writes lengths of bit sequences, this way…
The design of the channel part of a digital communication system (e.g., error correction, modulation) is heavily based on the assumption that the data to be transmitted forms a fair bit stream. However, simple source encoders such as short…
Training and serving Large Language Models (LLMs) require partitioning data across multiple accelerators, where collective operations are frequently bottlenecked by network bandwidth. Lossless compression using Huffman codes is an effective…
An explicit algorithm for performing Schumacher's noiseless compression of quantum bits is given. This algorithm is based on a combinatorial expression for a particular bijection among binary strings. The algorithm, which adheres to the…
Huffman coding finds a prefix code that minimizes mean codeword length for a given probability distribution over a finite number of items. Campbell generalized the Huffman problem to a family of problems in which the goal is to minimize not…
This paper proposes a novel model of the two-level scalar quantizer with extended Huffman coding. It is designed for the average bit rate to approach the source entropy as close as possible provided that the signal to quantization noise…
There are two main approaches in compressed sensing: the geometric approach and the combinatorial approach. In this paper we introduce an information theoretic approach and use results from the theory of Huffman codes to construct a…