相关论文: Twenty (or so) Questions: $D$-ary Length-Bounded P…

In this letter, we develop an efficient linear programming (LP) decoding algorithm for low-density parity-check (LDPC) codes. We first relax the maximum likelihood (ML) decoding problem to a LP problem by using check-node decomposition.…

A framework with two scalar parameters is introduced for various problems of finding a prefix code minimizing a coding penalty function. The framework encompasses problems previously proposed by Huffman, Campbell, Nath, and Drmota and…

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,…

The capacity achieving probability mass function (PMF) of a finite signal constellation with an average power constraint is in most cases non-uniform. A common approach to generate non-uniform input PMFs is Huffman shaping, which consists…

In this paper we study binary trees with choosable edge lengths, in particular rooted binary trees with the property that the two edges leading from every non-leaf to its two children are assigned integral lengths $l_1$ and $l_2$ with…

Today there are many universal compression algorithms, but in most cases is for specific data better using specific algorithm - JPEG for images, MPEG for movies, etc. For textual documents there are special methods based on PPM algorithm or…

Locally Decodable Codes (LDCs) are error-correcting codes $C\colon\Sigma^n\rightarrow \Sigma^m,$ encoding \emph{messages} in $\Sigma^n$ to \emph{codewords} in $\Sigma^m$, with super-fast decoding algorithms. They are important mathematical…

The monotone minimal perfect hash function (MMPHF) problem is the following indexing problem. Given a set $S= \{s_1,\ldots,s_n\}$ of $n$ distinct keys from a universe $U$ of size $u$, create a data structure $DS$ that answers the following…

The Run Length Encoding (RLE) compression method is a long standing simple lossless compression scheme which is easy to implement and achieves a good compression on input data which contains repeating consecutive symbols. In its pure form…

Effective training of today's large language models (LLMs) depends on large batches and long sequences for throughput and accuracy. To handle variable-length sequences on hardware accelerators, it is common practice to introduce padding…

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,…

Given $m$ documents of total length $n$, we consider the problem of finding a longest string common to at least $d \geq 2$ of the documents. This problem is known as the \emph{longest common substring (LCS) problem} and has a classic $O(n)$…

This article presents a new search algorithm for the NP-hard problem of optimizing functions of binary variables that decompose according to a graphical model. It can be applied to models of any order and structure. The main novelty is a…

Binary codes are widely used to represent the data due to their small storage and efficient computation. However, there exists an ambiguity problem that lots of binary codes share the same Hamming distance to a query. To alleviate the…

The linearly constrained matrix rank minimization problem is widely applicable in many fields such as control, signal processing and system identification. The tightest convex relaxation of this problem is the linearly constrained nuclear…

We solve an open problem related to an optimal encoding of a straight line program (SLP), a canonical form of grammar compression deriving a single string deterministically. We show that an information-theoretic lower bound for representing…

The number of zeros and the number of ones in a binary string are referred to as the composition of the string, and the prefix-suffix compositions of a string are a multiset formed by the compositions of the prefixes and suffixes of all…

We propose several improvements for Linear Programming (LP) decoding algorithms for High Density Parity Check (HDPC) codes. First, we use the automorphism groups of a code to create parity check matrix diversity and to generate valid cuts…

This paper is about the problem of finding a shortest $s$-$t$ path using at most $h$ edges in edge-weighted graphs. The Bellman--Ford algorithm solves this problem in $O(hm)$ time, where $m$ is the number of edges. We show that this running…

Iterative decoding of non-binary LDPC codes is currently performed using either the Sum-Product or the Min-Sum algorithms or slightly different versions of them. In this paper, several low-complexity quasi-optimal iterative algorithms are…