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We introduce the concept of generalized concatenated quantum codes. This generalized concatenation method provides a systematical way for constructing good quantum codes, both stabilizer codes and nonadditive codes. Using this method, we…

Quantum Physics · Physics 2009-05-24 Markus Grassl , Peter Shor , Graeme Smith , John Smolin , Bei Zeng

In this paper will be presented new approach to entropy coding: family of generalizations of standard numeral systems which are optimal for encoding sequence of equiprobable symbols, into asymmetric numeral systems - optimal for freely…

Information Theory · Computer Science 2009-05-21 Jarek Duda

New stabilizer codes with parameters better than the ones available in the literature are provided in this work, in particular quantum codes with parameters $[[127,63, \geq 12]]_2$ and $[[63,45, \geq 6]]_4$ that are records. These codes are…

Information Theory · Computer Science 2024-05-01 Carlos Galindo , Fernando Hernando , Diego Ruano

In this paper, we analyze the coding delay and the average coding delay of random linear network codes (a.k.a. dense codes) and chunked codes (CC), which are an attractive alternative to dense codes due to their lower complexity, over line…

Information Theory · Computer Science 2012-07-26 Anoosheh Heidarzadeh , Amir H. Banihashemi

In this paper, an extension of raptor codes is introduced which keeps all the desirable properties of raptor codes, including the linear complexity of encoding and decoding per information bit, unchanged. The new design, however, improves…

Information Theory · Computer Science 2016-11-17 Kaveh Mahdaviani , Masoud Ardakani , Chintha Tellambura

We consider a new family of codes, termed asymmetric Lee distance codes, that arise in the design and implementation of DNA-based storage systems and systems with parallel string transmission protocols. The codewords are defined over a…

Information Theory · Computer Science 2016-12-16 Ryan Gabrys , Han Mao Kiah , Olgica Milenkovic

This paper presents a new encryption scheme called Compact Coding that encodes information in time, phase, and intensity domains, simultaneously. While these approaches have previously been used one at a time, the proposed scheme brings to…

Quantum Physics · Physics 2016-07-13 Rasha El Hajj , Pramode Verma , Kam Wai Clifford Chan

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…

Information Theory · Computer Science 2024-10-03 Parag Dhounde , Avinash Bhute

Describes a near-linear-time algorithm for a variant of Huffman coding, in which the letters may have non-uniform lengths (as in Morse code), but with the restriction that each word to be encoded has equal probability. [See also ``Huffman…

Data Structures and Algorithms · Computer Science 2015-06-02 Mordecai Golin , Neal E. Young

For $n,d,w \in \mathbb{N}$, let $A(n,d,w)$ denote the maximum size of a binary code of word length $n$, minimum distance $d$ and constant weight $w$. Schrijver recently showed using semidefinite programming that $A(23,8,11)=1288$, and the…

Combinatorics · Mathematics 2018-12-03 Andries E. Brouwer , Sven C. Polak

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…

Machine Learning · Computer Science 2020-02-06 Inbal Lav , Shai Avidan , Yoram Singer , Yacov Hel-Or

Recently A. Schrijver derived new upper bounds for binary codes using semidefinite programming. In this paper we adapt this approach to codes on the unit sphere and we compute new upper bounds for the kissing number in several dimensions.…

Metric Geometry · Mathematics 2008-04-10 Christine Bachoc , Frank Vallentin

The scope of this paper is twofold. First, to emphasize the use of the mod 1 map in exploring the digit distribution of random variables. We show that the well-known base- and scale-invariance of Benford variables are consequences of their…

Probability · Mathematics 2013-12-24 Azar Khosravani , Constantin Rasinariu

In a recent paper, Tang and Ding introduced a class of binary cyclic codes of rate close to one half with a designed lower bound on their minimum distance. The definition involves the base $2$ expansion of the integers in their defining…

Information Theory · Computer Science 2023-09-22 Minjia Shi , Sihui Tao , Jon-Lark Kim , Patrick Sole

In this correspondence, first-tier indirect (direct) discernible constellation expansions are defined for generalized orthogonal designs. The expanded signal constellation, leading to so-called super-orthogonal codes, allows the achievement…

Information Theory · Computer Science 2011-09-06 Dumitru Mihai Ionescu , Zhiyuan Yan

Traditional distributed source coding rarely considers the possible link between separate encoders. However, the broadcast nature of wireless communication in sensor networks provides a free gossip mechanism which can be used to simplify…

Information Theory · Computer Science 2010-10-19 Zichong Chen , Guillermo Barrenetxea , Martin Vetterli

We propose a new code design that aims to distribute an LDPC code over a relay channel. It is based on a split-and-extend approach, which allows the relay to split the set of bits connected to some parity-check of the LDPC code into two or…

Information Theory · Computer Science 2010-04-30 Valentin Savin

In this paper we propose constellations with suitable structure which allow one to construct codes with excellent diversity using geometrical symmetry and numerical methods. We also demonstrate how these structured constellations…

Optimization and Control · Mathematics 2007-05-23 Guangyue Han , Joachim Rosenthal

We prove an upper bound for the length of an arithmetic progression represented by an irreducible integral binary quadratic form or a norm form, which depends only on the form and the progression's common difference. For quadratic forms,…

Number Theory · Mathematics 2019-08-14 Christian Elsholtz , Christopher Frei

A general class of the almost instantaneous fixed-to-variable-length (AIFV) codes is proposed, which contains every possible binary code we can make when allowing finite bits of decoding delay. The contribution of the paper lies in the…

Information Theory · Computer Science 2023-09-08 Ryosuke Sugiura , Yutaka Kamamoto , Takehiro Moriya