Results 291 to 300 of about 8,529,401 (324)

A topological theory for qLDPC: non-Clifford gates and magic state fountain on homological product codes with constant rate and beyond the N1/3 distance barrier

arXiv.org
We develop a topological theory for fault-tolerant quantum computation in quantum low-density parity-check (qLDPC) codes. We show that there exist hidden simplicial or CW complex structures encoding the topological data for all qLDPC and CSS codes ...
Guanyu Zhu
semanticscholar   +1 more source

Maximally Extendable Product Codes are Good Coboundary Expanders

IEEE Annual Symposium on Foundations of Computer Science
We investigate the coboundary expansion property of tensor product codes, known as product expansion, which plays an important role in recent constructions of good quantum LDPC codes and classical locally testable codes.
G. Kalachev, Pavel Panteleev
semanticscholar   +1 more source

On the Weight Hierarchy of Product Codes

Designs, Codes and Cryptography, 2004
In this paper the generalization of a formula concerning to product codes with more than two components is given. Especially the generalization of the Wei-Yang formula to the product codes with an arbitrary number of components is given and proven. This is done by using some definitions, theorems, propositions and an example.
Conchita Martínez-Pérez, Wolfgang Willems   +1 more
openaire   +1 more source

Improved Code Shortening for Block and Product Codes

2006 IEEE 63rd Vehicular Technology Conference, 2006
Code shortening is commonly performed in practice but its analytical decoding performance is not well understood. In this letter, we present tight bounds for estimating the weight enumerator and hence BER (bit error rate) performance of linear shortened and shortened-extended block/product codes operating in AWGN and Rayleigh fading channels.
Kai Ching Lim, Yong Liang Guan 0001
openaire   +1 more source

New binary and ternary LCD codes from matrix-product codes

Linear and multilinear algebra, 2020
Linear complementary dual (LCD) codes are linear codes satisfying . Researchers have proved to construct linear codes over finite fields , q>3, is equivalent to construct LCD codes. This means that the investigation of binary and ternary LCD codes is the
Xiusheng Liu, Hualu Liu, Long Yu
semanticscholar   +1 more source

On products of graphs for LDPC codes

Proceedings 2003 IEEE Information Theory Workshop (Cat. No.03EX674), 2004
The notion of product block codes, whose generator matrix is the tensor product of the constituent generator matrices, is well established. Typically, they have good performance and a decoding algorithm with complexity on the order of the complexity of the decoding algorithms of the constituent codes.
Jun Xu 0004, Shu Lin 0001, Ian F. Blake
openaire   +1 more source

Weight hierarchy of a product code

IEEE Transactions on Information Theory, 1995
The authors give formulas for the computation of the first few members of the weight hierarchy of a product code. They also present basic patterns for the supports of subcodes in which the minimum cardinalities can be found. Based on this the formula for each term of the hierarchy can be found but the required proofs are slightly involved (the formulas
Angela I. Barbero, Juan Tena
openaire   +2 more sources

Concatenated codes, matrix-product codes and their schur product [PDF]

, 2021
The aim of thesis is two-fold. Firstly, we introduce concatenated codes, matrixproduct codes and elaborate on their relation. It is known that a matrix-product code can be seen as a concatenated code. We give a proof of this fact. Conversely, we show how a particular concatenated code can be viewed as a matrix-product code.
openaire  

Binary Message Passing Decoding of Product Codes Based on Generalized Minimum Distance Decoding : (Invited Paper)

Annual Conference on Information Sciences and Systems, 2019
We propose a binary message passing decoding algorithm for product codes based on generalized minimum distance decoding (GMDD) of the component codes, where the last stage of the GMDD makes a decision based on the Hamming distance metric.
Alireza Sheikh, A. G. Amat, G. Liva
semanticscholar   +1 more source

Turbo-Product-Coded QVSB

IEEE Transactions on Broadcasting, 2006
In this paper, a turbo-product-coded, quadrature-vestigial-sideband (QVSB), digital modulation and coding scheme are presented. This scheme is more complex than the VSB modulation and coding format employed for high-definition television; and it achieves spectral-efficiency performance within 4 to 5dB of the Shannon-Bound, with relatively conservative ...
John Poklemba, David Wenzel
openaire   +1 more source