Results 11 to 20 of about 1,066,179 (25)
Quantum resource theory of coding for error correction [PDF]
Phys. Rev. A 110, 032413 (2024)Error-correction codes are central for fault-tolerant information processing. Here we develop a rigorous framework to describe various coding models based on quantum resource theory of superchannels. We find, by treating codings as superchannels, a hierarchy of coding models can be established, including the entanglement assisted or unassisted settings,
arxiv +1 more source
A family of asymptotically good quantum codes based on code concatenation [PDF]
arXiv, 2008 We explicitly construct an infinite family of asymptotically good concatenated quantum stabilizer codes where the outer code uses CSS-type quantum Reed-Solomon code and the inner code uses a set of special quantum codes. In the field of quantum error-correcting codes, this is the first time that a family of asymptotically good quantum codes is derived ...
arxiv
arXiv, 2017 In this paper we study Z2Z4Z8-additive codes, which are the extension of recently introduced Z2Z4-additive codes. We determine the standard forms of the generator and parity-check matrices of Z2Z4Z8-additive codes. Moreover, we investigate Z2Z4Z8-cyclic codes giving their generator polynomials and spanning sets.
arxiv
Entanglement-assisted quantum MDS codes constructed from constacyclic codes [PDF]
arXiv, 2018 Recently, entanglement-assisted quantum error correcting codes (EAQECCs) have been constructed by cyclic codes and negacyclic codes. In this paper, by analyzing the cyclotomic cosets in the defining set of constacyclic codes, we constructed three classes of new EAQECCs which satisfy the entanglement-assisted quantum Singleton bound.
arxiv
An Equivalence between Network Coding and Index Coding [PDF]
arXiv, 2012 We show that the network coding and index coding problems are equivalent. This equivalence holds in the general setting which includes linear and non-linear codes. Specifically, we present an efficient reduction that maps a network coding instance to an index coding one while preserving feasibility.
arxiv
A Search Algorithm to Find Multiple Sets of One Dimensional Unipolar (Optical) Orthogonal Codes with Same Code-length and Low Weight [PDF]
arXiv, 2013 This paper describes a search algorithm to find multiple sets of one dimensional unipolar (optical) orthogonal codes characterized by parameters, binary code sequence of length (n bits) and weight w (number of bit 1s in the sequence) as well as auto-correlation and cross-correlation constraint respectively for the codes within a set.
arxiv
Zero-error Slepian-Wolf Coding of Confined Correlated Sources with Deviation Symmetry [PDF]
arXiv, 2013 In this paper, we use linear codes to study zero-error Slepian-Wolf coding of a set of sources with deviation symmetry, where the sources are generalization of the Hamming sources over an arbitrary field. We extend our previous codes, Generalized Hamming Codes for Multiple Sources, to Matrix Partition Codes and use the latter to efficiently compress ...
arxiv
Protograph-Based Raptor-Like LDPC Codes [PDF]
arXiv, 2014 This paper proposes a class of rate-compatible LDPC codes, called protograph-based Raptor-like (PBRL) codes. The construction is focused on binary codes for BI-AWGN channels. As with the Raptor codes, additional parity bits are produced by exclusive-OR operations on the precoded bits, providing extensive rate compatibility.
arxiv
Stopping Sets of Algebraic Geometry Codes [PDF]
arXiv, 2013 Stopping sets and stopping set distribution of a linear code play an important role in the performance analysis of iterative decoding for this linear code. Let $C$ be an $[n,k]$ linear code over $\f$ with parity-check matrix $H$, where the rows of $H$ may be dependent. Let $[n]=\{1,2,...,n\}$ denote the set of column indices of $H$.
arxiv
Design of Quantum Stabilizer Codes From Quadratic Residues Sets [PDF]
arXiv, 2014 We propose two types, namely Type-I and Type-II, quantum stabilizer codes using quadratic residue sets of prime modulus given by the form $p=4n\pm1$. The proposed Type-I stabilizer codes are of cyclic structure and code length $N=p$. They are constructed based on multi-weight circulant matrix generated from idempotent polynomial, which is obtained from
arxiv