Article
Computer Science, Theory & Methods
Heqian Xu, Guangkui Xu, Wei Du
Summary: This paper introduces the concept of Niederreiter-Rosenbloom-Tsfasman LCD (NRT LCD) codes in the metric space, which are a generalization of Euclidean LCD codes with wider applications.
ADVANCES IN MATHEMATICS OF COMMUNICATIONS
(2022)
Article
Computer Science, Hardware & Architecture
Mohamed Amine Belhamra, El Mamoun Souidi
Summary: Network coding is a novel forwarding technique that promises to change many aspects of networking. This paper introduces Error Correction Network Coding (ECNC), a new approach that introduces redundancy in the time domain for error correction in NC schemes. ECNCs can be used jointly with the space domain error-correcting codes proposed for NC.
Article
Computer Science, Information Systems
Mohamed Marey, Hala Mostafa
Summary: The study develops a maximum-likelihood (ML) classifier that discriminates among SFBC-OFDM signals using the soft outputs of a channel decoder, showing considerably better classification performance compared to classical classifiers.
Article
Computer Science, Artificial Intelligence
Kun-Hong Liu, Jie Gao, Yong Xu, Kai-Jie Feng, Xiao-Na Ye, Sze-Teng Liong, Li-Yan Chen
Summary: Error-Correcting Output Codes (ECOC) algorithms enable multi-class classification by reassigning classes to positive/negative groups based on the subordination degrees. In this paper, a Soft-Coded ECOC scheme is proposed using real values to fill codematrices, and classes are divided into two groups by maximizing the ratio of inter-group distance to intra-group distance. The algorithm achieves more balanced classification results and improves the multiclass classification ability.
PATTERN RECOGNITION
(2022)
Article
Computer Science, Information Systems
Elisa Gorla, Flavio Salizzoni
Summary: In this paper, a new definition of generalized weights of convolutional codes is proposed, taking into account the underlying module structure of the code. The basic properties of the proposed generalized weights are derived and their relation with the previous definition is discussed. Upper bounds on the weight hierarchy of MDS and MDP codes are established and it is shown that the generalized weights of MDS codes can be determined by the length, rank, and internal degree of the code. An anticode bound for convolutional codes is also proven and optimal anticodes are defined. The weight hierarchy of optimal anticodes is computed.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2023)
Article
Telecommunications
Sida Li, Yimeng Zhang, Zhiping Huang, Jing Zhou, Yongjie Zhao
Summary: This paper proposes a novel framework for code type classification based on Hidden Markov Model (HMM), which models and analyzes the structural differences of different types of error correcting codes (ECCs) using transition and emission probabilities. An HMM-based classifier is proposed and enhanced with soft decision message and relative posterior probability to improve performance in noisy transmission environments.
IEEE TRANSACTIONS ON COGNITIVE COMMUNICATIONS AND NETWORKING
(2023)
Article
Engineering, Electrical & Electronic
Xinwei Zhao, Shancheng Zhao, Qin Huang, Xiao Ma
Summary: This paper presents generalized integrated interleaved (GII) zipper codes, which couple multiple zipper codes together using the constraint of the GII code. An enhanced anchor decoder (AD) is proposed to reduce miscorrections by assigning anchor reliability during GII decoding. The size and multiplicity of the minimum-sized stall patterns (MSSPs) of GII-zipper codes are also analyzed, showing that they are larger than those of zipper codes. Extensive simulation results confirm the performance advantages of GII-zipper codes, outperforming comparable zipper codes and achieving further gains with the enhanced AD. Specifically, a GII-staircase code with a rate of 0.846 achieves 0.74 dB above capacity at a bit error rate (BER) of 10^(-15).
IEEE TRANSACTIONS ON COMMUNICATIONS
(2023)
Article
Mathematics
Daniel Camazon Portela, Juan Antonio Lopez Ramos
Summary: The aim of this article is to provide lower bounds for the parameters of algebraic geometric error-correcting codes constructed from projective bundles over Deligne-Lusztig surfaces. The methods utilized intersection theory extensively to extend the codes constructed from higher-dimensional varieties and curves. General bounds are obtained for projective bundles of rank 2 over standard Deligne-Lusztig surfaces, and specific examples from surfaces of type A(2) and (2)A(4) are given.
Article
Physics, Multidisciplinary
Zhuo Li, Lijuan Xing
Summary: The universal framework for quantum error-correcting codes presented in this study is based on group algebra, providing a way to characterize the properties of quantum codes and generate new results. By utilizing the properties of the group algebra, this framework allows for a comprehensive understanding of quantum codes.
Article
Computer Science, Information Systems
Zihui Yan, Cong Liang, Huaming Wu
Summary: DNA-based data storage, as a powerful tool for storing digital information, has been continuously developed and received more attention. In this paper, the authors propose a segmented-edit error-correcting code called DNA-LM code, which has a systematic structure and can efficiently recover information from large-scale DNA strands. It does not require the endpoint of the received segment as prerequisite information for decoding. Furthermore, the authors generalize the decoding algorithm to handle duplicated DNA strands while maintaining linear time complexity in the codeword length and the number of duplications.
IEEE TRANSACTIONS ON EMERGING TOPICS IN COMPUTING
(2023)
Article
Quantum Science & Technology
Hanwei Xiao, Xiaoguang Chen
Summary: This paper proposes a framework of quantum convolutional codes that can handle continuous errors, by concatenating GKP code and utilizing the output information of the decoding circuit through multiple iterations to further reduce errors.
QUANTUM INFORMATION PROCESSING
(2022)
Article
Mathematics, Applied
Nabin Kumar Pokhrel, Pankaj Kumar Das, Aleksandar Radonjic
Summary: This paper presents a class of integer codes capable of correcting burst asymmetric errors and analyzes their probability of erroneous decoding for different bit error rates. The codes are also evaluated from a rate-efficiency point of view and the obtained results show that for many data lengths they require less check-bits than optimal burst error correcting codes.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2023)
Article
Optics
Stefanie J. Beale, Joel J. Wallman
Summary: This paper presents methods for incorporating noisy measurement operations into simulations of quantum error-correcting codes, studying measurement errors on readout qubits, and reducing the computational complexity of calculating the exact effective logical noise. These methods can be used to reduce the size of a lookup table and better approximate soft decoding schemes.
Article
Quantum Science & Technology
Weiwei Wang, Jiantao Li
Summary: In this paper, two classes of entanglement-assisted quantum MDS codes (EAQMDS codes) are constructed using generalized Reed-Solomon codes. These codes have parameters that are not covered by previously known ones, and their lengths are not divisors of q(2)+/- 1. The parameter c, representing the number of entangled bits, is also more flexible.
QUANTUM INFORMATION PROCESSING
(2022)
Article
Computer Science, Information Systems
Andreas Lenz, Rawad Bitar, Antonia Wachter-Zeh, Eitan Yaakobi
Summary: This paper studies function-correcting codes designed to protect the function evaluation of a message against errors. It shows the equivalence between FCCs and irregular-distance codes, and derives general upper and lower bounds on the optimal redundancy of irregular-distance codes. Furthermore, simplified suboptimal bounds are provided for easier evaluation. The paper also applies the general results to specific functions and compares them to standard error-correcting codes.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2023)
Article
Mathematics
Marcelo Muniz S. Alves, Eliezer Batista, Joost Vercruysse
JOURNAL OF ALGEBRA
(2015)
Article
Mathematics
Marcelo M. S. Alves, Eliezer Batista, Michael Dokuchaev, Antonio Paques
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY
(2016)
Review
Automation & Control Systems
Cristiano Torezzan, Luciano Panek, Marcelo Firer
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2016)
Article
Mathematics, Applied
Giuliano G. La Guardia, Marcelo M. S. Alves
LINEAR ALGEBRA AND ITS APPLICATIONS
(2016)
Article
Mathematics
Edson Ribeiro Alvares, Marcelo Muniz Alves, Maria Julia Redondo
JOURNAL OF ALGEBRA
(2017)
Article
Mathematics
Marcelo Muniz S. Alves, Eliezer Batista, Michael Dokuchaev, Antonio Paques
ISRAEL JOURNAL OF MATHEMATICS
(2013)
Article
Mathematics, Applied
Edson R. Alvares, Marcelo M. S. Alves, Eliezer Batista
JOURNAL OF PURE AND APPLIED ALGEBRA
(2013)
Article
Mathematics
Marcelo Muniz S. Alves, Eliezer Batista, Joost Vercruysse
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
(2019)
Article
Computer Science, Information Systems
Welington Santos, Marcelo Muniz Alves
IEEE TRANSACTIONS ON INFORMATION THEORY
(2020)
Article
Computer Science, Information Systems
Luciano Panek, Nayene Michele Paiao Panek
Summary: The paper investigates metrics on linear spaces induced by chain orders and weights, determines the cardinality and classification of optimal anticodes, and identifies all diameter perfect codes for a set of relevant instances on the metric spaces.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2021)
Article
Mathematics
Marcelo Muniz S. Alves, Eliezer Batista, Felipe Castro, Glauber Quadros, Joost Vercruysse
Summary: The paper introduces the notion of a partial corepresentation of a given Hopf algebra over a coalgebra, as well as the concept of a partial H-comodule. It proves the existence of a universal coalgebra H-par associated with the original Hopf algebra H, and introduces the concept of a H-par coalgebroid.
JOURNAL OF ALGEBRA
(2021)
Article
Computer Science, Information Systems
Luciano Panek, Jerry Anderson Pinheiro
IEEE TRANSACTIONS ON INFORMATION THEORY
(2020)
Article
Computer Science, Theory & Methods
Luciano Panek, Jerry Anderson Pinheiro, Marcelo Muniz Alves, Marcelo Firer
ADVANCES IN MATHEMATICS OF COMMUNICATIONS
(2020)
Proceedings Paper
Physics, Applied
M. Firer, L. Panek, L. L. R. Rifo
XI BRAZILIAN MEETING ON BAYESIAN STATISTICS (EBEB 2012)
(2012)
