Article
Engineering, Electrical & Electronic
Hiteshvi Manish Solanki, Pradeep Kiran Sarvepalli
Summary: This study focuses on the performance of topological subsystem color codes (TSCCs) over the erasure channel. Two erasure decoders are proposed, employing a mapping of TSCCs to topological color codes (TCCs) and the technique of gauge fixing. Experimental results show the threshold of fault-tolerant gates derived from TSCCs, and the performance can be further improved by combining with an optimal erasure decoder for topological color codes.
IEEE TRANSACTIONS ON COMMUNICATIONS
(2023)
Article
Computer Science, Information Systems
Arun B. Aloshious, Pradeep Kiran Sarvepalli
Summary: Three dimensional toric codes are stabilizer codes that can be decoded on arbitrary lattices, which is beneficial for studying the performance of color codes.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2021)
Article
Engineering, Electrical & Electronic
Mohammad Rowshan, Andreas Burg, Emanuele Viterbo
Summary: This research introduces a one-to-one convolutional transform as a pre-coding step before polar transform, resulting in Polarization-Adjusted Convolutional (PAC) codes. Strategies such as adaptive heuristic metric and tree search constraints are proposed to reduce the complexity of sequential decoding for PAC/polar codes. Efficient computation method for intermediate LLRs and partial sums is provided, contributing to improved decoding efficiency and avoiding intermediate information storage or decoding process restart. Performance, complexity, and resource requirements of three decoding algorithms are compared in the study.
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY
(2021)
Article
Engineering, Electrical & Electronic
Aleksandar Minja, Vojin Senk
Summary: This paper introduces the MAP decoding method for Kerdock and Preparata codes and also presents a sub-optimal APP decoder. Both these decoders show good error-correcting performance and complexity.
IEEE TRANSACTIONS ON COMMUNICATIONS
(2022)
Article
Physics, Multidisciplinary
Edson Donizete de Carvalho, Waldir Silva Soares Jr, Eduardo Brandani da Silva
Summary: In this work, a new type of tessellation induced by an n-dimensional sublattice on an n-dimensional lattice is demonstrated, leading to the derivation of toric codes and color codes with various parameters. Particularly, for n=2, different ways of covering the fundamental units of hexagonal sublattices are obtained through lattice partition, resulting in the construction of new toric codes and color codes in the flat torus.
Article
Computer Science, Information Systems
Jose Gomez-Torrecillas, Gabriel Navarro, Jose Patricio Sanchez-Hernandez
Summary: A large class of MDS linear codes with efficient decoding algorithms were constructed in this paper, using methods from Linear Algebra. The codes were presented through parity-check matrices, and the decoding algorithm involved matrix and linear map manipulations. The proof of correctness of the decoding algorithm in a more sophisticated mathematical context was postponed to a later section. Additionally, the Reed-Solomon skew-differential codes were positioned within the general context of codes defined by skew polynomial rings.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2021)
Article
Telecommunications
Qiaoqiao Xia, Xin Wang, Huajun Liu, Qing Lin Zhang
Summary: The study introduces a novel hybrid projection algorithm (HPA) that alternately uses approximate even-vertex projection algorithm (EVA) and other accurate projection algorithms to increase the percentage of unuseful projections, achieving better decoding performance while reducing projection time. Compared to the cut search algorithm (CSA), the proposed algorithm significantly saves average projection and decoding time.
IEEE COMMUNICATIONS LETTERS
(2021)
Article
Engineering, Electrical & Electronic
Chong-Dao Lee
Summary: This paper introduces two subclasses of BCH codes, odd-like/even-like quasi-reversible BCH codes, and presents their step-by-step decoding process. The weight evaluation, pivotal condensation process, and the use of a newly proposed error-locator polynomial contribute to the lower computational complexity and higher error-correcting capability of these codes.
IEEE TRANSACTIONS ON COMMUNICATIONS
(2022)
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
Computer Science, Information Systems
Lukas Holzbaur, Hedongliang Liu, Alessandro Neri, Sven Puchinger, Johan Rosenkilde, Vladimir Sidorenko, Antonia Wachter-Zeh
Summary: The paper presents new general lower and upper bounds on the fraction of error matrices decodable by Schmidt et al.'s decoding algorithm for interleaved Reed-Solomon codes, making it the only known decoding algorithm for interleaved alternant codes with such bounds.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2021)
Article
Engineering, Electrical & Electronic
Nghia Doan, Seyyed Ali Hashemi, Marco Mondelli, Warren J. J. Gross
Summary: This paper presents a novel recursive list decoding algorithm for Reed-Muller codes based on successive permutations. By utilizing a low-complexity successive permutation scheme, the algorithm reduces computational complexity and decoding latency while maintaining error-correction performance and memory consumption.
IEEE TRANSACTIONS ON COMMUNICATIONS
(2022)
Article
Telecommunications
Xinwei Zhao, Shancheng Zhao, Zhetao Li
Summary: This letter proposes an enhanced anchor decoding algorithm for staircase codes with hard reliability scores. The algorithm assigns the scores based on observations of the decoding results and effectively prevents miscorrections. Simulation results demonstrate the improved performance of the algorithm compared to the existing algorithm.
IEEE COMMUNICATIONS LETTERS
(2022)
Article
Engineering, Electrical & Electronic
Daniel Nicolas Bailon, Martin Bossert, Johann-Philipp Thiers, Juergen Freudenberger
Summary: This work investigates concatenated codes based on the Plotkin construction, utilizing extended BCH codes as component codes. The proposed construction improves code parameters and allows for more flexible code rates compared to RM codes. New soft-input decoding algorithms are introduced, leveraging the recursive structure of the concatenation and cyclic structure of the component codes. The decoding algorithms achieve near-maximum-likelihood performance with reduced complexity.
IEEE TRANSACTIONS ON COMMUNICATIONS
(2022)
Article
Engineering, Electrical & Electronic
Vera Miloslavskaya, Branka Vucetic, Yonghui Li, Giyoon Park, Ok-Sun Park
Summary: A novel method for recursively constructing a set of precoded polar codes of various rates and lengths is presented, aiming to minimize decoding error probability under constraints such as minimum distance, supercode, and subcode. Simulation results show that the proposed precoded polar codes offer better frame error rate compared to polar codes with CRC and e-BCH polar subcodes under certain decoding algorithms.
IEEE TRANSACTIONS ON COMMUNICATIONS
(2021)
Article
Engineering, Electrical & Electronic
Mohammad Rowshan, Emanuele Viterbo
Summary: This paper introduces polarization-adjusted convolutional (PAC) codes, which use a one-to-one convolutional transform and polar transform to improve the Hamming distance properties of polar codes, and improve error correction performance by adjusting constraint length, list size, and sorting strategy. Analysis shows that the path sorting complexity in local sorting of the paths in the parallel list Viterbi algorithm (LVA) is significantly lower than global sorting in list decoding.
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY
(2021)
