Article
Computer Science, Information Systems
Emna Ben Yacoub
Summary: The definitions of trapping and absorbing sets are extended to generalized low-density parity-check (GLDPC) codes, with fully absorbing sets being stable under the bit flipping algorithm. Finite-length and asymptotic trapping and absorbing set enumerators for GLDPC codes are derived using generating functions. The proposed definitions yield harmful graph structures for bit flipping decoders. Generating functions are also used to derive trapping and absorbing set enumerators for non-binary irregular LDPC codes.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2023)
Article
Engineering, Electrical & Electronic
Bashirreza Karimi, Amir H. Banihashemi
Summary: This article presents a design for finite-length irregular protograph-based quasi-cyclic LDPC codes that achieve good waterfall performance and low error floor by eliminating specific dominant ETS in the Tanner graph. The design is based on a search algorithm to identify and avoid problematic ETS structures, resulting in superior performance compared to similar state-of-the-art codes.
IEEE TRANSACTIONS ON COMMUNICATIONS
(2021)
Article
Engineering, Electrical & Electronic
Qianfan Wang, Suihua Cai, Xiao Ma
Summary: This paper applies free-ride coding to construct coupled LDPC codes, which allows transmission of extra bits without bandwidth expansion. The proposed codes outperform the basic LDPC codes in terms of error rate and do not sacrifice code rate.
IEEE TRANSACTIONS ON COMMUNICATIONS
(2023)
Article
Telecommunications
Farzane Amirzade, Mohammad-Reza Sadeghi, Daniel Panario
Summary: This paper focuses on the improvement of QC-LDPC codes by eliminating harmful trapping sets through increasing the girth. By utilizing edge-coloring technique and graph theory concepts such as rainbow cycles, it is shown that the removal of certain cycles not only eliminates them but also several other harmful trapping sets. The findings are applied to array-based LDPC codes, leading to significant simplification and optimization of necessary conditions to eliminate these cycles from the Tanner graph.
IEEE COMMUNICATIONS LETTERS
(2022)
Article
Engineering, Electrical & Electronic
Emna Ben Yacoub, Gianluigi Liva
Summary: This paper derives the finite-length trapping and (elementary) absorbing set enumerators for nonbinary protograph-based LDPC code ensembles. Both constrained and unconstrained edge labeling approaches are considered. The normalized logarithmic asymptotic distributions of trapping and (elementary) absorbing sets are obtained through an efficient method that requires solving a system of equations. Using these results, the asymptotic distributions of trapping and (elementary) absorbing sets are evaluated for some example nonbinary protograph-based LDPC code ensembles.
IEEE TRANSACTIONS ON COMMUNICATIONS
(2023)
Article
Multidisciplinary Sciences
Lawrence Z. Cohen, Isaac H. Kim, Stephen D. Bartlett, Benjamin J. Brown
Summary: This paper presents a low-overhead fault-tolerant quantum computing scheme based on quantum low-density parity-check (LDPC) codes, which enables many logical qubits to be encoded using a modest number of physical qubits through long-range interactions. In this approach, logic gates operate through logical Pauli measurements, preserving both the protection of LDPC codes and low overheads in terms of required additional qubits. Compared to surface codes with the same code distance, there are estimated order-of-magnitude improvements in overheads for processing about 100 logical qubits using this approach. Given the high thresholds demonstrated by LDPC codes, it is suggested that fault-tolerant quantum computation at this scale may be achievable with a few thousand physical qubits at comparable error rates to current approaches.
Article
Computer Science, Theory & Methods
Gianira N. Alfarano, Julia Lieb, Joachim Rosenthal
Summary: This paper provides a construction method for (n, k, delta) LDPC convolutional codes over arbitrary finite fields, using sets of integers forming a (k, w)-(weak) difference triangle set as supports of some columns of the sliding parity-check matrix. The parameters of the convolutional code are related to the parameters of the underlying difference triangle set, and conditions are presented to ensure that the Tanner graph associated with the sliding parity-check matrix satisfies the full rank condition. Relaxing these conditions, a lower bound on the field size is provided to avoid 2l-cycles, which is important for improving code performance and preventing the presence of low-weight codewords and absorbing sets.
DESIGNS CODES AND CRYPTOGRAPHY
(2021)
Article
Mathematics, Applied
You Gao, Yun-Fei Yao, He Ma
Summary: This article introduces a class of LDPC codes designed based on symplectic space over finite fields. It mainly focuses on estimating the important parameter of stopping distance and obtaining the lower bound on the stopping distance of the codes designed on the premise of symplectic space.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Engineering, Electrical & Electronic
Sima Naseri, Amir H. Banihashemi
Summary: In this paper, a design technique is proposed for constructing variable-regular time-invariant spatially-coupled low-density parity-check (SC-LDPC) codes with small constraint length and low error floor. The proposed technique reduces the error floor by imposing simple constraints on the short cycles in the code's Tanner graph, leading to the elimination of the most dominant trapping sets of the code. The designed codes outperform the state-of-the-art in terms of error floor performance and/or decoding complexity and latency.
IEEE TRANSACTIONS ON COMMUNICATIONS
(2021)
Article
Multidisciplinary Sciences
J. Pablo Bonilla Ataides, David K. Tuckett, Stephen D. Bartlett, Steven T. Flammia, Benjamin J. Brown
Summary: Research shows that using the XZZX code for fault-tolerant quantum computation offers remarkable performance and can surpass the hashing bound in experimentally relevant noise parameters. In cases where qubit dephasing is the dominant noise, this code has a practical decoder and exceeds previous thresholds. The code demonstrates favorable sub-threshold resource scaling and maintains advantages when performing fault-tolerant quantum computation, showing better performance and requiring fewer resources compared to the surface code.
NATURE COMMUNICATIONS
(2021)
Article
Multidisciplinary Sciences
Renyu Wang, Leonid P. Pryadko
Summary: Generalized bicycle codes are a type of quantum error-correcting code constructed from binary circulant matrices. They have linear distance scaling and low-weight stabilizer generators, which can potentially improve performance in the presence of measurement errors.
Article
Engineering, Electrical & Electronic
Yun-Jiang Wang, Zhuo-Yan Xiao, Yi Zhang, Xing-Yu Xiong, Sha Shi
Summary: Variable-rate coding schemes that maintain the same encoder/decoder architectures are in demand in practical communication systems and quantum settings. However, introducing variable-rate coding schemes into the quantum coding domain is challenging due to the need for systematic generation of new quantum codes and sharing of encoder-decoder components. In this correspondence, a multiple-rate coding scheme is introduced into the quantum coding domain by constructing non-homogeneous quantum LDPC codes from a row-circulant classical parity-check matrix. The method allows for shared stabilizer circuits among the resulting quantum codes.
IEEE TRANSACTIONS ON COMMUNICATIONS
(2023)
Article
Physics, Multidisciplinary
Maxime A. Tremblay, Nicolas Delfosse, Michael E. Beverland
Summary: Quantum low density parity check (LDPC) codes offer a potential solution for building low-overhead fault-tolerant quantum computers. However, their general lack of geometric constraints can lead to complex layouts and performance degradation. To address this issue, we propose a 2D layout for quantum LDPC codes by decomposing their Tanner graphs into planar layers. Our findings demonstrate that, under certain conditions, we can achieve low circuit-noise threshold and reduce the number of required physical qubits.
PHYSICAL REVIEW LETTERS
(2022)
Article
Telecommunications
Emna Ben Yacoub, Gianluigi Liva
Summary: In this paper, the finite-length fully absorbing set enumerators for binary protograph-based LDPC code ensembles are derived using generating functions. The normalized logarithmic asymptotic distribution of fully absorbing sets is efficiently obtained. The asymptotic distribution of fully absorbing sets is evaluated for some protograph-based LDPC code ensembles, and the numerical results demonstrate how these distributions can be used to estimate the error floor performance of protograph LDPC codes.
IEEE COMMUNICATIONS LETTERS
(2022)
Article
Computer Science, Information Systems
Anthony Leverrier, Gilles Zemor
Summary: We present sequential and parallel decoders for quantum Tanner codes, which can correct arbitrary errors of weight linear in the code length, respectively in linear or logarithmic time. By applying the Tanner code construction to an expanding square complex with robust local codes, we obtain a family of asymptotically good quantum low-density parity-check codes. Additionally, the same decoders can be easily adapted to the expander lifted product codes of Panteleev and Kalachev. We also provide a tighter bound on the minimum distance of quantum Tanner codes by exploiting recently established bounds on the robustness of random tensor codes.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2023)
