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Lara Dolecek - One of the best experts on this subject based on the ideXlab platform.

  • multi dimensional spatially coupled code design enhancing the cycle properties
    arXiv: Information Theory, 2019
    Co-Authors: Homa Esfahanizadeh, Lev Tauz, Lara Dolecek
    Abstract:

    A Circulant-based spatially-coupled (SC) code is constructed by partitioning the Circulants in the parity-check matrix of a block code into several components and piecing copies of these components in a diagonal structure. By connecting several SC codes, multi-dimensional SC (MD-SC) codes are constructed. In this paper, we present a systematic framework for constructing MD-SC codes with notably better cycle properties than their one-dimensional counterparts. In our framework, the multi-dimensional coupling is performed via an informed relocation of problematic Circulants. This work is general in the terms of the number of constituent SC codes that are connected together, the number of neighboring SC codes that each constituent SC code is connected to, and the length of the cycles whose populations we aim to reduce. Finally, we present a decoding algorithm that utilizes the structures of the MD-SC code to achieve lower decoding latency. Compared to the conventional SC codes, our MD-SC codes have a notably lower population of small cycles, and a dramatic BER improvement. The results of this work can be particularly beneficial in data storage systems, e.g., 2D magnetic recording and 3D Flash systems, as high-performance MD-SC codes are robust against various channel impairments and non-uniformity.

  • multi dimensional spatially coupled code design through informed relocation of Circulants
    Allerton Conference on Communication Control and Computing, 2018
    Co-Authors: Homa Esfahanizadeh, Ahmed Hareedy, Lara Dolecek
    Abstract:

    A Circulant-based spatially-coupled (SC) code is constructed by partitioning the Circulants of an underlying block code into a number of components, and then coupling copies of these components together. By connecting (coupling) several SC codes, multi-dimensional SC (MD-SC) codes are constructed. In this paper, we present a systematic framework for constructing MD-SC codes with notably better cycle properties than their 1D-SC counterparts. In our framework, informed multi-dimensional coupling is performed via an optimal relocation and an (optional) power adjustment of problematic Circulants in the constituent SC codes. Compared to the 1D-SC codes, our MD-SC codes are demonstrated to have up to 85% reduction in the population of the smallest cycle, and up to 3.8 orders of magnitude BER improvement in the early error floor region. The results of this work can be particularly beneficial in data storage systems, e.g., 2D magnetic recording and 3D Flash systems, as high-performance MD-SC codes are robust against various channel impairments and non-uniformity.

  • multi dimensional spatially coupled code design through informed relocation of Circulants
    arXiv: Information Theory, 2018
    Co-Authors: Homa Esfahanizadeh, Ahmed Hareedy, Lara Dolecek
    Abstract:

    A Circulant-based spatially-coupled (SC) code is constructed by partitioning the Circulants of an underlying block code into a number of components, and then coupling copies of these components together. By connecting (coupling) several SC codes, multi-dimensional SC (MD-SC) codes are constructed. In this paper, we present a systematic framework for constructing MD-SC codes with notably better girth properties than their 1D-SC counterparts. In our framework, informed multi-dimensional coupling is performed via an optimal relocation and an (optional) power adjustment of problematic Circulants in the constituent SC codes. Compared to the 1D-SC codes, our MD-SC codes are demonstrated to have up to 85% reduction in the population of the smallest cycle, and up to 3.8 orders of magnitude BER improvement in the early error floor region. The results of this work can be particularly beneficial in data storage systems, e.g., 2D magnetic recording and 3D Flash systems, as high-performance MD-SC codes are robust against various channel impairments and non-uniformity.

Homa Esfahanizadeh - One of the best experts on this subject based on the ideXlab platform.

  • multi dimensional spatially coupled code design enhancing the cycle properties
    arXiv: Information Theory, 2019
    Co-Authors: Homa Esfahanizadeh, Lev Tauz, Lara Dolecek
    Abstract:

    A Circulant-based spatially-coupled (SC) code is constructed by partitioning the Circulants in the parity-check matrix of a block code into several components and piecing copies of these components in a diagonal structure. By connecting several SC codes, multi-dimensional SC (MD-SC) codes are constructed. In this paper, we present a systematic framework for constructing MD-SC codes with notably better cycle properties than their one-dimensional counterparts. In our framework, the multi-dimensional coupling is performed via an informed relocation of problematic Circulants. This work is general in the terms of the number of constituent SC codes that are connected together, the number of neighboring SC codes that each constituent SC code is connected to, and the length of the cycles whose populations we aim to reduce. Finally, we present a decoding algorithm that utilizes the structures of the MD-SC code to achieve lower decoding latency. Compared to the conventional SC codes, our MD-SC codes have a notably lower population of small cycles, and a dramatic BER improvement. The results of this work can be particularly beneficial in data storage systems, e.g., 2D magnetic recording and 3D Flash systems, as high-performance MD-SC codes are robust against various channel impairments and non-uniformity.

  • multi dimensional spatially coupled code design through informed relocation of Circulants
    Allerton Conference on Communication Control and Computing, 2018
    Co-Authors: Homa Esfahanizadeh, Ahmed Hareedy, Lara Dolecek
    Abstract:

    A Circulant-based spatially-coupled (SC) code is constructed by partitioning the Circulants of an underlying block code into a number of components, and then coupling copies of these components together. By connecting (coupling) several SC codes, multi-dimensional SC (MD-SC) codes are constructed. In this paper, we present a systematic framework for constructing MD-SC codes with notably better cycle properties than their 1D-SC counterparts. In our framework, informed multi-dimensional coupling is performed via an optimal relocation and an (optional) power adjustment of problematic Circulants in the constituent SC codes. Compared to the 1D-SC codes, our MD-SC codes are demonstrated to have up to 85% reduction in the population of the smallest cycle, and up to 3.8 orders of magnitude BER improvement in the early error floor region. The results of this work can be particularly beneficial in data storage systems, e.g., 2D magnetic recording and 3D Flash systems, as high-performance MD-SC codes are robust against various channel impairments and non-uniformity.

  • multi dimensional spatially coupled code design through informed relocation of Circulants
    arXiv: Information Theory, 2018
    Co-Authors: Homa Esfahanizadeh, Ahmed Hareedy, Lara Dolecek
    Abstract:

    A Circulant-based spatially-coupled (SC) code is constructed by partitioning the Circulants of an underlying block code into a number of components, and then coupling copies of these components together. By connecting (coupling) several SC codes, multi-dimensional SC (MD-SC) codes are constructed. In this paper, we present a systematic framework for constructing MD-SC codes with notably better girth properties than their 1D-SC counterparts. In our framework, informed multi-dimensional coupling is performed via an optimal relocation and an (optional) power adjustment of problematic Circulants in the constituent SC codes. Compared to the 1D-SC codes, our MD-SC codes are demonstrated to have up to 85% reduction in the population of the smallest cycle, and up to 3.8 orders of magnitude BER improvement in the early error floor region. The results of this work can be particularly beneficial in data storage systems, e.g., 2D magnetic recording and 3D Flash systems, as high-performance MD-SC codes are robust against various channel impairments and non-uniformity.

Zhaolin Jiang - One of the best experts on this subject based on the ideXlab platform.

  • Isomorphic Operators and Functional Equations for the Skew-Circulant Algebra
    2020
    Co-Authors: Zhaolin Jiang
    Abstract:

    The skew-Circulant matrix has been used in solving ordinary differential equations. We prove that the set of skew-Circulants with complex entries has an idempotent basis. On that basis, a skew-cyclic group of automorphisms and functional equations on the skew-Circulant algebra is introduced. And different operators on linear vector space that are isomorphic to the algebra of × complex skew-Circulant matrices are displayed in this paper

  • explicit form of the inverse matrices of tribonacci Circulant type matrices
    Abstract and Applied Analysis, 2015
    Co-Authors: Li Liu, Zhaolin Jiang
    Abstract:

    It is a hot topic that Circulant type matrices are applied to networks engineering. The determinants and inverses of Tribonacci Circulant type matrices are discussed in the paper. Firstly, Tribonacci Circulant type matrices are defined. In addition, we show the invertibility of Tribonacci Circulant matrix and present the determinant and the inverse matrix based on constructing the transformation matrices. By utilizing the relation between left Circulant, -Circulant matrices and Circulant matrix, the invertibility of Tribonacci left Circulant and Tribonacci -Circulant matrices is also discussed. Finally, the determinants and inverse matrices of these matrices are given, respectively.

  • On optimal backward perturbation analysis for the linear system with skew Circulant coefficient matrix.
    Computational and mathematical methods in medicine, 2013
    Co-Authors: Zhaolin Jiang, Nuo Shen, Jianwei Zhou
    Abstract:

    We first give the style spectral decomposition of a special skew Circulant matrix C and then get the style decomposition of arbitrary skew Circulant matrix by making use of the Kronecker products between the elements of first row in skew Circulant and the special skew Circulant C. Besides that, we obtain the singular value of skew Circulant matrix as well. Finally, we deal with the optimal backward perturbation analysis for the linear system with skew Circulant coefficient matrix on the base of its style spectral decomposition.

Ahmed Hareedy - One of the best experts on this subject based on the ideXlab platform.

  • multi dimensional spatially coupled code design through informed relocation of Circulants
    Allerton Conference on Communication Control and Computing, 2018
    Co-Authors: Homa Esfahanizadeh, Ahmed Hareedy, Lara Dolecek
    Abstract:

    A Circulant-based spatially-coupled (SC) code is constructed by partitioning the Circulants of an underlying block code into a number of components, and then coupling copies of these components together. By connecting (coupling) several SC codes, multi-dimensional SC (MD-SC) codes are constructed. In this paper, we present a systematic framework for constructing MD-SC codes with notably better cycle properties than their 1D-SC counterparts. In our framework, informed multi-dimensional coupling is performed via an optimal relocation and an (optional) power adjustment of problematic Circulants in the constituent SC codes. Compared to the 1D-SC codes, our MD-SC codes are demonstrated to have up to 85% reduction in the population of the smallest cycle, and up to 3.8 orders of magnitude BER improvement in the early error floor region. The results of this work can be particularly beneficial in data storage systems, e.g., 2D magnetic recording and 3D Flash systems, as high-performance MD-SC codes are robust against various channel impairments and non-uniformity.

  • multi dimensional spatially coupled code design through informed relocation of Circulants
    arXiv: Information Theory, 2018
    Co-Authors: Homa Esfahanizadeh, Ahmed Hareedy, Lara Dolecek
    Abstract:

    A Circulant-based spatially-coupled (SC) code is constructed by partitioning the Circulants of an underlying block code into a number of components, and then coupling copies of these components together. By connecting (coupling) several SC codes, multi-dimensional SC (MD-SC) codes are constructed. In this paper, we present a systematic framework for constructing MD-SC codes with notably better girth properties than their 1D-SC counterparts. In our framework, informed multi-dimensional coupling is performed via an optimal relocation and an (optional) power adjustment of problematic Circulants in the constituent SC codes. Compared to the 1D-SC codes, our MD-SC codes are demonstrated to have up to 85% reduction in the population of the smallest cycle, and up to 3.8 orders of magnitude BER improvement in the early error floor region. The results of this work can be particularly beneficial in data storage systems, e.g., 2D magnetic recording and 3D Flash systems, as high-performance MD-SC codes are robust against various channel impairments and non-uniformity.

Zhong-zhi Bai - One of the best experts on this subject based on the ideXlab platform.

  • fast matrix splitting preconditioners for higher dimensional spatial fractional diffusion equations
    Journal of Computational Physics, 2020
    Co-Authors: Zhong-zhi Bai
    Abstract:

    Abstract The discretizations of two- and three-dimensional spatial fractional diffusion equations with the shifted finite-difference formulas of the Grunwald-Letnikov type can result in discrete linear systems whose coefficient matrices are of the form D + T , where D is a nonnegative diagonal matrix and T is a block-Toeplitz with Toeplitz-block matrix or a block-Toeplitz with each block being block-Toeplitz with Toeplitz-block matrix. For these discrete spatial fractional diffusion matrices, we construct diagonal and block-Circulant with Circulant-block splitting preconditioner for the two-dimensional case, and diagonal and block-Circulant with each block being block-Circulant with Circulant-block splitting preconditioner for the three-dimensional case, to further accelerate the convergence rates of Krylov subspace iteration methods, and we analyze the eigenvalue distributions for the corresponding preconditioned matrices. Theoretical results show that except for a small number of outliners the eigenvalues of the preconditioned matrices are located within a complex disk centered at 1 with the radius being exactly less than 1, and numerical experiments demonstrate that these structured preconditioners can significantly improve the convergence behavior of the Krylov subspace iteration methods. Moreover, this approach is superior to the geometric multigrid method and the preconditioned conjugate gradient methods incorporated with the approximate inverse Circulant-plus-diagonal preconditioners in both iteration counts and computing times.