Related papers: Efficient QP-ADMM Decoder for Binary LDPC Codes an…
This paper considers signal detection in massive multiple-input multiple-output (MIMO) systems with general additive hardware impairments and one-bit quantization. First, we present the quantization-unaware and Bussgang decomposition-based…
In recent years, several convergent multi-block variants of the alternating direction method of multipliers (ADMM) have been proposed for solving the convex quadratic semidefinite programming via its dual, which is naturally a 3-block…
Quantum low-density parity-check (LDPC) codes, a class of quantum error correcting codes, are considered a blueprint for scalable quantum circuits. To use these codes, one needs efficient decoding algorithms. In the classical setting, there…
An algorithm for constructing parity-check matrices of non-binary quasi-cyclic low-density parity-check (NB QC-LDPC) codes is proposed. The algorithm finds short cycles in the base matrix and tries to eliminate them by selecting the…
Many problems in control theory can be formulated as semidefinite programs (SDPs). For large-scale SDPs, it is important to exploit the inherent sparsity to improve the scalability. This paper develops efficient first-order methods to solve…
This paper propose a decoder architecture for low-density parity-check convolutional code (LDPCCC). Specifically, the LDPCCC is derived from a quasi-cyclic (QC) LDPC block code. By making use of the quasi-cyclic structure, the proposed…
This paper proposes a dual Riemannian alternating direction method of multipliers (ADMM) for solving low-rank semidefinite programs with unit diagonal constraints. We recast the ADMM subproblem as a Riemannian optimization problem over the…
Belief-propagation (BP) decoding for quantum low-density parity-check (QLDPC) codes is appealing due to its low complexity, yet it often exhibits convergence issues due to quantum degeneracy and short cycles that exist in the Tanner graph.…
It is widely accepted that quantum error correction is essential for realizing large-scale fault-tolerant quantum computing. Recent experiments have demonstrated error correction codes operating below threshold, primarily using local planar…
Quantum low-density parity-check (QLDPC) codes offer a promising route to scalable fault-tolerant quantum computation, but their performance under iterative decoding is strongly influenced by short-cycle structure and other harmful…
The generalized alternating direction method of multipliers (ADMM) of Xiao et al. [{\tt Math. Prog. Comput., 2018}] aims at the two-block linearly constrained composite convex programming problem, in which each block is in the form of…
Quantum Error Correction (QEC) is an essential field of research towards the realization of large-scale quantum computers. On the theoretical side, a lot of effort is put into designing error-correcting codes that protect quantum data from…
In this paper, the elliptic PDE-constrained optimization problem with box constraints on the control is studied. To numerically solve the problem, we apply the 'optimize-discretize-optimize' strategy. Specifically, the alternating direction…
The equivalent binary parity check matrices for the binary images of the cycle-free non-binary LDPC codes have numerous bit-level cycles. In this paper, we show how to transform these binary parity check matrices into their cycle-free…
We formulate maximum likelihood (ML) channel decoding as a quadratic unconstraint binary optimization (QUBO) and simulate the decoding by the current commercial quantum annealing machine, D-Wave 2000Q. We prepared two implementations with…
Quantum and Classical computers continue to work together in tight cooperation to solve difficult problems. The combination is thus suggested in recent times for decoding the Low Density Parity Check (LDPC) codes, for the next generation…
We consider automorphism ensemble decoding (AED) of quasi-cyclic (QC) low-density parity-check (LDPC) codes. Belief propagation (BP) decoding on the conventional factor graph is equivariant to the quasi-cyclic automorphisms and therefore…
In this paper, we introduce an efficient iterative solver for the joint linear-programming (LP) decoding of low-density parity-check (LDPC) codes and finite-state channels (FSCs). In particular, we extend the approach of iterative…
The Alternating Direction Method of Multipliers (ADMM) has now days gained tremendous attentions for solving large-scale machine learning and signal processing problems due to the relative simplicity. However, the two-block structure of the…
In this paper, we present a low-complexity joint detection-decoding algorithm for nonbinary LDPC codedmodulation systems. The algorithm combines hard-decision decoding using the message-passing strategy with the signal detector in an…