Related papers: Efficient decoding algorithm using triangularity o…
Vector set orthogonal normalization and matrix QR decomposition are fundamental problems in matrix analysis with important applications in many fields. We know that Gram-Schmidt process is a widely used method to solve these two problems.…
Integer least-squares problems, concerned with solving a system of equations where the components of the unknown vector are integer-valued, arise in a wide range of applications. In many scenarios the unknown vector is sparse, i.e., a large…
The union-find decoder is a leading algorithmic approach to the correction of quantum errors on the surface code, achieving code thresholds comparable to minimum-weight perfect matching (MWPM) with amortised computational time scaling…
Topological quantum error-correcting codes are a promising candidate for building fault-tolerant quantum computers. Decoding topological codes optimally, however, is known to be a computationally hard problem. Various decoders have been…
This paper describes a new QR factorization algorithm which is especially designed for massively parallel platforms combining parallel distributed multi-core nodes. These platforms make the present and the foreseeable future of…
In this paper we present a novel method for decoding multiple input - multiple output (MIMO) transmission, which combines sphere decoding (SD) and zero forcing (ZF) techniques to provide near optimal low complexity and high performance…
The 3D MIMO code is a robust and efficient space-time coding scheme for the distributed MIMO broadcasting. However, it suffers from the high computational complexity if the optimal maximum-likelihood (ML) decoding is used. In this paper we…
Ordered statistics decoding has been instrumental in addressing decoding failures that persist after normalized min-sum decoding in short low-density parity-check codes. Despite its benefits, the high computational complexity of effective…
Providing closed-form estimates of the decoding failure rate of iterative decoders for low- and moderate-density binary parity-check codes has attracted significant interest in the research community. Recently, interest in this topic has…
The sphere decoder (SD) is an attractive low-complexity alternative to maximum likelihood (ML) detection in a variety of communication systems. It is also employed in multiple-input multiple-output (MIMO) systems where the computational…
The realization of fault-tolerant quantum computers hinges on the construction of high-speed, high-accuracy, real-time decoding systems. The persistent challenge lies in the fundamental trade-off between speed and accuracy: efforts to…
The purpose of this work is to present an effective tool for computing different QR-decompositions of a complex nonsingular square matrix. The concept of the discrete signal-induced heap transform (DsiHT, Grigoryan 2006) is used. This…
The surface code is one of the most popular quantum error correction codes. It comes with efficient decoders, such as the Minimum Weight Perfect Matching (MWPM) decoder and the Union-Find (UF) decoder, allowing for fast quantum error…
In this paper, we propose an efficient reliability based segmentation-discarding decoding (SDD) algorithm for short block-length codes. A novel segmentation-discarding technique is proposed along with the stopping rule to significantly…
Multi-scale architecture, including hierarchical vision transformer, has been commonly applied to high-resolution semantic segmentation to deal with computational complexity with minimum performance loss. In this paper, we propose a novel…
Computing spherical harmonic decompositions is a ubiquitous technique that arises in a wide variety of disciplines and a large number of scientific codes. Because spherical harmonics are defined by integrals over spheres, however, one must…
We propose a new decoder for "matchable'' qLDPC codes that uses a Markov Chain Monte Carlo algorithm - called the worm algorithm - to approximately compute the probabilities of logical error classes given a syndrome. The algorithm hence…
We present a quantum algorithm that analyzes time series data simulated by a quantum differential equation solver. The proposed algorithm is a quantum version of the dynamic mode decomposition algorithm used in diverse fields such as fluid…
We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such a technique consists in a specific scaling similarity transformation that reduces…
We consider the decoding of LDPC codes over GF(q) with the low-complexity majority algorithm from [1]. A modification of this algorithm with multiple thresholds is suggested. A lower estimate on the decoding radius realized by the new…