Related papers: Optimal Decoding with the Worm
Reed-Muller (RM) codes exhibit good performance under maximum-likelihood (ML) decoding due to their highly-symmetric structure. In this paper, we explore the question of whether the code symmetry of RM codes can also be exploited to achieve…
Matching algorithms can be used for identifying errors in quantum systems, being the most famous the Blossom algorithm. Recent works have shown that small distance quantum error correction codes can be efficiently decoded by employing…
Efficient decoding to estimate error locations from outcomes of syndrome measurement is the prerequisite for quantum error correction. Decoding in presence of circuit-level noise including measurement errors should be considered in case of…
With the development of quantum hardware bringing the error-corrected quantum circuits to the near future, the lack of an efficient polynomial-time decoding algorithms for logical circuits presents a critical bottleneck. While quantum…
In Linear Programming (LP) decoding of a Low-Density-Parity-Check (LDPC) code one minimizes a linear functional, with coefficients related to log-likelihood ratios, over a relaxation of the polytope spanned by the codewords \cite{03FWK}. In…
This paper considers the average complexity of maximum likelihood (ML) decoding of convolutional codes. ML decoding can be modeled as finding the most probable path taken through a Markov graph. Integrated with the Viterbi algorithm (VA),…
In this paper, we propose an efficient decoding algorithm for short low-density parity check (LDPC) codes by carefully combining the belief propagation (BP) decoding and order statistic decoding (OSD) algorithms. Specifically, a modified BP…
Linear Programming (LP) is an important decoding technique for binary linear codes. However, the advantages of LP decoding, such as low error floor and strong theoretical guarantee, etc., come at the cost of high computational complexity…
When binary linear error-correcting codes are used over symmetric channels, a relaxed version of the maximum likelihood decoding problem can be stated as a linear program (LP). This LP decoder can be used to decode error-correcting codes at…
Quantum error correction is instrumental in protecting quantum systems from noise in quantum computing and communication settings. Pauli channels can be efficiently simulated and threshold values for Pauli error rates under a variety of…
Conventional decoding algorithms for polar codes strive to balance achievable performance and computational complexity in classical computing. While maximum likelihood (ML) decoding guarantees optimal performance, its NP-hard nature makes…
A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error…
Due to the high sensitivity of qubits to environmental noise, which leads to decoherence and information loss, active quantum error correction(QEC) is essential. Surface codes represent one of the most promising fault-tolerant QEC schemes,…
Fault-tolerant quantum computation (FTQC) is expected to address a wide range of computational problems. To realize large-scale FTQC, it is essential to encode logical qubits using quantum error-correcting codes. High-rate concatenated…
Real quantum computers will be subject to complicated, qubit-dependent noise, instead of simple noise such as depolarizing noise with the same strength for all qubits. We can do quantum error correction more effectively if our decoding…
There has been a rise in decoding quantum error correction codes with neural network based decoders, due to the good decoding performance achieved and adaptability to any noise model. However, the main challenge is scalability to larger…
In this paper we propose a new efficient message passing algorithm for decoding LDPC transmitted over a channel with strong phase noise. The algorithm performs approximate bayesian inference on a factor graph representation of the channel…
Realizing the full potential of quantum computation requires quantum error correction (QEC), with most recent breakthrough demonstrations of QEC using the surface code. QEC codes use multiple noisy physical qubits to encode information in…
The discovery of new quantum error-correcting codes that encode several logical qubits into relatively few physical qubits motivates the development of efficient and accurate methods of decoding these systems. Here, we adopt the…
This paper introduces three key initiatives in the pursuit of a hybrid decoding framework characterized by superior decoding performance, high throughput, low complexity, and independence from channel noise variance. Firstly, adopting a…