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Random linear network coding is a particularly decentralized approach to the multicast problem. Use of random network codes introduces a non-zero probability however that some sinks will not be able to successfully decode the required…

The state-of-the-art error correcting codes are based on large random constructions (random graphs, random permutations, ...) and are decoded by linear-time iterative algorithms. Because of these features, they are remarkable examples of…

In this paper, we propose a novel neural network model called RNN Encoder-Decoder that consists of two recurrent neural networks (RNN). One RNN encodes a sequence of symbols into a fixed-length vector representation, and the other decodes…

A novel and efficient neural decoder algorithm is proposed. The proposed decoder is based on the neural Belief Propagation algorithm and the Automorphism Group. By combining neural belief propagation with permutations from the Automorphism…

Efficient and accurate decoding of quantum error-correcting codes is essential for fault-tolerant quantum computation, however, it is challenging due to the degeneracy of errors, the complex code topology, and the large space for logical…

Probabilistic forecasting of high dimensional multivariate time series is a notoriously challenging task, both in terms of computational burden and distribution modeling. Most previous work either makes simple distribution assumptions or…

Error-correcting codes enable reliable communication, yet practical soft decoding remains challenging across code families and block lengths. We propose SB-ECC, a score-based decoder that casts decoding as continuous-time denoising. A…

Deep Neural Networks (DNNs) have performed admirably in classification tasks. However, the characterization of their classification uncertainties, required for certain applications, has been lacking. In this work, we investigate the issue…

Time-varying stochastic optimization problems frequently arise in machine learning practice (e.g. gradual domain shift, object tracking, strategic classification). Although most problems are solved in discrete time, the underlying process…

Despite their success and widespread adoption, the opaque nature of deep neural networks (DNNs) continues to hinder trust, especially in critical applications. Current interpretability solutions often yield inconsistent or oversimplified…

Tensor-network codes enable the construction of large stabilizer codes out of tensors describing smaller stabilizer codes. An application of tensor-network codes was an efficient and exact decoder for holographic codes. Here, we show how to…

Codes based on sparse matrices have good performance and can be efficiently decoded by belief-propagation (BP). Decoding binary stabilizer codes needs a quaternary BP for (additive) codes over GF(4), which has a higher check-node complexity…

With deep neural networks providing state-of-the-art machine learning models for numerous machine learning tasks, quantifying the robustness of these models has become an important area of research. However, most of the research literature…

The problem of low complexity, close to optimal, channel decoding of linear codes with short to moderate block length is considered. It is shown that deep learning methods can be used to improve a standard belief propagation decoder,…

Mitigating errors in computing and communication systems has seen a great deal of research since the beginning of the widespread use of these technologies. However, as we develop new methods to do computation or communication, we also need…

We develop a most likely error Pauli error decoding algorithm for stabiliser codes based on general purpose integer optimisation. Using this decoder we analyse the performance of holographic codes against Pauli errors and find numerical…

We consider hard-decision iterative decoders for product codes over the erasure channel, which employ repeated rounds of decoding rows and columns alternatingly. We derive the exact asymptotic probability of decoding failure as a function…

Topological error correcting codes, and particularly the surface code, currently provide the most feasible roadmap towards large-scale fault-tolerant quantum computation. As such, obtaining fast and flexible decoding algorithms for these…

Decoding algorithms based on approximate tensor network contraction have proven tremendously successful in decoding 2D local quantum codes such as surface/toric codes and color codes, effectively achieving optimal decoding accuracy. In this…

We propose a scalable decoding framework for correcting correlated hook errors in stabilizer measurement circuits. Traditional circuit-level decoding attempts to estimate the precise location of faults by constructing an extended Tanner…