Related papers: Accuracy and Efficiency of Simplified Tensor Netwo…
We introduce and analyse an efficient decoder for the quantum Tanner codes of that can correct adversarial errors of linear weight. Previous decoders for quantum low-density parity-check codes could only handle adversarial errors of weight…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…
The exact partition function of the two-dimensional nearest neighbour Ising model pertaining to square lattices is derived for N sites in the case of a non-vanishing magnetic field.When the magnetic field is zero,the partition functions…
Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a…
Tensor computations, with matrix multiplication being the primary operation, serve as the fundamental basis for data analysis, physics, machine learning, and deep learning. As the scale and complexity of data continue to grow rapidly, the…
Tree ensembles are very popular machine learning models, known for their effectiveness in supervised classification and regression tasks. Their performance derives from aggregating predictions of multiple decision trees, which are renowned…
We consider a simple network, where a source and destination node are connected with a line of erasure channels. It is well known that in order to achieve the min-cut capacity, the intermediate nodes are required to process the information.…
The successive cancellation list decoding algorithm for polar codes yields near-optimal decoding performance at the cost of high implementation complexity. The successive cancellation stack algorithm has been shown to provide similar…
Exact solution of the Ising model on the simple cubic lattice is one of the long-standing open problems in rigorous statistical mechanics. Indeed, it is generally believed that settling it would constitute a methodological breakthrough,…
Tensor networks provide extremely powerful tools for the study of complex classical and quantum many-body problems. Over the last two decades, the increment in the number of techniques and applications has been relentless, and especially…
In this study, we investigate the characteristics of scheduling sequences that enable efficient decoding of generalized low-density parity-check (GLDPC) codes under the layered message-passing algorithm. In particular, we show that…
In this work, we study linear error-correcting codes against adversarial insertion-deletion (insdel) errors, a topic that has recently gained a lot of attention. We construct linear codes over $\mathbb{F}_q$, for…
ITensor is a system for programming tensor network calculations with an interface modeled on tensor diagram notation, which allows users to focus on the connectivity of a tensor network without manually bookkeeping tensor indices. The…
This chapter deals with the topic of designing reliable and efficient codes for the storage and retrieval of large quantities of data over storage devices that are prone to failure. For long, the traditional objective has been one of…
Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…
Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…
We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network…
Lattice rules and polynomial lattice rules are quadrature rules for approximating integrals over the $s$-dimensional unit cube. Since no explicit constructions of such quadrature methods are known for dimensions $s > 2$, one usually has to…
In a distributed storage network, reliability and bandwidth optimization can be provided by regenerating codes. Recently table based regenerating codes viz. DRESS (Distributed Replication-based Exact Simple Storage) codes has been proposed…
We are presenting an algorithm capable of simplifying tensor polynomials with indices when the building tensors have index symmetry properties. These properties include simple symmetry, cyclicity and those due to the presence of partial and…