Related papers: Linked-Cluster Technique for Finding the Distance …
Spatially-coupled LDPC codes are known to have excellent asymptotic properties. Much less is known regarding their finite-length performance. We propose a scaling law to predict the error probability of finite-length spatially-coupled…
Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. To get $q$-ary quantum MDS codes, it suffices to find linear MDS codes $C$ over $\mathbb{F}_{q^2}$ satisfying $C^{\perp_H}\subseteq C$ by the Hermitian…
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…
We construct several explicit instances of quantum Tanner codes, a class of asymptotically good quantum low-density parity check (qLDPC) codes. The codes are constructed using dihedral groups and random pairs of classical codes and exhibit…
An LDPC coded modulation scheme with probabilistic shaping, optimized interleavers and noniterative demapping is proposed. Full-field simulations show an increase in transmission distance by 8% compared to uniformly distributed input.
We demonstrate that numerical linked cluster expansions (NLCE) yield a powerful approach to calculate time-dependent correlation functions for quantum many-body systems in one dimension. As a paradigmatic example, we study the dynamics of…
In this tutorial-style review we discuss basic concepts of coupled cluster theory and recent developments that increase its computational efficiency for calculations of molecules, solids and materials in general. We will touch upon the…
This paper presents a design technique for obtaining regular time-invariant low-density parity-check convolutional (RTI-LDPCC) codes with low complexity and good performance. We start from previous approaches which unwrap a low-density…
Product LDPC codes take advantage of LDPC decoding algorithms and the high minimum distance of product codes. We propose to add suitable interleavers to improve the waterfall performance of LDPC decoding. Interleaving also reduces the…
Quantum low-density parity-check (qLDPC) codes are an important component in the quest for quantum fault tolerance. Dramatic recent progress on qLDPC codes has led to constructions which are asymptotically good, and which admit linear-time…
Quantum low-density parity-check (qLDPC) codes are promising candidates for fault-tolerant quantum computation due to their high encoding rates and distances. However, implementing logical operations using qLDPC codes presents significant…
In efforts to scale the size of quantum computers, modularity plays a central role across most quantum computing technologies. In the light of fault tolerance, this necessitates designing quantum error-correcting codes that are compatible…
Finding a good clustering of vertices in a network, where vertices in the same cluster are more tightly connected than those in different clusters, is a useful, important, and well-studied task. Many clustering algorithms scale well,…
We present a novel algorithm, called Links, designed to perform online clustering on unit vectors in a high-dimensional Euclidean space. The algorithm is appropriate when it is necessary to cluster data efficiently as it streams in, and is…
A novel code construction based on spatially coupled low-density parity-check (SC-LDPC) codes is presented. The proposed code ensembles are described by protographs, comprised of several protograph-based chains characterizing individual…
We develop a new approach for asymmetric LDPC-based information reconciliation in order to adapt to the current channel state and achieve better performance and scalability in practical resource-constrained QKD systems. The new scheme…
Parameters of LDPC codes, such as minimum distance, stopping distance, stopping redundancy, girth of the Tanner graph, and their influence on the frame error rate performance of the BP, ML and near-ML decoding over a BEC and an AWGN channel…
We introduce twisted unitary $t$-groups, a generalization of unitary $t$-groups under a twisting by an irreducible representation. We then apply representation theoretic methods to the Knill-Laflamme error correction conditions to show that…
Probabilistic circuits (PCs) are a powerful modeling framework for representing tractable probability distributions over combinatorial spaces. In machine learning and probabilistic programming, one is often interested in understanding…
A novel method guaranteeing nondecreasing girth is presented for constructing longer low-density parity-check (LDPC) codes from shorter ones. The parity-check matrix of a shorter base code is decomposed into N (N>=2) non-overlapping…