Related papers: Reducing the Error Floor
It is shown that some well-known and some new cyclic codes with orthogonal parity-check equations can be constructed in the finite-field transform domain. It is also shown that, for some binary linear cyclic codes, the performance of the…
Quantum error correction, which utilizes logical qubits that are encoded as redundant multiple physical qubits to find and correct errors in physical qubits, is indispensable for practical quantum computing. Surface code is considered to be…
Polar codes are high density parity check codes and hence the sparse factor graph, instead of the parity check matrix, has been used to practically represent an LP polytope for LP decoding. Although LP decoding on this polytope has the…
A framework for linear-programming (LP) decoding of nonbinary linear codes over rings is developed. This framework facilitates linear-programming based reception for coded modulation systems which use direct modulation mapping of coded…
We define multilevel codes on bipartite graphs that have properties analogous to multilevel serial concatenations. A decoding algorithm is described that corrects a proportion of errors equal to half the Blokh-Zyablov bound on the minimum…
In this work we present some results that allow to improve the decoding radius in solving polynomial linear systems with errors in the scenario where errors are additive and randomly distributed over a finite field. The decoding radius…
In this paper we investigate the role of local information in the decoding of the repetition and surface error correction codes for the protection of quantum states. Our key result is an improvement in resource efficiency when local…
Large language models (LLMs) have recently achieved remarkable success in various reasoning tasks in the field of natural language processing. This success of LLMs has also motivated their use in graph-related tasks. Among others, recent…
Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have…
We discuss error floor asympotics and present a method for improving the performance of low-density parity check (LDPC) codes in the high SNR (error floor) region. The method is based on Tanner graph covers that do not have trapping sets…
Polar codes attract more and more attention of researchers in recent years, since its capacity achieving property. However, their error-correction performance under successive cancellation (SC) decoding is inferior to other modern channel…
Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem. The LP problem is defined by a set of…
Belief Propagation (BP) and Linear Programming (LP) decodings of Low Density Parity Check (LDPC) codes are discussed. We summarize results of instanton/pseudo-codeword approach developed for analysis of the error-floor domain of the codes.…
Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a…
Coded computing has emerged as a promising framework for tackling significant challenges in large-scale distributed computing, including the presence of slow, faulty, or compromised servers. In this approach, each worker node processes a…
Quantum error-correcting codes (QECCs) are necessary for fault-tolerant quantum computation. Surface codes are a class of topological QECCs that have attracted significant attention due to their exceptional error-correcting capabilities and…
We propose several improvements for Linear Programming (LP) decoding algorithms for High Density Parity Check (HDPC) codes. First, we use the automorphism groups of a code to create parity check matrix diversity and to generate valid cuts…
The recently proposed SCLF decoding algorithm for polar codes improves the error-correcting performance of state-of-the-art SCL decoding. However, it comes at the cost of a higher complexity. In this paper, partitioned polar codes tailored…
QR decomposition is an essential operation for solving linear equations and obtaining least-squares solutions. In high-performance computing systems, large-scale parallel QR decomposition often faces node faults. We address this issue by…
Product codes (PCs) protect a two-dimensional array of bits using short component codes. Assuming transmission over the binary symmetric channel, the decoding is commonly performed by iteratively applying bounded-distance decoding to the…