17 papers · ranked by Valyu relevance
Victor V. Albert, Philippe Faist
Barcode scans, clear phone calls, reliable data storage, satellite communication, and large-scale quantum computation are all made possible by error correction. We present a handbook version of The Error Correction Zoo, a curated reference of methods for protecting classical or quantum information from errors during…
Shukai Wang, Cuiling Fan, Chunming Tang, Zhengchun Zhou
The binary asymmetric channel is a model for practical communication systems where the error probabilities for symbol transitions $0\rightarrow 1$ and $1\rightarrow0$ differ substantially. In this paper, we introduce the notion of asymmetric Hamming bidistance (AHB) and its two-dimensional distribution, which…
Yang‐Hui He, Alexander Kasprzyk, Q Le, Dmitrii Riabchenko
Linear error-correcting codes form the mathematical backbone of modern digital communication and storage systems, but identifying champion linear codes (linear codes achieving or exceeding the best known minimum Hamming distance) remains challenging. By training a transformer to predict the minimum Hamming distance of…
Sujata Bansal, Pramod Kumar Kewat
Polycyclic codes offer a natural generalization of cyclic codes and provide a broader algebraic framework for constructing linear codes with good parameters. In this paper, we study binary polycyclic codes associated with powers of irreducible polynomials. We first determine their complete algebraic structure and then…
Willie K. Harrison, Truman Welling, Andrew Swain, Morteza Shoushtari + 1 more
Physical-layer security can aid in establishing secure telecommunication networks including cellular, Internet of Things, and telemetry networks, among others. Channel sounding techniques and/or telemetry systems for reporting channel conditions, coupled with superior wiretap code design are necessary to implement such…
Gengsheng L. Zeng
The Ising model is able to memorize some patterns or solutions as stable states. An Ising network may automatically converge to a pre-stored solution for a random input. However, in many cases, the Ising model cannot perform this task. The gap is that for a set of desired patterns, one may not be able to construct an…
Lucas Waite, Nuh Aydin
This paper investigates the relationship between coding theory and extremal combinatorics by representing codes in general metric spaces as independent sets in proximity graphs. We provide a generalized framework for the Gilbert-Varshamov (GV) bound applicable to codes over any finite metric space and explore the…
Kees Schouhamer Immink, Jos H. Weber, Tuan Thanh Nguyen, Kui Cai + 2 more
The design of low-complexity and efficient constrained codes has been a major research item for many years. This paper reports on a versatile method named concatenated constrained codes for designing efficient fixed-length constrained codes with small complexity. A concatenated constrained code comprises two (or more)…
Jens Zentgraf, Johanna Elena Schmitz, Andreas Keller, Sven Rahmann
Technological advances in single-cell RNA sequencing (scRNA-seq) allow us to sequence the transcriptomes of thousands of single cells in parallel, resulting in massive amounts of raw sequence data that must be processed efficiently to obtain a genes × cells expression matrix. In droplet-based scRNA-seq protocols, the…
Lihong Cao
The human brain encodes a virtually infinite repertoire of semantic concepts using a finite number of neurons, a feat that defies the capacity limits of classical attractor networks. While “Concept Cells” in the medial temporal lobe (MTL) exhibit extreme sparsity, the information-theoretic principles governing their…
Vu Minh Chau, Nguyen Ngoc Kiet, Pham Quang Minh, Mai Xuan Ngoc + 2 more
Hamming Quasi-Cyclic (HQC) has been selected by NIST for standardization as an additional code-based key-encapsulation mechanism, providing algorithmic diversity alongside lattice-based post-quantum cryptography. Efficient deployment of HQC on mobile and embedded platforms, however, requires careful optimization of its…
Authors not listed
RNA molecules fold into complex three-dimensional structures that determine their function. A wide range of mathematical frameworks, such as chord diagrams, fatgraphs, and context-free grammars, have been used to represent these structures; however, these models have largely been developed from mathematical motivations…
Ying Chen, Jianrong Bao, Yanhai Shang, Chao Liu + 5 more
To obtain efficient channel codes with high power efficiency at moderate signal-to-noise ratios (SNRs), an efficient high-rate protograph quasi-cyclic (QC) low-density parity-check (LDPC) codes is optimally constructed. By an optimized protograph template, the code framework is firstly produced by the extensions of the…
Boris Ryabko
A new approach to the problem of error correction in communication channels is proposed, in which the input sequence is transformed in such a way that the interdependence of symbols is significantly increased. Then, after the sequence is transmitted over the channel, this property is used for error correction so that…
Authors not listed
The Hidden Subgroup Problem (HSP) unifies several landmark quantum algorithms, yet systematic exploration of its variants and modern applications has slowed. This paper revives HSP-based algorithm design by examining new group structures with direct relevance to post-quantum cryptography, lattice problems, and…
Haziq Moinudeen, Alp Duygu
Functional protein sequence space is often described either by the sparsity of functional sequences or by the connectivity of neutral networks. These quantities characterize different properties: density measures the fraction of all sequences that are functional, whereas connectivity describes relationships among…
Guoming Song, Dongming Pi, Shancheng Zhao, Chi Wan Sung
Product codes (PCs) are widely used in high-speed communication systems due to their attractive trade-off between error-correction performance and complexity. To further meet the rapidly growing demand for higher data rates, soft-aided hard-decision decoders (SA-HDDs) have been developed. In this paper, we present a…