Least squares quantization in PCM
1982/03/01 by S. Lloyd, Sheelagh Lloyd · 509 citations
Computer Science · Engineering · #Coding theory and cryptography #Advanced Wireless Communication Techniques #Error Correcting Code Techniques
paper · doi:10.1109/tit.1982.1056489
Abstract
It has long been realized that in pulse-code modulation (PCM), with a given ensemble of signals to handle, the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall. It has been shown by Panter and Dite that, in the limit as the number of quanta becomes infinite, the asymptotic fractional density of quanta per unit voltage should vary as the one-third power of the probability density per unit voltage of signal amplitudes. In this paper the corresponding result for any finite number of quanta is derived; that is, necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy. The optimization criterion used is that the average quantization noise power be a minimum. It is shown that the result obtained here goes over into the Panter and Dite result as the number of quanta become large. The optimum quautization schemes for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2b</tex> quanta, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b=1,2, ⋯, 7</tex> , are given numerically for Gaussian and for Laplacian distribution of signal amplitudes.
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- Topological Structure Description for Artcode Detection Using the Shape of Orientation Histogram
- Fast Haar Transforms for Graph Neural Networks
- Learning to Cluster Faces via Transformer
- Characterizing English Variation across Social Media Communities with BERT
- Approximate DBSCAN under Differential Privacy
- Explainable Graph Spectral Clustering For GloVe-like Text Embeddings
- EFU: Enforcing Federated Unlearning via Functional Encryption
- Summarizing Classed Region Maps with a Disk Choreme
- Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement
- Compressive Mining: Fast and Optimal Data Mining in the Compressed\n Domain
- A Simple PTAS for Weighted k-means and Sensor Coverage
- Mixture of Experts Guided by Gaussian Splatters Matters: A new Approach to Weakly-Supervised Video Anomaly Detection
- Deep Language Geometry: Constructing a Metric Space from LLM Weights
- Exact and Heuristic Algorithms for Constrained Biclustering
- SPaRFT: Self-Paced Reinforcement Fine-Tuning for Large Language Models
- Open-world Point Cloud Semantic Segmentation: A Human-in-the-loop Framework
- Bootstrap Deep Spectral Clustering with Optimal Transport
- Fast and energy-efficient technique for jammed region mapping in wireless sensor networks
- Unsupervised and semi-supervised clustering methods to identify and refine participant experience levels in educational research
- Neighborhood-Preserving Voronoi Treemaps
- Geodesic Centroidal Voronoi Tessellations: Theories, Algorithms and Applications
- Scalable Varied-Density Clustering via Graph Propagation
- Unraveling Hidden Representations: A Multi-Modal Layer Analysis for Better Synthetic Content Forensics
- Finite-State Markov Modeling of Leaky Waveguide Channels in Communication-based Train Control (CBTC) Systems
- On Convergence of Epanechnikov Mean Shift
- Network Anomaly Detection: A Survey and Comparative Analysis of Stochastic and Deterministic Methods
- Differentially private k-means clustering via exponential mechanism and max cover
- FaceGCD: Generalized Face Discovery via Dynamic Prefix Generation
- From Seeing to Experiencing: Scaling Navigation Foundation Models with Reinforcement Learning
- TDAPNet: Prototype Network with Recurrent Top-Down Attention for Robust Object Classification under Partial Occlusion
- EPTAS for k-means Clustering of Affine Subspaces
- Sketching Datasets for Large-Scale Learning (long version)
- Tree Index: A New Cluster Evaluation Technique
- An ℓp theory of PCA and spectral clustering
- Semi-discrete unbalanced optimal transport and quantization
- Functional Factorial K-means Analysis
- RoD-TAL: A Benchmark for Answering Questions in Romanian Driving License Exams
- GMM-Based Time-Varying Coverage Control
- Unsupervised Learning of GMM with a Uniform Background Component
- Balancing the Communication Load of Asynchronously Parallelized Machine Learning Algorithms
- Dilation, smoothed distance, and minimization diagrams of convex\n functions
- Clustering is semidefinitely not that hard: Nonnegative SDP for manifold disentangling
- Asymmetric Co-Teaching for Unsupervised Cross Domain Person Re-Identification
- Density Adaptive Parallel Clustering
- clusterNOR: A NUMA-Optimized Clustering Framework
- Hierarchical Manifold Clustering on Diffusion Maps for Connectomics (MIT\n 18.S096 final project)
- Mining for Spatially-Near Communities in Geo-Located Social Networks
- Scaling Up Graph Neural Networks Via Graph Coarsening
- Alignment of color discrimination in humans and image segmentation networks
- C2FNAS: Coarse-to-Fine Neural Architecture Search for 3D Medical Image Segmentation
- Random projection trees for vector quantization
- Machine learning in geo- and environmental sciences: From small to large scale
- Discovering Communities of Malapps on Android-based Mobile Cyber-physical Systems
- An efficient K-means algorithm for Massive Data
- Learned Sectors: A fundamentals-driven sector reclassification project
- A Virtual Processor brings back the Free Lunch
- Towards human-interpretable, automated learning of feedback control for the mixing layer
- An Algorithmic Pipeline for Analyzing Multi-parametric Flow Cytometry\n Data
- Cluster-based Wireless Energy Transfer for Low Complex Energy Receivers
- Multi-Robot Gaussian Process Estimation and Coverage: A Deterministic Sequencing Algorithm and Regret Analysis
- Learning Manifolds with K-Means and K-Flats
- Time-Series Analysis via Low-Rank Matrix Factorization Applied to Infant-Sleep Data
- On the Centroids of Symmetrized Bregman Divergences
- Revisiting Training Strategies and Generalization Performance in Deep Metric Learning
- Anomaly Detection in Bitcoin Network Using Unsupervised Learning Methods
- Optimal Shape-Gain Quantization for Multiuser MIMO Systems with Linear Precoding
- A Dynamic Algorithm for Facilitated Charging of Plug-In Electric Vehicles
- Graph-Community Detection for Cross-Document Topic Segment Relationship Identification
- Strong Black-box Adversarial Attacks on Unsupervised Machine Learning Models
- Interpretable Image Clustering via Diffeomorphism-Aware K-Means
- A Deep Factorization of Style and Structure in Fonts
- Learning clusters of partially observed linear dynamical systems
- FedChip: Federated LLM for Artificial Intelligence Accelerator Chip Design
- Breaking the Communication-Privacy-Accuracy Trilemma
- Mayday--integrative analytics for expression data. [europepmc]
- Automatic generation of absolute myocardial blood flow images using [15O]H2O and a clinical PET/CT scanner. [europepmc]
- Variational cross-validation of slow dynamical modes in molecular kinetics. [europepmc]
- Kernel regression based segmentation of optical coherence tomography images with diabetic macular edema. [europepmc]
- Conservation of immune gene signatures in solid tumors and prognostic implications. [europepmc]
- Machine learning and systems genomics approaches for multi-omics data. [europepmc]
- Effects of Aging on Cortical Neural Dynamics and Local Sleep Homeostasis in Mice. [europepmc]
- Atomic resolution mechanism of ligand binding to a solvent inaccessible cavity in T4 lysozyme. [europepmc]
- Scutoids are a geometrical solution to three-dimensional packing of epithelia. [europepmc]
- Machine Learning in Agriculture: A Review. [europepmc]
- Correspondence between cerebral glucose metabolism and BOLD reveals relative power and cost in human brain. [europepmc]
- Long non-coding RNAs discriminate the stages and gene regulatory states of human humoral immune response. [europepmc]
- Meta-Analytic Methodology for Basic Research: A Practical Guide. [europepmc]
- The Application of Deep Learning in Cancer Prognosis Prediction. [europepmc]
- DNA Methylation Profiling of Human Hepatocarcinogenesis. [europepmc]
- Unsupervised Learning Methods for Molecular Simulation Data. [europepmc]
- miQC: An adaptive probabilistic framework for quality control of single-cell RNA-sequencing data. [europepmc]
- Cardiac radiotherapy induces electrical conduction reprogramming in the absence of transmural fibrosis. [europepmc]
- Markov State Models to Study the Functional Dynamics of Proteins in the Wake of Machine Learning. [europepmc]
- Statistical power for cluster analysis. [europepmc]
- QMugs, quantum mechanical properties of drug-like molecules. [europepmc]
- Linker-Dependent Folding Rationalizes PROTAC Cell Permeability. [europepmc]
- Interpretable deep learning translation of GWAS and multi-omics findings to identify pathobiology and drug repurposing in Alzheimer's disease. [europepmc]
- Review of single-cell RNA-seq data clustering for cell-type identification and characterization. [europepmc]
- Toward universal cell embeddings: integrating single-cell RNA-seq datasets across species with SATURN. [europepmc]
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