Rejection-Sampled Universal Quantization for Smaller Quantization Errors
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Abstract (arXiv)
We construct a randomized vector quantizer which has a smaller maximum error compared to all known lattice quantizers with the same entropy for dimensions 5, 6, ..., 48, and also has a smaller mean squared error compared to known lattice quantizers with the same entropy for dimensions 35, ..., 47, in the high resolution limit. Moreover, our randomized quantizer has a desirable property that the quantization error is always uniform over the ball and independent of the input. Our construction is based on applying rejection sampling on universal quantization, which allows us to shape the error distribution to be any continuous distribution, not only uniform distributions over basic cells of a lattice as in conventional dithered quantization. We also characterize the high SNR limit of one-shot channel simulation for any additive noise channel under a mild assumption (e.g., the AWGN channel), up to an additive constant of 1.45 bits.
Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 10 of its 82 references that are in the map. First posted on arXiv 5 Feb 2024.
Builds on
10 of 82 references.
References · 10
- 2020Universally Quantized Neural Compressioncited by 64
- 2018Minimal Random Code Learning: Getting Bits Back from Compressed Model Parameterscited by 58
- 2020Compressing Images by Encoding Their Latent Representations with Relative Entropy Codingcited by 39
- 2022Joint Privacy Enhancement and Quantization in Federated Learningcited by 35
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- 2022Understanding Entropy Coding With Asymmetric Numeral Systems (ANS): a Statistician's Perspectivecited by 12
- 2023Compression with Exact Error Distribution for Federated Learningcited by 11
- 2023Communication-Efficient Laplace Mechanism for Differential Privacy via Random Quantizationcited by 9
- 2023Communication Efficient Private Federated Learning Using Ditheringcited by 9
- 2023Layered Randomized Quantization for Communication-Efficient and Privacy-Preserving Distributed Learningcited by 6
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Citing papers per year: 2025: 1; 2026: 3.
4 papers.
- 2025Communication-Efficient and Privacy-Adaptable Mechanism for Federated Learningcited by 2
- 2026Communication-Efficient and Privacy-Adaptable Mechanism -- a Federated Learning Scheme with Convergence Analysiscited by 1
- 2026Deep Randomized Distributed Function Computation (DeepRDFC): Neural Distributed Channel Simulationcited by 1
- 2026Privacy-Aligned Personalized Federated Learning with Compact Adaptation and Variable-Length Gaussian Communicationcited by 0
- 2026Privacy-Aligned Personalized Federated Learning with Compact Adaptation and Variable-Length Gaussian Communication14 Sep 2026
- 2026Deep Randomized Distributed Function Computation (DeepRDFC): Neural Distributed Channel Simulation11 Mar 2026
- 2026Communication-Efficient and Privacy-Adaptable Mechanism -- a Federated Learning Scheme with Convergence Analysis15 Jan 2026
- 2025Communication-Efficient and Privacy-Adaptable Mechanism for Federated Learning21 Jan 2025
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