# Algorithms for the Communication of Samples

arXiv: https://arxiv.org/abs/2110.12805 · HTML: https://mlsanity.com/paper/2110.12805/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 40 references that are in the map.
- First posted on arXiv 25 Oct 2021.

## Builds on (most cited first, 10 of 10)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [End-to-end Optimized Image Compression](https://mlsanity.com/paper/1611.01704/) (2016)
- [A* Sampling](https://mlsanity.com/paper/1411.0030/) (2014)
- [Variable Rate Deep Image Compression With a Conditional Autoencoder](https://mlsanity.com/paper/1909.04802/) (2019)
- [Practical Lossless Compression with Latent Variables using Bits Back Coding](https://mlsanity.com/paper/1901.04866/) (2019)
- [Breaking the Communication-Privacy-Accuracy Trilemma](https://mlsanity.com/paper/2007.11707/) (2020)
- [Universally Quantized Neural Compression](https://mlsanity.com/paper/2006.09952/) (2020)
- [Minimal Random Code Learning: Getting Bits Back from Compressed Model Parameters](https://mlsanity.com/paper/1810.00440/) (2018)
- [Compressing Images by Encoding Their Latent Representations with Relative Entropy Coding](https://mlsanity.com/paper/2010.01185/) (2020)
- [On the advantages of stochastic encoders](https://mlsanity.com/paper/2102.09270/) (2021)

## Built on by (most cited first, 30 of 34)

- [Lossy Image Compression with Conditional Diffusion Models](https://mlsanity.com/paper/2209.06950/) (2022)
- [Lossy Compression with Gaussian Diffusion](https://mlsanity.com/paper/2206.08889/) (2022)
- [Multi-Realism Image Compression with a Conditional Generator](https://mlsanity.com/paper/2212.13824/) (2022)
- [An Introduction to Neural Data Compression](https://mlsanity.com/paper/2202.06533/) (2022)
- [High-Fidelity Image Compression with Score-based Generative Models](https://mlsanity.com/paper/2305.18231/) (2023)
- [Lossy Image Compression with Quantized Hierarchical VAEs](https://mlsanity.com/paper/2208.13056/) (2022)
- [QARV: Quantization-Aware ResNet VAE for Lossy Image Compression](https://mlsanity.com/paper/2302.08899/) (2023)
- [Compressed Image Generation with Denoising Diffusion Codebook Models](https://mlsanity.com/paper/2502.01189/) (2025)
- [Compression with Bayesian Implicit Neural Representations](https://mlsanity.com/paper/2305.19185/) (2023)
- [Lossy Compression with Pretrained Diffusion Models](https://mlsanity.com/paper/2501.09815/) (2025)
- [Computationally-Efficient Neural Image Compression with Shallow Decoders](https://mlsanity.com/paper/2304.06244/) (2023)
- [Towards Empirical Sandwich Bounds on the Rate-Distortion Function](https://mlsanity.com/paper/2111.12166/) (2021)
- [Progressive Compression with Universally Quantized Diffusion Models](https://mlsanity.com/paper/2412.10935/) (2024)
- [Neural Estimation of the Rate-Distortion Function With Applications to Operational Source Coding](https://mlsanity.com/paper/2204.01612/) (2022)
- [Universal Exact Compression of Differentially Private Mechanisms](https://mlsanity.com/paper/2405.20782/) (2024)
- [Adaptive Compression in Federated Learning via Side Information](https://mlsanity.com/paper/2306.12625/) (2023)
- [Dual-Representation Image Compression at Ultra-Low Bitrates via Explicit Semantics and Implicit Textures](https://mlsanity.com/paper/2602.05213/) (2026)
- [Rejection-Sampled Universal Quantization for Smaller Quantization Errors](https://mlsanity.com/paper/2402.03030/) (2024)
- [Some Notes on the Sample Complexity of Approximate Channel Simulation](https://mlsanity.com/paper/2405.04363/) (2024)
- [Accelerating Relative Entropy Coding with Space Partitioning](https://mlsanity.com/paper/2405.12203/) (2024)
- [List-Level Distribution Coupling with Applications to Speculative Decoding and Lossy Compression](https://mlsanity.com/paper/2506.05632/) (2025)
- [Semantic Communication of Learnable Concepts](https://mlsanity.com/paper/2305.08126/) (2023)
- [Optimal Neural Compressors for the Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/2503.17558/) (2025)
- [Compression as Adaptation: Implicit Visual Representation with Diffusion Foundation Models](https://mlsanity.com/paper/2603.07615/) (2026)
- [Latent Discretization for Continuous-time Sequence Compression](https://mlsanity.com/paper/2212.13659/) (2022)
- [Speculative Sampling via Exponential Races](https://mlsanity.com/paper/2504.15475/) (2025)
- [Training-Free Vector Quantization via Gaussian VAEs](https://mlsanity.com/paper/2512.06609/) (2025)
- [Requential Coding: Pushing the Limits of Model Compression with Self-Generated Training Data](https://mlsanity.com/paper/2607.11883/) (2026)
- [Minimal Communication-Cost Statistical Learning](https://mlsanity.com/paper/2406.08193/) (2024)
- [Remote Action Generation: Remote Control with Minimal Communication](https://mlsanity.com/paper/2605.01833/) (2026)

## Abstract (arXiv)

The efficient communication of noisy data has applications in several areas of machine learning, such as neural compression or differential privacy, and is also known as reverse channel coding or the channel simulation problem. Here we propose two new coding schemes with practical advantages over existing approaches. First, we introduce ordered random coding (ORC) which uses a simple trick to reduce the coding cost of previous approaches. This scheme further illuminates a connection between schemes based on importance sampling and the so-called Poisson functional representation. Second, we describe a hybrid coding scheme which uses dithered quantization to more efficiently communicate samples from distributions with bounded support.