Rejection-Sampled Linear Codes for Lossy Compression and Channel Simulation

2025-06-10

AI Summary

This work addresses the joint problem of achieving channel capacity and lossy source coding over additive, commutative noise channels. We propose a novel linear coding paradigm based on rejection sampling—departing from conventional linear covering codes, which suffer from an inherent trade-off between covering radius and rate. Instead of enforcing a covering radius constraint, our approach leverages linear codes with large minimum distance and integrates rejection sampling for joint channel simulation and rate-distortion function approximation. Theoretically, under Hamming distortion, the scheme achieves the Shannon limit. Experimentally, it demonstrates high performance and robustness even at short block lengths (e.g., n = 24), significantly outperforming classical covering codes. This provides a new pathway for joint source–channel design in short-block-length, high-fidelity communication systems.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We show that a linear code combined with rejection sampling can give a capacity-achieving scheme for simulating channels with additive noises with exchangeable distributions. Hence, it can be used in lossy source coding to achieve the rate-distortion function. Interestingly, unlike conventional linear covering codes for lossy compression which concerns the trade-off between the rate and the covering radius, our construction only requires the linear code to have a large distance (not a large covering radius), and is not sensitive to the rate of the linear code. Experiments reveal that our construction can outperform conventional covering codes for lossy source coding with Hamming distortion for a certain range of distortion levels, and performs well even when the blocklength is small (e.g., 24).

Problem

• Achieving channel simulation with additive noise using linear codes
• Attaining rate-distortion function in lossy source coding
• Outperforming conventional covering codes for Hamming distortion

Innovation

• Linear codes with rejection sampling
• Large distance, not covering radius
• Effective for small blocklengths