A Theoretical Framework for Rate-Distortion Limits in Learned Image Compression

Abstract: We present a novel systematic theoretical framework to analyze the rate-distortion (R-D) limits of learned image compression. While recent neural codecs have achieved remarkable empirical results, their distance from the information-theoretic limit remains unclear. Our work addresses this gap by decomposing the R-D performance loss into three key components: variance estimation, quantization strategy, and context modeling. First, we derive the optimal latent variance as the second moment under a Gaussian assumption, providing a principled alternative to hyperprior-based estimation. Second, we quantify the gap between uniform quantization and the Gaussian test channel derived from the reverse water-filling theorem. Third, we extend our framework to include context modeling, and demonstrate that accurate mean prediction yields substantial entropy reduction. Unlike prior R-D estimators, our method provides a structurally interpretable perspective that aligns with real compression modules and enables fine-grained analysis. Through joint simulation and end-to-end training, we derive a tight and actionable approximation of the theoretical R-D limits, offering new insights into the design of more efficient learned compression systems.