Weak Source Coding: Entropy-Tightened Bounds via Clustering of Atypical Sequences

This paper develops a weak decoding version of Shannon’s source coding theorem. We propose clustering atypical sequences into k classes, thereby refining the traditional error bound. The central result shows that if atypical clusters are small and sparsely placed, the reliability function can be improved. Supplementary analysis using Han’s inequality demonstrates that the largest cluster exhibits entropy collapse, enabling a strictly smaller bound on the probability of the dominant error event. Together, these results suggest that machine learning-inspired clustering can marginally improve the error exponent in source coding.