This paper proposes a theoretical framework to analyze the convergence properties of compression error bounds across quantization paradigms, establishing bounds on empirical quantization error and developing a unified methodology for scalar, vector, and neural compression schemes.
Key findings
Novel upper and lower bounds on the convergence rate of empirical quantization error are established.
Minimax optimal rates for high-dimensional compression are derived.
A unified analysis methodology is developed, applicable to various compression schemes.
Limitations & open questions
The theoretical framework may have limitations in practical applications with finite codebook sizes.
The analysis assumes certain conditions on the source distribution, which may not always hold in real-world scenarios.