SQNR Analysis of Power-of-Two Level Quantizer and Integer 3 Quantizer

In this paper, we present a detailed comparative analysis of two 3-bit quantizer models suitable for low bit-width quantization: the Power-of-Two Level Quantizer (PoTLQ) and the Integer 3 Quantizer (INT3). PoTLQ is a symmetric, non-uniform quantizer whose positive representation levels double successively, enabling a compact and hardware-friendly implementation. INT3, on the other hand, is a symmetric, uniform quantizer with integer-valued representation levels. While both quantizers offer simplicity in design and ease of implementation, the robustness of their performance to changes in input data variance remains insufficiently explored. In this paper, we therefore conduct a theoretical and numerical analysis of the performance of both quantizer models by comparing their signal-to-quantization noise ratio (SQNR) behavior under varying input variances. The analysis provides insights into achieving a trade-off between non-uniform and uniform quantization in low bit-width scenarios, offering guidance on quantizer selection based on input variance dynamic.