Rate-Distortion Analysis of Dead-Zone Plus Uniform Threshold Scalar Quantization and Its Application—Part I: Fundamental Theory

This paper provides a systematic rate-distortion (R-D) analysis of the dead-zone plus uniform threshold scalar quantization (DZ+UTSQ) with nearly uniform reconstruction quantization (NURQ) for generalized Gaussian distribution (GGD), which consists of two aspects: R-D performance analysis and R-D modeling. In R-D performance analysis, we first derive the preliminary constraint of optimum entropy-constrained DZ+UTSQ/NURQ for GGD, under which the property of the GGD distortion-rate (D-R) function is elucidated. Then for the GGD source of actual transform coefficients, the refined constraint and precise conditions of optimum DZ+UTSQ/NURQ are rigorously deduced in the real coding bit rate range, and efficient DZ+UTSQ/NURQ design criteria are proposed to reasonably simplify the utilization of effective quantizers in practice. In R-D modeling, inspired by R-D performance analysis, the D-R function is first developed, followed by the novel rate-quantization (R-Q) and distortion-quantization (D-Q) models derived using analytical and heuristic methods. The D-R, R-Q, and D-Q models form the source model describing the relationship between the rate, distortion, and quantization steps. One application of the proposed source model is the effective two-pass VBR coding algorithm design on an encoder of H.264/AVC reference software, which achieves constant video quality and desirable rate control accuracy.