1. A video encoding device comprising: an encoder that calculates thresholds for un-quantized coefficients of a video block, wherein the thresholds identify when quantized coefficients become non-zero for different quantization parameters (QP's), and generates a ρ-QP look-up table (LUT) mapping numbers of non-zero coefficients after quantization (ρ's) to the QP's using the thresholds; and a memory that stores the ρ-QP LUT.