Dynamic Range Analysis in High Efficiency Video Coding Residual Coding and Reconstruction

We present a method for analyzing dynamic range along the residual coding and reconstruction pathways during video coding by deriving bounds on the maximum absolute value of intermediary data using a simple combination of triangle inequality and reformulation using Kronecker products. The proposed method is then applied toward analyzing the residual coding and reconstruction process in the emerging High Efficiency Video Coding (HEVC) standard. Our analysis shows that, for an input residual with a bitdepth of $(B+1)$ that uses a uniform quantizer, the dynamic range of quantized levels and dequantized coefficients are no more than $(B+7)~{\\rm bits}$ and 17 bits, respectively. Furthermore, a 16 bits transpose buffer is sufficient, while up to 5 bits of bitdepth expansion can occur in the reconstructed residual. The analysis is validated by simulation results with both randomly generated residual and encoding/decoding test video sequences using the HEVC reference software.