Definition

A transform coder with the KLT and optimal bit allocation we define the distortion to be $$D_{\text{tc}}=kh_{g}2^{-2\bar{b}}\det (\mathbf{R_{X}})^{1/k}=kh_{g}2^{-2\bar{b}}\left( \prod_{i=1}^{k}\lambda_{i} \right)^{1/k}$$where $\lambda_{1},\dots,\lambda_{k}$ are the eigenvalues of $\mathbf{R_{X}}$.