On computing code word utilization for component coded digital video

In the component coded digital video, luminance, (Y) and two color difference components (C1, C2) are separately converted to digital. The components are computed by multiplying red-green-blue (RGB) vectors by a matrix. This component matrix has a special structure in the sense that the color difference components become zero for white or gray shades being encoded. The matrixing operation alters the dynamic range of the computed, Y, C1, C2 components compared to the dynamic range of RGB signals. A mathematical treatment is presented by which the effect of quantization of these components on dematrixed RGB signals is studied; the efficiency with which a color system utilizes component codes can thereby be calculated. It is shown that of all the word combinations available for quantization, optimum code word utilization is only 25%. Matrices are presented for the optimum code utilization