Data encoding efficiency in pixel detector readout with charge information

The average minimum number of bits needed for lossless readout of a pixel detector is calculated, in the regime of interest for particle physics where only a small fraction of pixels have a non-zero value per frame. This permits a systematic comparison of the readout efficiency of different encoding implementations. The calculation is compared to the number of bits used by the FE-I4 pixel readout chip of the ATLAS experiment.