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This paper proposes the use of higher order statistical moments in document image processing to improve the performance of systems which transmit side information through the print and scan channel. Examples of such systems are multilevel 2-D bar codes and certification via text luminance modulation. These systems print symbols with different luminances, according to the target side information. In previous works, the detection of a received symbol is usually performed by evaluating the average luminance or spectral characteristics of the received signal. This paper points out that, whenever halftoning algorithms are used in the printing process, detection can be improved by observing that third and fourth order statistical moments of the transmitted symbol also change, depending on the luminance level. This work provides a thorough analysis for those moments used as detection metrics. A print and scan channel model is exploited to derive the relationship between the modulated luminance level and the higher order moments of a halftone image. This work employs a strategy to merge the different moments into a single metric to achieve a reduced detection error rate. A transmission protocol for printed documents is proposed which takes advantage of the resulting higher robustness achieved with the combined detection metrics. The applicability of the introduced document image analysis approach is validated by comprehensive computer simulations.