In this paper, we deal with the design of high-rate multilevel two-dimensional (2D) bar codes for the print-and-scan channel. Firstly, we introduce a framework for evaluating the performance limits of these codes by studying an inter-symbol interference (ISI) free, synchronous, and noiseless print-and-scan channel, where the input and output alphabets are finite and the printer device uses halftoning to simulate multiple gray levels. Secondly, we present a new model for the print-and-scan channel specifically adapted to the problem of communications via multilevel 2D bar codes. This model, inspired by our experimental work, assumes no ISI and perfect synchronization, but independence between the channel input and the noise is not supposed. We adapt the theory of multilevel coding with multistage decoding (MLC/MSD) to the print-and-scan channel. Finally, we present experimental results confirming the utility of our channel model, and showing that multilevel 2D bar codes using MLC/MSD can reliably achieve the high capacity storage requirements of many multimedia security and management applications.