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 derive an upper bound on the maximum achievable rate of these codes by studying an inter-symbol interference (ISI) free, perfectly synchronized, and noiseless print-and-scan channel, in which the printer device uses halftoning to simulate multiple gray levels. Secondly, we briefly review three state-of-the-art coded modulation techniques for the additive white Gaussian noise channel (AWGN) in the high signal-to-noise (SNR) ratio regime, namely, multilevel coding with multistage decoding (MLC/MSD), multilevel coding with parallel independent decoding (MLC/PID), and bit-interleaved coded modulation (BICM). Thirdly, we present a new model of the print-and-scan channel specifically adapted to the multilevel 2D bar code application. 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 study the problem of finding the information capacity of our channel model and extend the theory of MLC/MSD to this type of channels. Finally, we present experimental results confirming the validity of our channel model, and showing that multilevel 2D bar codes using MLC/MSD can reliably achieve the high-rate storage requirements of many multimedia security and data management applications.