Channel capacity analysis of 2D barcodes: QR Code and CQR Code-5

Abstract

This paper presents an encoder and decoder channel capacity study on the QR Code (Quick Response Code) and CQR Code-5 (5-color Colored Quick Response Code) transmission environment. Our work shows that the QR Code and CQR Code-5 data storage and retrieval is an asymmetric and no erasure channel of information transmission, where each two-dimensional barcode channel counts with a maximum number of distinguishable symbols. This channel capacity study uses mutual information theory and consider that the QR Code and CQR Code-5 input symbols are mapped into a sequence that produces the output sequence of each channel. The output sequence has a distribution that depends on the input sequence and the conditional probability of every input and output symbol, where is possible to reconstruct the input symbols at the output with low error probability in function of the software robustness of each two-dimensional barcodes.