Optimized Modulation and Coding for Dual Modulated QR Codes

We present optimized modulation and coding for the recently introduced dual modulated QR (DMQR) codes that extend traditional QR codes to carry additional secondary data in the orientation of elliptical dots that replace black modules in the barcode images. By dynamically adjusting the dot size, we realize gains in embedding strength for both the intensity modulation and the orientation modulation that carry the primary and secondary data, respectively. Furthermore, we develop a model for the coding channel for the secondary data that enables soft-decoding via 5G NR (new radio) codes already supported by mobile devices. The performance gains for the proposed optimized designs are characterized via theoretical analysis, simulations, and actual experiments using smartphone devices. The theoretical analysis and simulations inform our design choices for the modulation and coding, and the experiments characterize the overall improvement in performance for the optimized design over the prior unoptimized designs. Importantly, the optimized designs significantly increase usability of DMQR codes with commonly used QR code beautification that cannibalizes a portion of the barcode image area for the insertion of a logo or image. In experiments with a capture distance of 15 inches, the optimized designs increase the decoding success rates between 10% and 32% for the secondary data while also providing gains for primary data decoding at larger capture distances. When used with beautification in typical settings, the secondary message is decoded with a high success rate for the proposed optimized designs, whereas it invariably fails for the prior unoptimized designs.