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Author(s): Mark A. Skylar-Scott [sup.1] [sup.2] , Jochen Mueller [sup.1] [sup.2] , Claas W. Visser [sup.1] [sup.2] , Jennifer A. Lewis [sup.1] [sup.2] Author Affiliations: (1) Harvard John A. Paulson [...], There is growing interest in voxelated matter that is designed and fabricated voxel by voxel.sup.1-4. Currently, inkjet-based three-dimensional (3D) printing is the only widely adopted method that is capable of creating 3D voxelated materials with high precision.sup.1-4, but the physics of droplet formation requires the use of low-viscosity inks to ensure successful printing.sup.5. By contrast, direct ink writing, an extrusion-based 3D printing method, is capable of patterning a much broader range of materials.sup.6-13. However, it is difficult to generate multimaterial voxelated matter by extruding monolithic cylindrical filaments in a layer-by-layer manner. Here we report the design and fabrication of voxelated soft matter using multimaterial multinozzle 3D (MM3D) printing, in which the composition, function and structure of the materials are programmed at the voxel scale. Our MM3D printheads exploit the diode-like behaviour that arises when multiple viscoelastic materials converge at a junction to enable seamless, high-frequency switching between up to eight different materials to create voxels with a volume approaching that of the nozzle diameter cubed. As exemplars, we fabricate a Miura origami pattern.sup.14 and a millipede-like soft robot that locomotes by co-printing multiple epoxy and silicone elastomer inks of stiffness varying by several orders of magnitude. Our method substantially broadens the palette of voxelated materials that can be designed and manufactured in complex motifs. Voxelated soft matter is designed and fabricated using multimaterial multinozzle three-dimensional printing, which switches between different viscoelastic inks along the same print filament to print multiple materials simultaneously.

The exact closed-form expression for the bit-error rate (BER) of rectangular quadrature amplitude modulation (QAM) is given. The presented formula is independent of the bit mapping and it is thus particularly useful in the design and analysis of modulation schemes employing non-Gray mapping. Compared with the so-called expurgated bound and the union bound, our expression is shown to accurately predict the BER in the low signal-to-noise ratio range where the bounding techniques fail. Index Terms--Bit-error rate (BER), Gray mapping, non-Gray mapping, performance evaluation, quadrature amplitude modulation (QAM).