We present a cross-entropy (CE)-based method to design 2-D zero reference codes (ZRCs) with minimum diffractive effects. Without diffraction effects, the optimum ZRC design problem is known as autocorrelation approximation. However, in high-resolution grating systems, limitations are given by the diffraction in the design of ZRCs. If the diffraction is considered, the output signal registered in the photodiode will widen and degrade, invalidating the autocorrelation approximation for the 2-D ZRC design. To minimize the diffractive effects in the design of 2-D ZRC, this paper first formulates the 2-D ZRC design problem with diffractive effects as a particular combinatorial optimization problem. Next, it proposes the application of the CE method to solve the problem. Compared with the conventional genetic algorithm (GA)-assisted 2-D ZRC design method, the simulation results show that the proposed CE method obtains better 2-D ZRCs that are less sensitive to diffractive effects. About 11.43 times less searching is required for the proposed CE method than for the GA. This indicates that the proposed CE method can obtain good ZRCs with minimum diffractive effects while maintaining low complexity.
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