“…While one can in principle still get a reduction in the error by using a finer quantization alphabet (i.e., a smaller δ), this is often not feasible in practice because the quantization alphabet is fixed once the hardware is built, or not desirable as one may prefer a simple, e.g., 1-bit embedding. In order to address this problem, noise-shaping quantization methods, such as Sigma-Delta (Σ∆) modulation and alternative decoding methods (see, e.g., [21,31,6,32,42,17,26,69,27,20,9,36]), have been proposed in the settings of quantization of bandlimited functions, finite frame expansions, and compressed sensing measurements. However, these methods have not been studied in the framework of binary embedding problems.…”