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An exhaustive analysis of the distortion-compensated dither modulation (DC-DM) data-hiding method with repetition coding is presented. Two decoding strategies, maximum likelihood lattice decoding and Euclidean distance decoding, are discussed and some simplifications presented. An exact performance analysis in terms of the bit error rate (BER) is given; such an exact analysis is currently not available in the literature. Two methods for computing the exact BER and several approximations and bounds, most of them in closed form, are provided. These approximations are employed to propose two novel improvements on the standard DC-DM method with repetition: the use of a weighted Euclidean distance, with optimizable weights, and a vector form of the distortion compensation parameter. Both account for significant performance improvements. DC-DM is compared with quantization methods in the projected domain, showing worse performance against additive noise attacks but higher robustness to cropping attacks. A performance analysis of DC-DM under coarse quantization that can be specialized to JPEG compression is also supplied. All our results are validated with numerical simulations with both synthetic data and real images.