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In joint watermarking and compression (JWC), a key process is quantization which embeds watermarks into a host signal while digitizing the host signal subject to requirements on the embedding rate, compression rate, quantization distortion, and robustness. Using fixed-rate scalar quantization for watermarking and compression, in this paper, we mainly consider how to design binary JWC systems to maximize the robustness of the systems in the presence of additive Gaussian attacks under constraints on the compression rate and quantization distortion. We first investigate optimum decoding of a binary JWC system, and demonstrate by experiments that in the distortion-to-noise ratio (DNR) region of practical interest, the minimum distance (MD) decoder achieves performance comparable to that of the maximum likelihood decoder in addition to having advantages of low computation complexity and being independent of the statistics of the host signal. We then present optimum binary JWC encoding schemes using fixed-rate scalar quantization and the MD decoder. Simulation results show that optimum binary JWC systems using nonuniform quantization are better than optimum binary JWC systems using uniform quantization. Furthermore, in comparison with separate watermarking and compression systems, optimum binary JWC systems using nonuniform quantization achieve significant DNR gains in the DNR region of practical interest. Finally, spread transform dither modulation is applied to improving the robustness of the JWC systems at low DNRs.