Information hiding in host data, or transparent digital watermarking, can be treated as an application of digital communications in which the hidden information is conveyed through a channel where the noise includes the host data and stems from other sources. The amount of information to be hidden is called the payload. At the detector, the hidden information (the watermark) should be retrieved with high confidence. We present a theoretical performance analysis of this information hiding problem in terms of payload, detection error rate, SNR, bandwidth of the watermarking channel, and channel coding for error correction. The detector is assumed to be a correlator, which is known to be optimal for Gaussian noise. However, our analysis does not require that the host data has a Gaussian distribution. Since our analysis does not depend on the synchronization between the watermark signal and the detector or on the maximum watermark power as constrained by preserving the fidelity, our result defines the theoretical performance limits. We present two decision rules designed to satisfy the given false alarm and code word error rate, based on energy detection and SNR estimation. We then apply two watermarking schemes, one with constant strength and the other with adaptive strength, in order to determine the watermarking design parameters by examining how the SNR is decreased against random and quantization noises.