Whereas cryptography easily arouses attacks by means of encrypting a secret message into a suspicious form, steganography is advantageous for its resilience to attacks by concealing the message in an innocent-looking cover signal. Minimal distortion steganography, one of the mainstream steganography frameworks, embeds messages while minimizing the distortion caused by the modification on the cover elements. Due to the unavailability of the original cover signal for the receiver, message embedding is realized by finding the coset leader of the syndrome function of steganographic codes migrated from channel coding, which is complex and has limited performance. Fortunately, deep generative models and the robust semantic of generated data make it possible for the receiver to perfectly reproduce the cover signal from the stego signal. With this advantage, we propose cover-reproducible steganography where the source coding, e.g., arithmetic coding, serves as the steganographic code. Specifically, the decoding process of arithmetic coding is used for message embedding and its encoding process is regarded as message extraction. Taking text-to-speech and text-to-image synthesis tasks as two examples, we illustrate the feasibility of cover-reproducible steganography. Steganalysis experiments and theoretical analysis are conducted to demonstrate that the proposed methods outperform the existing methods in most cases.