An approximately optimal adaptive arithmetic coding (AC) system using a forbidden symbol (FS) over noisy channels was proposed which allows one to jointly and adaptively design the source decoding and channel correcting in a single process, with superior performance compared with traditional separated techniques.The concept of adaptiveness is applied not only to the source model but also to the amount of coding redundancy.In addition,an improved branch metric computing algorithm and a faster sequential searching algorithm compared with the system proposed by Grangetto were proposed.The proposed system is tested in the case of image transmission over the AWGN channel, and compared with traditional separated system in terms of packet error rate and complexity.Both hard and soft decoding were taken into account.