A new arithmetic coding system combining source channel coding and maximum a posteriori decoding were proposed.It combines source coding and error correction tasks into one unified process by introducing an adaptive forbidden symbol.The proposed system achieves fixed length code words by adaptively adjusting the probability of the forbidden symbol and adding tail digits of variable length.The corresponding improved MAP decoding metric was derived.The proposed system can improve the performance.Simulations were performed on AWGN channels with various noise levels by using both hard and soft decision with BPSK modulation.The results show its performance is slightly better than that of our adaptive arithmetic error correcting coding system using a forbidden symbol.