Improving the overall performance of reliable speech communication in ultrashort wave radios over very noisy channels is of great importance and practical use. An iterative joint source-channel (de-)coding and (de-)modulation (JSCCM) algorithm is proposed for ITU-T Rec.G.729EV by both exploiting the residual redundancy and passing soft information throughout the receiver while introducing a systematic global iteration process. Being fully compatible with existing transmitter structure, the proposed algorithm does not introduce additional bandwidth expansion and transmission delay. Simulations show substantial error correcting performance and synthesized speech quality improvement over conventional separate designed systems in delay and bandwidth constraint channels by using the JSCCM algorithm.