A new integrated framework for source and channel rate allocation is presented for video coding and transmission over wireless channels without feedback channels available. For a fixed total channel bit rate and a finite number of channel coding rates, the proposed scheme can obtain the near-optimal source and channel coding pair, and corresponding robust video coding scheme such that the expected end-to-end distortion of video signals can be minimized. With the assumption that the encoder has the stochastic information such as average SNR and Doppler frequency of the wireless channel, the proposed scheme takes into account robust video coding, channel coding, packetization, and error concealment techniques altogether. An improved method is proposed to recursively estimate the end-to-end distortion of video coding for transmission over error-prone channels. The proposed estimation is about 1-3 dB more accurate compared to the existing integer-pel based method. Rate-distortion optimized video coding is employed for the trade-off between coding efficiency and robustness to transmission errors.