Transform image coding using DCT is proved to be efficient in the absence of channel error but its performance degrades rapidly over noisy channel. In this paper, in the case of appling bit selcetive error correction coding that protects some significant bits in a codeword, an efficient allocation method of imformation bits and additive redundancy bits used for quantization and error correction coding respectively under constant transmission bit rate is proposed, and its performance is analyzed. As a result, without increasing trasmission bit rate, PSNR can be improved up to 7~8 [dB] below bit error rate $10^2$ and the image without blocking effect caused by bit error resulted from channel noise can be recostructed.