A generalized algorithm for designing an optimum VQ source codec in systems with channel coding is presented. Based on an AWGN channel model, the algorithm derives the distribution of the channel decoder soft-output and substitutes it in the expression for the system end-to-end distortion. The VQ encoder/decoder pair is then optimized by minimizing this end-to-end distortion. For a Gauss-Markov source, the proposed algorithm outperforms the conventional SOVQ source coding scheme by 5.0 dB in the decoded source SNR. Application of this algorithm for designing optimum low-bit-rate speech codec is given. A 4.0 kbps VQ based CELP codec is designed for performance evaluations, where all the CELP parameter encoder/decoder pairs are optimized by minimizing their end-to-end distortions, respectively. As a result, the speech distortion over the noisy channel is minimized. Subjective tests show that the proposed algorithm improves the decoded speech quality by 2.5 MOS relative to a regular SOVQ CELP speech coding system. The performances of the algorithm under channel mismatch conditions are also shown and discussed.