Low bit rate, high quality speech coding is a vital part in voice telecommunication systems. The introduction of CELP (1982) (Codebook Excited Linear Prediction) speech coding provides a feasible way to compress speech data to 4.8 kbps with high quality, but the formidable computational complexity required for real-time processing has prevented its wide application. In this thesis, we reduce the computational complexity to 5 MIPS (million instructions per second), which can be handled by even inexpensive DSP chips, while maintaining the same high quality. We hope our contribution can finally make CELP coding a widely applicable technology.