High quality, low bit rate speech coding system is becoming increasingly important in the world of modern telephone. Code excited linear predictive (CELP) coding is most efficient method for high quality speech coding at low bit rate. Most complexity in CELP coders comes from the search procedure used to determine the optimum innovation sequence. This book presents a study of three CELP coder algorithms, which are based on the goal of reducing the search procedure to minimum possible with good speech quality. The CELP coders' algorithm was found to give quite good-quality speech at 4.8 kb/s using autocorrelation approach, but still required high computation. A binary CELP coder algorithm is built on the two possible values -1 and +1 set of waveforms for an excitation bit rate of one bit per sample. The internal algebraic structure of the codebook leads to efficient and fast algorithm for selecting the optimum excitation. The proposed ternary CELP coder algorithm produces the same speech quality as obtained by CELP coders without needing any excitation codebook. A special algorithm has been developed for very low data rate 2.4 kb/s.