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Limited availability of bandwidth for mobile telecommunication has been the main reason behind the research and study in speech compression algorithms. To effectively compress speech one must go beyond manipulating the binary digits used to represent the signal. Understanding the details of voice and speech production has helped us to find effective and better ways of speech compression. Most modern speech compression algorithms use Linear Prediction along with Code book Excitation to effectively compress and decompress speech signals. Even though we have several telecommunication standards for speech compression, all of the standards use the concept of Linear Prediction and Code book Excitation at their core implementation. This Book explains the theoretical background of Code book Excited Linear Prediction (CELP) algorithm. In addition, a C code has been presented as a practical guide.