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The last decade has witnessed rapid growth and development within the telecommunication industry. This, in particular for speech coding, has been primarily driven by the enormous expansion of digital mobile communication. Whilst the available bandwidth in wired based terrestrial network is a relatively cheap and expandable resource, it becomes unavoidably limited in satellite or mobile communication systems. At the same time, a high quality speech communication system is preferred. This, on the other hand, requires high data rates. Therefore, key factors to design speech coder are both the optimisation of the bandwidth usage and provision of high quality of service. The research carried out in this thesis has mainly focused on the design and development of low to medium bit rate narrowband and wideband speech coding algorithms which are based on Analysis-by-Synthesis Linear Prediction Coding (AbS-LPC). In order to reduce the computational complexity as well as to improve the perceptual quality, the secondary excitation used in the developed coder is based on sparsely populated pulse vectors instead of a Gaussian codebook, used in the original famous Code Excited Linear Prediction (CELP) coder. The algorithms subsequently developed also incorporate a multi-rate operation i.e. speech and channel coding bit allocation can be varied for different level of error protection according to channel conditions. Moreover, the developed coder is designed to operate between 8 and 14 kb/s, at a gross bit rate of 22.8 kb/s in order to provide a reliable service in the existing mobile communication network. In addition to the multi-rate speech coders, a new approach to variable rate speech coder is presented. In this course of research, longer frame lengths are used when possible i.e. when the speech segment contains similar- characteristics. This is mainly to reduce the parameter updating rate, and hence the bit rate. Speech segmentation and voice classification are obtained via speech recognition. Different types of excitation are used for different voice classes in order to improve the speech quality and to further reduce the bit rate. However, some applications require very high quality speech which narrowband speech cannot offer. The work in this research also includes the development of wideband CELP coder that operates at much lower bit rate than the current standards whilst maintaining toll or near toll quality of speech.