The main objective of this dissertation work is to develop a speech coder which can be used for a variablerate channel such as a packet-switched voice network. First, a new concept of embedded quantization is introduced, and a design technique of the embedded quantizer is considered in the context of joint optimization of source and channel coding. For the purpose, a variable-rate channel is modeled by a noisy discrete memoryless channel. With the mean-square distortion measure, we derive necessary conditions of optimum embedded coders with uniform, uniform threshold and non-uniform quantization. We show that for the non-uniform and uniform threshold embedded coders, the overall quantization noise can be separated into quantization noise at the encoder and the channel error in the variable-rate channel. This separation makes it relatively easy to compute the overall quantization noise. For the non-uniform embedded quantizer, an iterative design algorithm is proposed, and numerical results for Gaussian and Laplacian sources are presented. Second, an adaptive differential PCM that may be used for embedded speech waveform coding is proposed. In this scheme, the quantization noise of an ADPCM is reduced significantly by employing an instantaneously adaptive PCM. Further, to reduce the subjectively annoying effects, a noise shaping filter structure suitable for the embedded ADPCM system is proposed. By computer simulation using real speech, we show a significant performance improvement (3 to 10 dB at the rates of 16 to 48 kbits/s) with the proposed scheme. Lastly, an embedded vector quantizer is investigated. For this purpose the tree search vector quantizer (TSVQ) and the multi-stage vector quantizer (MSVQ) are studied. For the MSVQ system a new design algorithm based on the cyclic coordinate descent technique is proposed. A code vector update equation is derived from the optimality condition of the MSVQ structure. Computer simulation results show that the proposed...