The Line Spectrum Pair (LSP) parameters have been established as one of the most efficient methods for representing the short-time speech spectra. The effectiveness of this method is due to two main properties, namely, the intraframe and the interframe correlation of the LSP parameters. In this thesis, several innovative schemes are developed for encoding LSP parameters. These schemes are all based upon tree-searched vector quantization (TSVQ), which exploit the intraframe correlation. When there is no channel noise, a differential coding scheme, called interblock noiseless coding (IBNC), is used with TSVQ to remove the interframe correlation. In order to achieve the desired reproduction fidelity, scalar quantizers are used to further encode the TSVQ error vector. With an encoding delay of only one frame, this technique achieves 1 dB2 spectral distortion at approximately 20 bits/frame, which is a noticeable improvement over previously reported results. In the case where the channel is noisy, two approaches are proposed for encoding the LSP parameters. The first approach (Channel-Optimized TSVQ) is to redesign the TSVQ encoder and decoder for the noisy channel. In the second approach (MAP detection), the interframce correlation is utilized in combating channel errors. Both of these methods have shown to be very effective.