In this thesis, the performances of adaptive differential pulse code modulation (ADPCM) originally proposed by Cummiskey et al. and delayed-decision ADPCM(DD-ADPCM) systems have been studied by computer simulation with particular emphasis on reducing the computational complexity and on improving the performance in a noisy channel. The DD-ADPCM that yields improved performance especially at low bit rates compared with the conventional ADPCM system showed a signal-to-quantization noise ratio (SQNR) gain of about 1dB per one sample delay. To reduce the computational loads that are caused by increment of the delay samples, a block decision scheme has been proposed for the DD-ADPCM. In addition, we have studied the use of convolutional coding and the reducedstate Viterbi algorithm in the DD-ADPCM so as to reduce the effect of noisy channel. The reduced-state Viterbi algorithm yielded almost the same performance as the conventional Viterbi algorithm, while reducing the computational load significantly.