Transmission of handwriting and sketches as a minimal bandwidth extension of conventional telephony has been employed for several years. Although these analog systems are useful, it is digital transmission which shows most promise in resistance to noise and distortion, and in compatibility with computer-generated graphics and PCM telephony. The bandwidth required by digital transmission must be reduced before such systems are  viable. In this thesis, the development of several bandwidth reduction schemes based on predictive encoding are discussed. The prediction model coefficients were obtained from experimental picture and handwriting data and this data was used to simulate the encoding algorithms. The compression ratios and the complexity of the various schemes are described.