This thesis is about non-binary convolutional turbo codes--codes constructed via parallel concatenation of two circular recursive systematic convolutional (CRSC) encoders linked by an interleaver. The focus of the work is on the understanding and design of non-binary convolutional turbo codes. This includes investigation of central components that influence non-binary convolutional turbo code performances, such as the component encoders and the interleaver, as well as the procedure of iterative decoding. The investigations are carried out for transmission on additive white Gaussian noise channels.  First, this thesis presents the theoretical background of channel coding and turbo coding. Next, a general and efficient maximum a posteriori (MAP) soft-input soft-output (SISO) decoding algorithm is presented. And then, the simplified Max-Log-MAP algorithm is derived for the double-binary convolutional turbo code, which follows the specifications of turbo coding/decoding in the DVB-RCS standard (Digital Video Broadcasting standard for Return Channel via Satellite), for twelve different block sizes and seven coding rates. The quantizer of turbo-decoder is designed for the goal of implementation. The effect of quantiztion on the performance of the decoder is analyzed and simulated. The correction coefficient of the simplified Max-Log-MAP algorithm is also discussed.  The DVB-RCS standard turbo code uses quaternary alphabet and QPSK modulation. In order to increase the bandwidth efficiency, we present an extended nonbinary turbo-coding scheme consisting of 8-ary triple-binary codes combined with 8PSK modulation. A comprehensive study over AWGN channel is carried out to show the good performance of the concatenated codes, the influence of various parameters and the symbol-by-symbol Max-Log-MAP algorithm