Application of convolutional codes over rings to low-rate DPCM image transmission

The transmission of DPCM-encoded images over a noisy channel is considered. As a consequence of the quantization process and of the imperfect source knowledge, the output of the DPCM source coder exhibits residual redundancy, which can be used to provide error control in the same way as the “artificial” redundancy inserted by a convolutional encoder. Exploiting this “natural” redundancy provides a power gain which is significant only for low signal-to-noise ratios. In order to obtain a power gain also for high signal-to-noise ratios, we advocate here the use of convolutional codes over the integer ring Z_M in conjunction with M-ary phase modulations, where M is the number of quantization levels. In particular, we describe a procedure for the selection of convolutional codes based on the minimization of the overall mean-square error (MSE). The latter includes the effects of source encoding and that of the noisy channel