The application of convolutional codes to continuous phase modulated communication channels

Convolutional codes are found which are optimal for certain continuous phase modulation (CPM) communication channels. The CPM channel is important due to its bandwidth efficiency. As a consequence of its constant amplitude, the CPM scheme also allows the design of efficient transmitters, as required for satellite communication. The specific CMP channels investigated in detail include binary and quaternary schemes, rectangular and raised cosine pulse shapes with pulse lengths of one and two, and several modulation indexes. The codes investigated include binary rate 1/2, 1/3, and 2/3. The concept of trellis code isomorphism is introduced which greatly reduces the size of the optimal code search problem. In addition, new conventions are introduced which allow a meaningful assessment to be made of the relative merits of coding/modulation schemes with different coding rates and modulation indexes. These are the normalized modulation index and a new form of normalized minimum Euclidean distance.