A decomposition approach to CPM

• Published in: IEEE transactions on information theory 1988-03, Vol.34 (2), p.260-270
• Main Author: Rimoldi, B.E.
• Format: Article
• Language: English
• Subjects: Applied sciences; Coding, codes; Continuous phase modulation; Convolution; Convolutional codes; Decoding; Digital modulation; Exact sciences and technology; Filters; Frequency shift keying; Galois fields; Information, signal and communications theory; Phase modulation; Phase shift keying; Signal and communications theory; Telecommunications and information theory
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/18.2634

It is shown that any continuous-phase-modulation (CPM) system can be decomposed into a continuous-phase encoder and a memoryless modulator in such a way that the former is a linear (modulo some integer P) time-invariant sequential circuit and the latter is also time invariant. This decomposition is exploited to obtain alternative realizations of the continuous-phase encoder (and hence of CPM) and also to obtain alternative forms of the optimum decoding algorithm. When P is a prime p so that the encoder is linear over the finite field GF(p), it is shown that cascading it with an outside convolutional encoder is equivalent to a single convolutional encoder. It is pointed out that the cascade of the modulator, the waveform channel (which it is assumed is characterized by additive white Gaussian noise), and the demodulator that operates over one symbol interval yield a discrete memoryless channel that can be studied without the distractions introduced by continuous-phase encoding.< >