Multiple symbol trellis coding of CPFSK

This paper describes a technique related to the design of a trellis encoder, combined with the full response M-ary continuous phase frequency shift keying (CPFSK) with modulation index 1/M. A new representation of CPFSK waveforms in N signaling intervals, is proposed as a function of an (N+1)-D vector. We also decompose the generation of the proposed CPFSK waveform into two stages, an N-consecutive continuous phase encoder (NCPE) and a memoryless modulator (MM). This decomposition makes it possible to design binary convolutional encoders with various code rates, cascaded to the NCPE. Specific optimal outer convolutional encoders of two and three-consecutive full response four-ary CPFSK with modulation index 1/4 are designed following Ungerboeck´s (1982) set partitioning approach. These codes achieve asymptotic coding gains up to 4.77 dB for the two consecutive case with code rate 3/4, and asymptotic coding gains up to 5.45 dB for the three-consecutive case with code rate 5/6