Coherent and Multi-symbol Noncoherent CPFSK: Capacity and Code Design

The capacity of coded continuous-phase frequency-shift keying (CPFSK) is found for additive white Gaussian noise (AWGN) channels under the assumption that the symbols at the modulator input are independent and uniformly distributed. Two forms of reception are considered, coherent detection and multi-symbol noncoherent block detection. Calculating the coherent capacity of CPFSK is facilitated by considering the system as a finite-state Markov channel. A methodology is proposed for designing systems that approach the capacity by using an irregular repeat-accumulate (IRA) code. The code is optimized directly from the system´s EXIT chart by using linear programming to determine the optimal variable-node degree distribution. Results are presented for a rate 1/2 MSK system that is within 0.43 dB and 0.33 dB of the coherent and 4-symbol noncoherent capacities, respectively.