Coherent Continuous-Phase Frequency-Shift Keying: Parameter Optimization and Code Design

The symmetric information rate of a modulation-constrained transmission system is the information-theoretic limit on performance under the assumption that the inputs are independent and uniformly distributed. The symmetric information rate for continuous-phase frequency-shift keying (CPFSK) over an AWGN channel may be estimated by considering the system to be a finite-state Markov channel and executing a BCJR-like algorithm. In this paper, the estimated symmetric information rate is used along with the exact expression for the 99% power bandwidth to determine the information-theoretic tradeoff between energy and spectral efficiency for CPFSK modulation. Using this tradeoff, the code rate and modulation index are jointly optimized for a particular spectral efficiency and alphabet size. Codes are then designed for the optimized system. The codes are comprised of variable nodes (which represent irregular repetition codes), check nodes (which represent single parity-check codes), and an interleaver connecting the variable and check nodes. The degree distributions of the code are optimized from the system's EXIT chart by using linear programming. Additional details of the code design, including labeling and interleaver design, are also discussed. Simulation results show that the optimized coded systems achieve bit error rates within 0.4 dB of the information-theoretic limits at BER = 10(-5).