On the symmetric information rate of CPM in the finite blocklength regime

Continuous phase modulation (CPM) is a family of bandwidth-efficient signaling schemes with memory. In this paper we introduce a simulation-based method to compute a lower bound, namely the dependence testing (DT) bound, on the maximum achievable rate of general CPM schemes under finite blocklength, probability of error, and equiprobable input distribution constraints. The proposed method utilizes a posteriori probabilities (APPs) of the state transitions on the trellis that models the CPM modulator. The bound on the maximum achievable rate is then used to lower bound the spectral efficiency of CPM schemes under the finite blocklength constraint. For the numerical results, we focus on minimum-shift keying (MSK) modulation, and compute the DT bound for MSK as a function of the signal-to-noise ratio (SNR). We simulate a serially concatenated convolutional code (SCCC) using MSK as the inner code, which performs within 1.1 dB of the DT bound theoretical curve for various coding rates.