Some Concatenated and Iterative Decoding Approaches for Continuous Phase Modulation

Several concatenated and iterative decoding approaches are used to improve the power efficiency of continuous phase modulation (CPM). First a symbol interleaver is used for serially concatenated CPM (SCCPM). Convergence of iterative decoding for this scheme can be earlier (lower SNR: Signal-to-Noise-Ratio) compared to bit interleaved SCCPM. Then a ring convolutional code (CC) is used as the outer code in this symbol interleaved SCCPM. By setting the denominator of the CPM modulation index equal to the alphabet size of the system (CPM, interleaver and ring CC), a natural combination of them is achieved. Further improvements on earlier convergence or error floors are achieved with this scheme. Finally, irregular repeat accumulate (IRA) codes with CPM (IRCPM) are considered. CPM now takes the role of the accumulator. This scheme shows even earlier convergence than SCCPM. To analyze the error floor performance, we derive the union bound for symbol interleaved SCCPM. In this bound analysis, we have to consider the order of nonzero permuted difference symbols that are not identical. We also derive the union bound for IRCPM from its equivalent structure. This structure introduces a virtual interleaver before CPM. Thus, the union bound analysis for SCCPM is now applicable.