Efficient Polar Code Construction for Higher-Order Modulation

An efficient algorithm for the construction of polar codes for higher-order modulation is presented based on information-theoretic principles. The bit reliabilities after successive demapping are estimated using the LM-rate, an achievable rate for mismatched decoding. The successive demapper bit channels are then replaced by binary input Additive White Gaussian Noise (biAWGN) surrogate channels and polar codes are constructed using a Gaussian approximation (GA). This LM-rate Demapper GA (LM-DGA) construction is used to construct polar codes for several demapping strategies proposed in literature. For all considered demappers, the LM-DGA constructed polar codes have the same performance as polar codes constructed by Monte Carlo (MC) simulation, but the LM-DGA construction is much faster. For 64-QAM, spectral efficiency 3 bits/ s/ Hz, and block length 1536 bits, simulation results show that LMDGA constructed polar codes with cyclic redundancy check and successive cancellation list decoding are 1 dB more power efficient than state-of-the-art AR4JA low-density parity-check codes.