A Polar Coding Scheme With Selected Index Modulation

Short to medium length polar codes achieve inferior decoding performance than other advanced channel codes under successive cancellation (SC). Sophisticated polar decoding enhances the corresponding performance while degrading the coding rate and complexity. For better decoding performance and efficiency, this paper presents a polar coding scheme with selected index modulation (PC-SIM). At the transmitter, PC-SIM integrates the concept of index modulation (IM) into polar encoding, using the indices of inactive unfrozen positions (IUPs) to carry implicit information. To boost coding rate without sacrificing decoding performance, PC-SIM selects more reliable unfrozen positions for IM and adds inactive information bits (IIBs) to offset rate losses. Additionally, Walsh-Hadamard Transform (WHT) is incorporated to lower the high peak-to-average power ratio (PAPR) in multi-carrier systems and reduce interference. At the receiver, PC-SIM performs polar decoding followed by repetition decoding to obtain index bits and information bits. Simulation results indicate that in Orthogonal Frequency Division Multiplexing (OFDM) systems, compared to conventional polar codes and existing IM-aided polar coding schemes, the proposed PC-SIM scheme significantly improves error performance, coding rate, and PAPR reduction. The proposed PC-SIM achieves around 0.3 dB over the conventional CRC-aided polar codes and IM-aided polar codes with higher coding rate at the bit error ratio (BER) of $4\times 10^{-4}$.