In this paper, by introducing nested parity-check (PC) functions, a new polarizing matrix extension-based hybrid automatic repeat request (PME-HARQ) scheme, called PC-PME-HARQ, is proposed. Such nested PC functions are constructed through a fixed-length cyclic shift register. This approach significantly enhances error correction capability, particularly for short and medium-length packet transmissions. Besides, a dynamic subchannel mapping and optimization framework is developed, which integrates subchannel reliability and distance spectrum to optimize bit-set configurations for varying transmission conditions. Furthermore, the information set approximation puncturing (ISAP) and reliability score-based puncturing (RSP) algorithms have been modified and optimized to outperform the traditional quasi-uniform puncturing (QUP) algorithm, providing improved rate compatibility and reducing Block Error Rate (BLER) in PME-HARQ systems. Simulation results demonstrate that the proposed PC-PME-HARQ scheme achieves substantial performance gains, offering both coding and diversity gains across multiple retransmissions, effectively surpassing the baseline schemes.

Benefiting from the powerful cyclic redundancy check aided successive cancellation list (CA-SCL) decoder, the polar codes have achieved competitive performances with respect to LDCP codes. However, its short codeword performance needs to be further improved for supporting reliable short package transmissions typically in massive machine-type communications (mMTC). In this paper, the short polar coding problem is tackled by developing a bit-flipping aided CA-SCL detection method. First, we reveal that error distribution of SCL decoding strongly relates to the row weights of generator matrix. Accordingly, we determine the flipping indices according to both their row weights and their polarized bit-channel reliabilities. The simulation results show that our row weight based successive cancellation list flipping (RWB-SCL-Flipping) decoding achieves around 0.3 dB gain compared with its counterpart in [1] while transmitting short codewords over AWGN channels.