Parity-Check Aided Polarizing Matrix Extension for Efficient IR-HARQ Transmission

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.