Rateless Polar Codes Exploiting Repetition Coding Principle with EXIT Analysis for Broadband Transmissions
This paper proposes a novel design of polar codes for rateless transmissions employing extended parity (EP) to enhance performance under broadband channel conditions. The idea of the proposed design is to achieve diversity across all samples by employing simple butterfly XOR operations, which inherently support rateless broadband transmissions. In particular, the design exploits the principle of repetition, where simple XOR operations do not only contribute to error protection but also strengthen the polarization effect and reinforce the rateless property of polar codes. The proposed codes are evaluated over Rayleigh fading, fully interleaved, and additive white Gaussian noise (AWGN) channels. The results show that the proposed codes achieve significant performance improvements, particularly in AWGN and fully interleaved environments, thereby confirming that the use of XOR operations effectively enhances transmission reliability. Furthermore, the proposed codes are investigated through extrinsic information transfer (EXIT) analysis using closed-form expressions. The analysis reveals that the decoding process exhibits faster convergence when EP is employed. In addition, computational complexity analysis shows that the additional overhead introduced by EP remains minimal. Importantly, the proposed structure preserves the standard polar transform and decoding graph, ensuring scalability similar to conventional polar codes. Hence, the proposed design balances performance and computational efficiency, making it a compelling solution for broadband scenarios and dynamic channel environments.