Abstract
A multi-cyclic redundancy check (Multi-CRC) polar code construction algorithm is proposed in this paper to solve the error propagation problem of successive cancellation decoding for polar codes. In this algorithm, the information sequence is optimized into several segments to allow decoding errors to be corrected in time, minimizing the impact of error propagation. An improved multi-successive cancellation bit flipping (M-SCFlip) decoding algorithm is proposed to execute the bit flipping operation after CRC check-in each segment. In the low-SNR region, the proposed new multi-CRC polar code with successive cancellation list (SCL) decoding has a slight frame-error rate (FER) degradation compared with the original CRC polar code. With the M-SCFlip decoding algorithm developed in this paper, it achieves a better FER performance compared with the CRC polar code with successive cancellation (SC) and SCL ( $L\!=\!2$ ) decoding algorithms. In addition, it has a lower decoding delay and requires a lower memory space. For example, at a FER of 10−4 with the same code length and effective code rate, the proposed multi-CRC polar code with M-CFlip decoding achieves a 1.19 dB and 0.79 dB gains over existing CRC polar codes with the SC and SCL ( $L\!=\!2$ ) decoding algorithms, respectively.
Highlights
Polar code with fixed coding structure has been proved to approach the Shannon limit asymptotically
Polar code differs from other linear block codes mainly in its channel polarization process [15]
The polar code with the segmented structure increases the number of cyclic redundancy check (CRC) check times and the bit flipping opportunities, which will lead to better decoding performance
Summary
Polar code with fixed coding structure has been proved to approach the Shannon limit asymptotically. For short-to-medium-length polar codes, SC decoding results in a poor error performance due to incomplete channel polarization [5], [6]. To solve this problem, successive cancellation list (SCL) and successive cancellation stack (SCS) decoding algorithms have been proposed [7]–[9]. We propose a polar code structure with multiple CRCs, aiming to mitigate the error propagation effects Since this multi-CRC structure results in more CRC opportunities, a multi-bit SCFlip algorithm, named M-SCFlip, fits well this structure to execute multi-bit flipping for a significantly improved decoding performance
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