Algorithm Details

Successive Cancellation List (SCL), Successive Cancellation (SC), and space-efficient SC decoding algorithms are based on [1]. One key difference in this implementation compared to the above paper is the incorporation of LLR values in the algorithm instead of a non-LLR implementation. Therefore, the LLR-based implementation is supported by an additional LLR path metric [2]. The polar code construction algorithm in this repository is based on the Gaussian Approximation (GA) method [3]. The use of CRC in polar SCL decoding is explained in [4]. Furthermore, This GitHub repository implements CRC-aided SCL decoding using a CRC matrix instead of a CRC polynomial. Apart from this difference, its SCL decoding implementation aligns closely with the approach used in this repository.

References

1. Tal, Ido, and Alexander Vardy. "List decoding of polar codes." IEEE Transactions on Information Theory, vol. 61, no. 5, 2015, pp. 2213-2226.
2. B. Yuan and K. K. Parhi, "Successive cancellation list polar decoder using log-likelihood ratios," 2014 48th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA, 2014, pp. 548-552.
3. Wu, Daolong, Ying Li, and Yue Sun. "Construction and block error rate analysis of polar codes over AWGN channel based on Gaussian approximation." IEEE Communications Letters, vol. 18, no. 7, 2014, pp. 1099-1102.
4. K. Niu and K. Chen, "CRC-Aided Decoding of Polar Codes," IEEE Communications Letters, vol. 16, no. 10, pp. 1668-1671, October 2012.