Sparsely Pre-Transformed Polar Codes for Low-Latency SCL Decoding

Deep polar codes, which employ multi-layered polar kernel pre-transforms in series, are recently introduced variants of pre-transformed polar codes. These codes can reduce the number of minimum-weight codewords, thus closely achieving finite-block length capacity with successive cancellation list (SCL) decoders in certain scenarios. However, for low-latency applications requiring small SCL decoder list sizes, reducing minimum-weight codewords doesn’t necessarily improve decoding performance. To address this limitation, we propose an alternative pre-transform technique to enhance the suitability of polar codes for SCL decoders with practical list sizes. Leveraging the fact that the SCL decoding error event set can be decomposed into two exclusive error event sets, our approach applies two different types of pre-transformations, each targeting the reduction of one of the two error event sets. Extensive simulation results across various block lengths and code rates demonstrate that our codes consistently outperform existing state-of-the-art pre-transformed polar codes, including CRC-aided polar codes and polarization-adjusted convolutional codes, when decoded using SCL decoders with small list sizes.