Polar codes are the first codes with a proven capacity-achieving capability, but their decoding faces several challenges, especially under long code lengths. In this paper, we target algorithmic improvements and analyses to enable the implementation of long polar codes (e.g., length 8K bits) by addressing key challenges in memory usage and computational complexity presented by successive cancellation list (SCL) polar decoding. Perturbation-enhanced (PE) SCL decoders with a list size of $L$ reach the decoding performance of the SCL decoder with a list size of $2L$. The proposed bias-enhanced (BE) SCL decoders, which simplify the PE SCL decoder based on insights gained by an ablation study, return similar decoding performance to PE SCL decoders. Also, proposed BE generalized partitioned SCL (GPSCL) decoders with a list size of $8$ have a $67\%$ reduction in the memory usage and similar decoding performance compared to SCL decoders with a list size of $16$, and it demonstrates that an accurate bias can be generated under a reduced number of codewords from the list and reduces the overhead from $\left(L-1\right)n$ XOR gates plus $n$ priority encoders to $n$ XOR gates, where $n$ is the code length. Furthermore, input-distribution-aware (IDA) decoding is applied to BE GPSCL decoders, which shows how an accurate bias is generated under a low-complexity decoder. Up to $5.4\times$ reduction in the computational complexity is achieved compared to SCL decoders with a list size of $16$, and negligible latency overhead is added to the decoding process. The degraded decoding performance is at most $0.05\text{ dB}$ compared to BE GPSCL decoders without IDA decoding. Lastly, we theoretically prove that the bias in the BE SCL decoder moves the received soft information toward valid polar codewords with a high likelihood, and explain the decoding performance gain.

翻译：极化码是首个被证明具有可达容量特性的编码，但其译码过程仍面临诸多挑战，尤其在长码长条件下。本文针对连续消除列表（SCL）极化译码在内存占用和计算复杂度方面的关键难题，提出算法改进与分析，旨在实现长极化码（如8K比特长度）的工程部署。列表大小为$L$的扰动增强型（PE）SCL译码器可达到列表大小为$2L$的SCL译码器的译码性能。基于消融实验洞察所提出的偏置增强型（BE）SCL译码器，在简化PE SCL译码器结构的同时，保持了与PE SCL译码器相近的译码性能。此外，所提出的列表大小为$8$的BE广义分区SCL（GPSCL）译码器相较于列表大小为$16$的SCL译码器，内存占用减少$67\%$，且译码性能相当；该方案证明可在缩减的列表码字条件下生成精确偏置，并将开销从$\left(L-1\right)n$个异或门加$n$个优先编码器降低至$n$个异或门（其中$n$为码长）。进一步地，将输入分布感知（IDA）译码应用于BE GPSCL译码器，揭示了在低复杂度译码器中生成精确偏置的机理。与列表大小为$16$的SCL译码器相比，计算复杂度降低高达$5.4$倍，且译码过程仅引入可忽略的时延开销。相较于未采用IDA译码的BE GPSCL译码器，其译码性能退化最大不超过$0.05\text{ dB}$。最后，我们从理论上证明了BE SCL译码器中的偏置能够以高概率将接收软信息驱动至有效极化码字方向，并解释了译码性能增益的成因。