In this paper, we introduce a novel class of pre-transformed polar codes, termed as deep polar codes. We first present a deep polar encoder that harnesses a series of multi-layered polar transformations with varying sizes. Our approach to encoding enables a low-complexity implementation while significantly enhancing the weight distribution of the code. Moreover, our encoding method offers flexibility in rate-profiling, embracing a wide range of code rates and blocklengths. Next, we put forth a low-complexity decoding algorithm called successive cancellation list with backpropagation parity checks (SCL-BPC). This decoding algorithm leverages the parity check equations in the reverse process of the multi-layered pre-transformed encoding for SCL decoding. Additionally, we present a low-latency decoding algorithm that employs parallel-SCL decoding by treating partially pre-transformed bit patterns as additional frozen bits. Through simulations, we demonstrate that deep polar codes outperform existing pre-transformed polar codes in terms of block error rates across various code rates under short block lengths, while maintaining low encoding and decoding complexity. Furthermore, we show that concatenating deep polar codes with cyclic-redundancy-check codes can achieve the meta-converse bound of the finite block length capacity within 0.4 dB in some instances.

本文介绍了一种新颖的预转换极化码类别，称为深度极化码。此类码具有低复杂度的编码实现和重复度增强，同时支持多种码率和码块长度，提出了一种低复杂度的解码算法和延迟低的并行解码算法，并通过模拟实验证明了其在短块长度下优于现有的预转换极化码，并展示了与循环冗余检验码级联可以在某些情况下达到有限块长度容量的元逆推 bound，与此 bound 之间仅相差 0.4 dB。