Deep Polar Codes
Geon Choi Namyoon Lee
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.