Deep Polar Codes

TL;DR

Deep polar codes introduce a multi-layered encoding and decoding framework that significantly improves error performance and flexibility over existing polar codes, while maintaining low complexity and approaching theoretical capacity bounds.

Contribution

The paper proposes a novel deep polar coding scheme with a new encoder and decoding algorithms, enhancing performance and flexibility compared to traditional polar codes.

Findings

Outperform existing pre-transformed polar codes in block error rates.

Achieve near-capacity performance within 0.4 dB of the meta-converse bound.

Maintain low encoding and decoding complexity.

Abstract

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.