Sparse Graphs for Belief Propagation Decoding of Polar Codes

TL;DR

This paper introduces a sparse graph representation for polar codes enabling belief propagation decoding similar to LDPC codes, reducing complexity and memory use with minimal performance loss.

Contribution

It presents a novel sparse graph approach for polar code decoding, allowing LDPC-like belief propagation with reduced complexity and hardware-friendly implementation.

Findings

Significant reduction in decoding complexity and memory requirements.

Negligible performance loss compared to original BP decoding.

Enhanced suitability for hardware implementations.

Abstract

We describe a novel approach to interpret a polar code as a low-density parity-check (LDPC)-like code with an underlying sparse decoding graph. This sparse graph is based on the encoding factor graph of polar codes and is suitable for conventional belief propagation (BP) decoding. We discuss several pruning techniques based on the check node decoder (CND) and variable node decoder (VND) update equations, significantly reducing the size (i.e., decoding complexity) of the parity-check matrix. As a result, iterative polar decoding can then be conducted on a sparse graph, akin to the traditional well-established LDPC decoding, e.g., using a fully parallel sum-product algorithm (SPA). This facilitates the systematic analysis and design of polar codes using the well-established tools known from analyzing LDPC codes. We show that the proposed iterative polar decoder has a negligible performance loss for short-to-intermediate codelengths compared to Arikan's original BP decoder. Finally, the proposed decoder is shown to benefit from both reduced complexity and reduced memory requirements and, thus, is more suitable for hardware implementations.