Sparse Graphs for Belief Propagation Decoding of Polar Codes

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 sumproduct algorithm (SPA)). We show that the proposed iterative polar decoder has a negligible performance loss for shortto-intermediate codelengths compared to Arıkan’s original BP decoder; whereas we observed that this loss diminishes for more BP iterations. Finally, the proposed decoder is shown to benefit from a reduced complexity and reduced memory requirements compared to Arıkan’s original BP decoder, thus it is more suitable for hardware implementations.