A Hypergraph Filtering based Iterative Decoding Approach for Linear Channel Codes

Efficient decoding for general linear channel codes has been a long standing problem. Message passing type algorithms can achieve near-optimal performance for channel codes with sparse check matrices and long code-lengths, but they may suffer from obvious performance loss when the aforementioned two conditions are not satisfied. In this paper, we propose an alternative hypergraph filtering based decoding scheme based on recently developed hypergraph signal processing (HGSP) frameworks. Specifically, we model the coded sequence as a hypergraph signal by regarding each coded bit as a vertex and representing each check constraint by a hyperedge. We then map the message passing in iterative decoding algorithms to the signal shifting in HGSP, based on which a hypergraph filtering (HF) based decoding scheme is developed. By further combining the modified random redundant iterative decoding (mRRD) technique, we finally develop a novel HF-mRRD scheme to approach the near-optimal decoding performance. Simulation results on both Hamming codes and BCH codes show that the proposed scheme obtains significant performance gains over standard message passing type algorithms, and achieve comparable or even better performance than the state-of-the-art deep learning based schemes.