Reduced complexity hard‐ and soft‐input BCH decoding with applications in concatenated codes

• Published in: IET circuits, devices & systems Vol. 15; no. 3; pp. 284 - 296
• Main Authors: Freudenberger, Jürgen, Nicolas Bailon, Daniel, Safieh, Malek
• Format: Journal Article
• Language: English
• Published: Stevenage John Wiley & Sons, Inc 01.05.2021; Wiley
• Subjects: Acceptance criteria; Algebra; Algorithms; BCH codes; Binary codes; Codes; Coding; Complexity; Concatenated codes; Critical path; Decoding; Error analysis; Error correction; Error correction & detection; error correction codes; Random access memory
• ISSN: 1751-858X; 1751-8598; 1751-8598
• DOI: 10.1049/cds2.12026

Error correction coding for optical communication and storage requires high rate codes that enable high data throughput and low residual errors. Recently, different concatenated coding schemes were proposed that are based on binary BCH codes with low error correcting capabilities. In this work, low‐complexity hard‐ and soft‐input decoding methods for such codes are investigated. We propose three concepts to reduce the complexity of the decoder. For the algebraic decoding we demonstrate that Peterson's algorithm can be more efficient than the Berlekamp–Massey algorithm for single, double, and triple error correcting BCH codes. We propose an inversion‐less version of Peterson's algorithm and a corresponding decoding architecture. Furthermore, we propose a decoding approach that combines algebraic hard‐input decoding with soft‐input bit‐flipping decoding. An acceptance criterion is utilised to determine the reliability of the estimated codewords. For many received codewords the stopping criterion indicates that the hard‐decoding result is sufficiently reliable, and the costly soft‐input decoding can be omitted. To reduce the memory size for the soft‐values, we propose a bit‐flipping decoder that stores only the positions and soft values of a small number of code symbols. This method significantly reduces the memory requirements and has little adverse effect on the decoding performance.