Low-latency low-complexity heap-based extended min-sum algorithms for non-binary low-density parity-check codes

• Published in: IET communications Vol. 9; no. 9; pp. 1191 - 1198
• Main Authors: Hwang, Youngjun, Yang, Kyeongcheol, Cheun, Kyungwhoon
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 11.06.2015
• Subjects: Algorithms; Complexity; Decoding; decoding complexity reduction; EMS; Error correcting codes; Galois fields; GF(q); heap‐based EMS algorithm; heap‐based I‐EMS algorithm; HI‐EMS algorithms; H‐EMS algorithm; improved EMS algorithms; I‐EMS algorithms; low‐latency low‐complexity heap‐based extended min‐sum algorithms; Messages; nonbinary low‐density parity‐check codes; parity check codes; Performance degradation; Serials; sorting process; trellis‐based EMS algorithm; H-EMS algorithm; parity check codes; trellis-based EMS algorithm; heap-based EMS algorithm; low-latency low-complexity heap-based extended min-sum algorithms; GF(q); performance degradation; nonbinary low-density parity-check codes; heap-based I-EMS algorithm; Galois fields; decoding; decoding complexity reduction; HI-EMS algorithms; I-EMS algorithms; improved EMS algorithms; sorting process
• ISSN: 1751-8628; 1751-8636; 1751-8636
• DOI: 10.1049/iet-com.2014.1107

The extended min-sum (EMS) and improved EMS (I-EMS) algorithms for non-binary low-density parity-check codes over GF(q) significantly reduce the decoding complexity with an acceptable performance degradation, but they suffer from high latency because of many serial computations, including a sorting process. On the other hand, the trellis-based EMS algorithm can greatly reduce the latency, but it does not solve the complexity problem in high-order fields (q ≥ 64). To improve the latency problem with low-complexity advantages, the authors propose heap-based EMS (H-EMS) and heap-based I-EMS (HI-EMS) algorithms that are modifications of the EMS and I-EMS algorithms, respectively. The authors also propose double H-EMS and double HI-EMS algorithms trading off the latency against the performance by heaping messages twice. Numerical results show that the H-EMS algorithm has 2.74–9.52 times lower latency than the EMS algorithm with a negligible performance degradation over a wide range of code rates, whereas the HI-EMS algorithm has 1.20–1.62 times lower latency than the I-EMS algorithm. Furthermore, the proposed algorithms may be employed regardless of the decoding schedules.