This paper presents a soft decoding scheme based on the binary representations transferred from the parity-check matrices (PCMs) for Reed-Solomon (RS) codes. Referring to the modified binary PCM that has a systematic part and a high-density part corresponding to the least reliable variable nodes (LRVNs) and the most reliable variable nodes (MRVNs), respectively, an informed dynamic scheduling method, called Nested-Polling Residual Belief Propagation (NP-RBP), is applied to the corresponding Tanner graph. As with the popular adaptive BP (ABP) decoding approach, adaptation in a binary PCM based on the reliability of variable nodes is also conducted in the proposed NP-RBP decoding. The NP-RBP enables the LRVNs to receive significant updates and limits the correlation accumulation from the short cycles in the MRVNs. In order to enhance the error-rate performance for long codes, a bit-flipping (BF) technique is conducted in order to correct a selection of the errors in the MRVNs such that the propagation of these errors in the subsequent NP-RBP process can be avoided. The resultant decoder is termed NP-RBP-BF. For short codes such as the (31, 25) and (63, 55) RS codes, NP-RBP is able to provide an error-rate performance close to the maximum-likelihood (ML) bound. A more significant improvement can be observed for long codes. For instance, when the proposed NP-RBP-BF decoding is applied to the (255, 239) RS code, it can provide a gain of about 0.4 dB compared to the ABP decoding and the performance gap to the ML bound can be narrowed to about 0.25 dB at a frame error rate of 2 x 10(-3).
- A Graph-Based Soft-Decision Decoding Scheme for Reed-Solomon Codes
- Huang-Chang Lee - Chang Gung UniversityJyun-Han Wu - Phison (Taiwan)Chung-Hsuan Wang - National Yang Ming Chiao Tung UniversityYeong-Luh Ueng - National Tsing Hua University
- IEEE
- 14
- MOST 111-2221-E-A49-065; MOST 110-2221-E-007-029-MY3; MOST 111-2221-E-182-031 / National Science and Technology Council, Taiwan
- Journal article
- 01/01/2023
- IEEE journal on selected areas in information theory, Vol.4, pp.420-433
- English