Two Enhanced Reliability-Based Decoding Algorithms for Nonbinary LDPC Codes

The weighted bit-reliability-based (wBRB) algorithm for nonbinary LDPC codes suffers certain loss of symbol-reliability. Thus, this paper enhances its soft-decision version by passing multiple symbol-reliability instead of bit-reliability. Furthermore, it demonstrates that plurality robustly indicates symbol-reliability of extrinsic information-sums. Thus, this paper enhances the hard-decision version by introducing symbol-reliability from plurality. Analysis results show that these two enhanced decoding algorithms significantly outperform the wBRB algorithm with reasonable overhead.

I. Introduction

Non-binary low-density parity-check (LDPC) codes over , as known as -ary LDPC codes, have been demonstrated to outperform their binary counterparts, especially for short and moderate code lengths [1]–[7]. However, the non-binary belief propagation (BP) decoding algorithms [1], [8], [9] require a large amount of computation and storage. The extended Min-Sum (EMS) [10]–[12], Min-Max [13]–[15] and trellis based EMS (T-EMS) [16]–[18] algorithms have been presented to reduce the complexity of the BP algorithms. However, their performance degrades as the complexity decreases. The iterative reliability-based majority-logic decoding algorithms [19]–[24], firstly proposed by Lin et al., enjoy low-complexity, but suffer error-floors for non-binary LDPC codes with low column weights. The multiple-votes symbol-flipping (MV-SF) decoding algorithm [25] propagates the most reliable values to the check node (CN), with the only information of their ranking. Thus, many researchers dedicated themselves to seek better trade-offs between performance and complexity.