Low-Complexity Symbol-Flipping Decoding Algorithms for Nonbinary LDPC Codes

Abstract

Low-density parity-check (LDPC) codes have been shown to have near Shannon-limit performance when a probabilistic decoding is used and the code length goes to infinity. On the other hand, non-binary low-density parity-check (NB-LDPC) codes outperform binary LDPC codes for short code lengths. However, the coding gain of NB-LDPC codes comes from the expense of computational complexity.

In this thesis, we consider the problem of a trade-off between reasonable complexity and good error-rate performance of decoding nonbinary LDPC codes over GF($q$). We first introduce the existing decoding algorithms of nonbinary LDPC codes and compare with decoding algorithms of binary LDPC codes. Second, low-complexity decoding algorithms of nonbinary LDPC codes is considered and two low-complexity symbol-flipping algorithms based on D-SFDP is proposed. These algorithms outperform the existing D-SFDP algorithm by improving the flipping metric. Proposed algorithms provide good trade-off between complexity and error performance.