Application of Nonbinary LDPC Codes for Communication over Fading Channels Using Higher Order Modulations

In this paper, we investigate the application of nonbinary low density parity check (LDPC) codes over Galois field GF(q) for both single-input single-output (SISO) and multipleinput multiple-output (MIMO) fading channels using higher order modulations. As opposed to the widely studied binary systems that employ joint detection and channel decoding, we propose a nonbinary system where optimal signal detection is performed only once followed by channel decoding. To reduce the complexity of proposed system, we first develop a low complexity LDPC decoding algorithm over GF(q) in the logarithmic domain. We then provide a quasi-cyclic construction of nonbinary LDPC codes which not only allows linear-time encoding, but also gives comparable performance to the best known progressive edge growth (PEG) codes. Our results show that the proposed system that employs regular nonbinary LDPC codes outperforms systems using the best optimized binary irregular LDPC codes in both performance and complexity.