Protograph-based q-ary LDPC codes for higher-order modulation

This paper introduces a protograph-based method for designing q-ary LDPC codes for use with modulations larger than QPSK. Simulations focus on a GF(16), 16-QAM example. The proposed construction method achieves the maximum gain when the average column weight is chosen so that the linear minimum distance growth property is satisfied. In this region, the benefit of a protograph-based design over a standard PEG approach was 0.3 dB. We found that a careful field-element selection algorithm provides about 0.1 dB of improvement over random field-element selection. Overall, the proposed improvements yielded 0.4 dB of gain over a PEG-based GF(16) code with randomly selected Galois field elements. The performance of this baseline GF(16) code was comparable to the best known binary LDPC code for 16-QAM, so that the proposed improvements allow the GF(16) LDPC code to outperform known binary approaches.