An Improved Full Rank Condition for Nonbinary LDPC Codes over BI-AWGN Channel

This paper improves the full rank condition (FRC) to construct nonbinary LDPC codes for binary AWGN channels, in which there is usually a one-bit error in one erroneous symbol. When assigning values to symbols in a cycle, our improved FRC condition not only considers rank deficiency, but also prefers values with the smallest probability that the related checks are mistakenly satisfied due to one-bit errors in these symbols. Finally, we present the IFRC-based optimization algorithm performs row-wise optimization on the non-zero elements of the parity-check matrix. Simulation results show the effectiveness of IFRC compared to FRC: the error-correcting performance is improved by 0.1dB to 0.5dB, and the error floor can be reduced by up to an order of magnitude.