Performance Advantage of Non-binary LDPC Codes At High Code Rate under AWGN Channel

Two different decoding algorithms for non-binary LDPC codes: the fast Fourier transform belief propagation (FFT-BP) decoding algorithm and the Log-domain belief propagation (Log-BP) decoding algorithm are introduced in this paper. Their performance advantage of two different decoding algorithms for LDPC Codes over GF(q) is investigated at high code rates (1/2~1) over AWGN channel. The performance curves show that with the decreasing of code rate, both coding gains and the distances from Shannon limit increase under the two algorithms, which means for non- binary LDPC Codes to be suitable for applications at high rates. Meanwhile it is shown that Log-BP decoding algorithm may contribute a considerable saving in computational complexity at the cost of sacrifice small performance, which is important for Log-BP decoding algorithm to be applied in hardware implementation.