FPGA Implementation Scheme of Mixed Logarithmic Domain FFT-BP Decoding Algorithm Based on Non-Binary LDPC Codes

In this paper, an improved decoding algorithm for Non-binary low density parity check (NB-LDPC) codes with low decoding complexity and suitable for field-programmable gate array (FPGA) implementation is proposed, which is a mixed logarithmic domain FFT-BP decoding algorithm (Mixed Log-FFT-BP) for the problem of high complexity of the existing decoding algorithms for Non-binary LDPC codes. The algorithm combines the traditional Log-BP algorithm with the FFT-BP algorithm, and simplifies the update of the check nodes in the iterative decoding process. A large number of convolution operations are converted into multiplication operations in frequency domain by using FFT transform and IFFT transform. The multiplication of the original FFT-BP algorithm is converted into the addition and look-up table operations in the logarithmic domain. Then, the logarithm of the probability information is directly solved, so that it can be decoded in the logarithmic domain, which saves the computation of the log likelihood ratio, and then reduces the complexity. Simulation results show that under the additive Gauss white noise channel, when the bit error rate is 10–5, compared with BP algorithm, Log-Bp algorithm and FFT-BP algorithm, the performance of Mixed Log-FFT-BP algorithm is not decreased, and all of them remain within the range of 0.1-0.2dB.