高码率多进制LDPC码在AWGN信道中的性能分析

Performance Analysis of High-rate Non-binary LDPC Codes Under AWGN Channels

为了解决多进制LDPC码原有译码算法复杂度较高,不利于硬件实现的问题,研究了多进制LDPC码的2种简化译码算法：基于快速傅里叶变换的信度传播译码算法（FFT-BP）和基于对数运算的Log-BP译码算法.同时分析了基于这2种译码算法的高码率（1/2～1）多进制LDPC码在AWGN信道中的性能优势.仿真结果表明：当多进制LDPC码采用这2种不同的译码算法时,随着码率的下降,编码增益和性能曲线与香农限的距离都会随之而增大,即多进制LDPC码适合于高码率情况下的应用.并在牺牲一定的信噪比时,Log-BP算法能够使多进制LDPC码的硬件复杂度得到较大的改善.

To solve the problem of high computational complexity and inconvenient for hardware implementation in original decoding algorithm for non-binary LDPC codes, two simplified decoding algorithms are introduced 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. The performance comparison between 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 by the decreasing of code rate, both coding gains and the distances from Shannon limit increase with the two algo- rithms, which means that non-binary LDPC Codes are suit for applications at high rates. Meanwhile it is shown that Log -BP decoding algorithm may contribute a considerable improvement in computational complexity at the cost of sacrificing some performance, which is important for Log - BP decoding algorithm to be applied in hardware implementation.