基于原型图的低码率LDPC码最小和译码算法改进方案

低密度奇偶校验(LDPC)码的译码硬件实现方案大多采用计算复杂度较低的修正最小和(NMS)算法，然而对于低码率LDPC码，由于校验节点度数低，NMS算法的修正误差较大，导致其译码性能和标准的置信传播(BP)算法相比有较大差异。该文针对基于原图构造的一类低码率LDPC码，提出了在NMS迭代译码中结合震荡抵消(OSC)处理和多系数(MF)修正技术的方案。结合低码率原型图LDPC码行重分布差异较大的特点，MF修正算法可以有效地减少计算误差，从而改善译码性能。另外低码率原型图LDPC码的收敛较慢，而OSC处理则可以较好地抑制正反馈信息，进一步提高NMS算法的性能增益。仿真结果表明，对于此类低码率LDPC码， MF-OSC-NMS算法可以达到接近BP算法的性能。OSC处理和MF修正技术硬件实现简单，与NMS算法相比几乎没有增加计算复杂度，因此MF-OSC-NMS算法是译码算法复杂度和性能之间一个较好的折中处理方案。

An Improvement on the Min-sum Algorithm for Low-rate Protograph LDPC Codes

The Normalized Min-Sum (NMS) algorithm can be implemented with low complexity and is widely used in the LDPC decoders, but there is a significant performance gap between the Belief Propagation (BP) algorithm and NMS algorithm for low-rate LDPC codes due to the inaccurate approximations of the check-nodes with low weight. In this paper, an improved NMS algorithm combined with the Oscillation (OSC) correction of bit-node updating and Multiple Factors (MF) modification of check-node updating is proposed. Although the row weights of the low-rate protograph LDPC codes may vary considerably, the error of the approximation in check-node updating can be effectively reduced by MF modification. Moreover, the OSC correction can reduce the positive feedback and achieve furthermore improvement on the decoding performance of low-rate protograph LDPC codes, where the decoding convergence is slow. Simulation results show that the OSC-MF-NMS algorithm can obtain a noticeable performance gain in decoding of low-rate protograph LDPC codes. The complexity of the OSC and MF process is quite low, so the proposed algorithm is a good trade-off between the decoding complexity and error performance.