摘要： 针对求解GF(2)域的线性方程组问题，改进现有的高斯消元算法，提出一种快速求解未知向量的硬件并行结构，通过增加消元与行循环位移的并行操作以降低时间复杂度，采用一类仿“smart memory”基本单元的互联完成整个算法在硬件上的映射。对结构的性能分析表明，对于密度远大于或小于0.5的n阶二值增广矩阵，并行结构平均计算时间约为2n个时钟周期，远小于软件算法时间(1/4n3)。在 3阶~50阶的二值非稀疏增广矩阵上的实现结果表明，与软件实现相比，该结构的性能可提高约2个数量级。
Abstract: This paper presents an efficient parallel architecture for fast solving linear system of equations over binary operations of GF(2), which is derived from a proposed hardware-optimized Gaussian elimination. The optimization of the Gaussian elimination with pivot element is realized by using parallel elimination and cyclic shift operations instead of loop nest in each iteration. A mesh structure of “smart memory” cells is proposed for building the whole parallel architecture where the modified algorithm is mapped onto. The average running time of the architecture for n-dimension binary matrix equals 2n cycles as opposed to about 1/4n3 in software. Experimental results show that the performance of the system is improved by about two orders of magnitude.
linear system of equations,
hardware-optimized Gaussian elimination