多输出外部反馈型LFSR均匀分布随机数生成器的分析与设计

Multi-output Fibonacci Type LFSR Based Uniform Random Number Generator:Design and Analysis

本文系统地分析了多输出外部反馈LFSR方法产生均匀分布随机数的工作原理、变换矩阵的特点、产生随机数的周期以及LFSR的级数选择等问题,并提出了基于多输出外部反馈LFSR方法设计均匀分布随机数生成器的具体步骤。本文在Xilinx Vertex Ⅳ FPGA上设计实现的23级16位输出的LFSR型均匀分布随机数生成器仅消耗了36个Slices资源和23个Flip Flops资源,工作频率可以达到993MHz,相对于多LFSR复用的实现方式,节约了90%以上的硬件资源。并且,该生成器产生的随机数可以通过K-S检测方法的质量评估。

Firstly, we analyze the principle of the multi-output Fibenacci type LFSR method, including the characteristics of the transformation matrix, the period of the output random numbers and the selection of the number of the stages. Then, we give the design procedure of how to design a multi-output Fibonacci type LFSR based uniform random number generator （URNG）. Finally, we design a 16-output-of-23-stages LFSR based URNG which occupies only 36 slices and 23 flip flops and whose frequency is as high as 993MHz. Compared to multi LFSRs based URNG, our design saves more than 90% hardware devices. At last, we evaluate the quality of the generated random numbers with K-S method and get very good result.