Correlation analysis of random number sequences based on pseudo random binary sequence generation

摘要

In this paper, the hardware structural correlation effects associated with digit pick-off positions on a maximal length linear feedback shift register (LFSR) in random number (RN) generation, based on a pseudorandom binary sequence (PRBS), are examined using the RN autocorrelation function (ACF). The ACF of the RN codeword sequence is derived analytically from the known noise-like autocorrelation property of the parent PRBS and is then employed to elucidate any structural deficiencies in the choice of digit pickoff points made from the underlying LFSR. Various permutations of the LFSR pickoff selection in the binary code weight assignment for RN construction are examined in the search of an optimal RN spike-like ACF akin to that for a PRBS. Results are presented for ACF evaluation for different binary weight pickoff topologies using RN simulation from a parent PRBS stream, which are in excellent agreement with theoretical calculations.