LINEAR FEEDBACK SHIFT CALCULATION APPARATUS, COMMUNICATION APPARATUS, MICROPROCESSOR, AND DATA OUTPUT METHOD IN A LINEAR FEEDBACK CALCULATION APPARATUS

摘要

A linear feedback shift calculation apparatus, into which input data is input, and which outputs output data, including: an L generation unit which generates q values of q₀ to q_N−2 represented by:; $$ \begin{array}{cc}{q}_k=\{\begin{array}{cc}{p}_0& \left(k=0\right)\\ p_k+\sum _{i=0}^{k-1}q_{k-1-i}\times p_i& \left(1\le k\le N-2\right)\end{array}& \mathrm{Equation}1\end{array}$$ ;(where, p₀, p₁, . . . , p_N−1, q₀, q₁, . . . , q_N−2 belong to Galois field GF(2)) from coefficients p₀ to p_N−2 among inputted coefficients p₋₁ to p_N−1 (wherein, N is a natural number of 2 or more); and a matrix calculation unit which outputs the output data calculated from the output data b₀ to b_N−1 represented by:; $$ \begin{array}{cc}\left(\begin{array}{c}{b}_{N-1}\\ b_{N-2}\\ ⋮\\ b_o\end{array}\right)=L\times \left(U\times \left(\begin{array}{c}{a}_{N-1}\\ a_{N-2}\\ ⋮\\ a_0\end{array}\right)+p_{-1}\times \left(\begin{array}{c}{a}_{-1}\\ a_{-2}\\ ⋮\\ a_{-N}\end{array}\right)\right)& \mathrm{Equation}2\\ \mathrm{and}& \\ L=\left(\begin{array}{cccccc}1& 0& \dots & 0& 0& 0\\ q_0& 1& 0& \dots & 0& 0\\ q_1& q_0& 1& 0& \dots & 0\\ ⋮& & \ddots & \ddots & \ddots & ⋮\\ q_{N-3}& q_{N-4}& \dots & q_0& 1& 0\\ q_{N-2}& q_{N-3}& \dots & q_1& q_0& 1\end{array}\right)U=\left(\begin{array}{cccccc}{p}_{N-1}& p_{N-2}& \dots & p_2& p_1& p_0\\ 0& p_{N-1}& p_{N-2}& \dots & p_2& p_1\\ 0& 0& p_{N-1}& p_{N-2}& \dots & p_2\\ ⋮& & \ddots & \ddots & \ddots & ⋮\\ 0& 0& \dots & 0& p_{N-1}& p_{N-2}\\ 0& 0& \dots & 0& 0& p_{N-1}\end{array}\right)& \mathrm{Equation}3\end{array}$$ ;from the q values q₀ to q_N−2, the coefficients p₋₁ to p_N−1 and the input data a_−N to a₋₁, a₀ to a_N−1.