Linearization Method and Linear Complexity

We focus on the relationship between the linearization method and linear complexity and show that the linearization method is another effective technique for calculating linear complexity. We analyze its effectiveness by comparing with the logic circuit method. We compare the relevant conditions and necessary computational cost with those of the Berlekamp-Massey algorithm and the Games-Chan algorithm. The significant property of a linearization method is that it needs no output sequence from a pseudo-random number generator (PRNG) because it calculates linear complexity using the algebraic expression of its algorithm. When a PRNG has n [bit] stages (registers or internal states), the necessary computational cost is smaller than O(2n). On the other hand, the Berlekamp-Massey algorithm needs O(N2) where N ( 2n) denotes period. Since existing methods calculate using the output sequence, an initial value of PRNG influences a resultant value of linear complexity. Therefore, a linear complexity is generally given as an estimate value. On the other hand, a linearization method calculates from an algorithm of PRNG, it can determine the lower bound of linear complexity.

Design of a Frequency Divider with Reduced Complexity Based on a Resonant Tunneling Diode

A novel edge-triggered D-flip-flop based on a resonant tunneling diode (RTD) is proposed and used to construct a binary frequency divider. The design is discussed in detail and the performance of the circuit is verified using SPICE. Relying on the nonlinear characteristics of RTD, we reduced the number of components used in our DFF circuit to only half of that required using conventional CMOS SCFL technology.