Bi-directional linear feedback shift register

Abstract

A unified bi-directional LFSR is fabricated from latches having dual (Forward and Reverse) inputs. Each such latch accepts its inputs upon receipt of a clock signal that is respectively associated with the forward or reverse direction. The appropriate collection of XOR gates exists between latch outputs and the inputs associated with a forward clock signal, so as to produce the forward sequence. Likewise, another appropriate collection of XOR gates exists between the latch outputs and the inputs associated with the reverse clock signal. To produce a 'reverse' LFSR corresponding to the polynomial that is the reciprocal of the polynomial for the 'forward' LFSR, the latches of the reciprocal (reverse direction) LFSR are construed as being numbered in the opposite order. That is, a single set of latches (register) has both a forward linear feedback network and a reverse linear feedback network. Only one of these two feedback networks is used at a time, but they can intermix forward and reverse steps and appear to index back and forth along the native sequence of the LFSR. That is, steps in reverse undo the most recent forward steps, and vice versa. The bi-directional LFSR is also equipped with a way to preset the latches to a preselected initial value, and it is compatible with the production of all zeros. This last feature is obtained by including an extra latch in the register �(n+1)-many latches for a desired n-many bit word! and using it as a valid bit to qualify as correct the remaining latches in the register.