The I/O permutations for a 3D PFA solution are solved in a manner similar to the 2D case as shown in the following figure. Essentially, the modulo computations are extended to include a third dimension, and three modulo-inverses are required to solve for the output permutation. These permutations can be expressed in a 3D matrix form, or as a 1D address permutation \(P_i\) or \(P_o\). The 1D formulation is preferred as it matches how the design is implemented in hardware.