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Sat Jun 28 12:52:36 CEST 2008

symmetric 2D LFSR

For a 2D LFSR grid, the problem to solve is rotation
ambiguity. Instead of using an LFSR generator for each direction, use
2 like in the 1D case, but tile them such that the structure is
rotation-symmetric. I.e. for N=3 the 4 LFSR are wrapped as:

X+     Y+     X-     Y-
1 2 3  3 6 9  9 8 7  7 4 1
4 5 6  2 5 8  6 5 4  8 5 2
7 8 9  1 4 7  3 2 1  9 6 3

Analogous to before, this gives 5N^2-4D equations and 4N^2 unknowns,
leading to the solvability condition:

                    N^2 >= 4D 

This looks like a nice idea, but using a 6x6 estimator for D=15 gives
underdetermined equations.. Apparently, there is some information lost
in the XOR. 

Intuition: do something like this in |R and you might reduce
condition, but it is hard to get to linear dependence. In a finite
space it is a lot easier to end up with linear dependence because
there is less room.



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