Though hard to visualize in multiple dimensions, a simple one-dimension example illustrates the basic procedure. Suppose the symbols are located at 2, 3, 4, ... Place all odd symbols in one group, and all even symbols in the second group. (This is not quite accurate, because Ungerboeck was looking at the two dimensional problem, but the principle is the same.) Take every other symbol in each group and repeat the procedure for each tree limb. He next described a method of assigning the encoded bit stream onto the symbols in a very systematic procedure. Once this procedure was fully described, his next step was to program the algorithms into a computer and let the computer search for the best codes. The results were astonishing. Even the most simple code (4 state) produced error rates nearly one one-thousandth of an equivalent uncoded system. For two years Ungerboeck kept these results private and only conveyed them to close colleagues. Finally, in 1982, Ungerboeck published a paper describing the principles of trellis modulation.