Page "Trellis modulation" Paragraph 3

The name trellis was coined because a state diagram of the technique, when drawn on paper, closely resembles the trellis lattice used in rose gardens.

The scheme is basically a convolutional code of rates ( r, r + 1 ).

Ungerboeck's unique contribution is to apply the parity check on a per symbol basis instead of the older technique of applying it to the bit stream then modulating the bits.

The key idea he termed Mapping by Set Partitions.

This idea was to group the symbols in a tree like fashion then separate them into two limbs of equal size.

At each limb of the tree, the symbols were further apart.

Although hard to visualize in multi-dimensions, a simple one dimension example illustrates the basic procedure.

Suppose the symbols are located at 2, 3, 4, .... Then take all odd symbols and place them in one group, and the 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 one for 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.