Comments on "A lower bound on the minimum Euclidean distance of trellis-coded modulation schemes"

Commentson a paper by Rouanne and Costello Jr. (IEEE Trans. Inform. Theory, vol.34, p.1011-20, 1988). It is shown that the derivation in the above paper is incorrect and hence the lower bound obtained is not valid for general trellis-coded modulation schemes. A corrected bound is presented to remedy this flaw. Also shown is a similar lower bound derived from the average distance structure. Both bounds have similar asymptotic behavior and are linear in the constraint length. Unfortunately, they are bad and not very useful for short and medium constraint lengths. The present author points out that there is still much room for further research in finding a good lower bound on the maximal minimum distance for trellis-coded modulation schemes.<>