Improved lower bounds on the symbol error probability for ISI channels

A lower bound on the symbol error probability obtained with maximum likelihood sequence detection on the intersymbol interference channel is derived. It is recognised that the bound can be substantially improved by considering every possible transmitted sequence and not only the ones generating the well-known d_min². Also, a method is devised which finds the additive components of the bound using a trellis search. It is demonstrated that for many channels, using a truncated upper bound as a lower bound yields incorrect results. This might be the case even if the upper bound is truncated to its first term corresponding to d_min²