Geometric representation of the tree-search detector

Fixed-delay tree search with decision feedback (FDTS/DF) has been proposed for retrieving data from hard disk drives. One problem with the algorithm as originally posed is the large number of serial operations that must be performed during one clock cycle. The authors explore the decision space in FDTS/DF using linear discriminants, which leads to a geometric depiction of the decision space. For channels with a d=0 minimum runlength constraint the number of serial computations reduces to one multiplication and one addition. More importantly, though, on high density channels with a d=1 minimum runlength constraint, the detector can be implemented as a multilevel decision feedback equalizer