Transition noise is known to be a major cause of errors for high densi
ty magnetic recordings This noise is signal dependent and can be model
ed as multiplicative noise in a linear channel model. Maximum-likeliho
od method was not considered for detection of signals in such noise in
the past. In this study, a detector model for an asymptotic maximum-l
ikelihood (AML) detection is developed for systems with such noise. Ba
sed on a linear partial response channel model, a recursive procedure
is obtained as a tree search algorithm, leading to the maximum likelih
ood detection asymptotically, as the tree-search depth is increased. P
erformance estimation will be discussed in a separate paper.