Binary Convolutional Codes with Application to Magnetic Recording

Calderbank, Heegard, and Ozarow [1] have suggested a method of designing codes for channels with intersymbol interference, such as the magnetic recording channel. These codes are designed to exploit intersymbol interference. The standard method is to minimize intersymbol interference by constraining the input to the channel using run-length limited sequences. Calderbank, Heegard, and Ozarow considered an idealized model of an intersymbol interference channel that leads to the problem of designing codes for a partial response channel with transfer function (1-DN)/2, where the channel inputs are constrained to be plus or minus 1. This is the problem we consider here. Channel inputs are generated using a non-trivial coset of a binary convolutional code. The coset is chosen to limit the zero- run length of the output of the channel and so maintain clock synchron- ization. The minimum squared Euclidean distance between outputs corresponding to distinct inputs is bounded below by the free distance of a second convolutional code which we call the magnitude code. An interesting feature of the analysis is that magnitude codes that are catastrophic may perform better than those that are non-catastrophic.