## BINARY CONVOLUTIONAL CODES WITH APPLICATION TO MAGNETIC RECORDING.

Summary form only given. A. R. Calderbank et. al. have suggested a method of designing codes for channels with intersymbol interference, such as the magnetic recording channel. They considered an idealized model of the magnetic recording channel that leads to the problem of designing codes for a partial response channel with transfer function (1 - D**N)/2 where the channel inputs are constrained to be plus or minus 1. This problem is considered here. Channel inputs are generated using a nontrivial coset of a binary convolution code. The coset is chosen to limit the zero-run length of the output of the channel and so maintain clock synchronization. The minimum squared Euclidean distance between outputs corresponding to distinct inputs is bounded below by the free distance of a second convolutional code called the magnitude code. An interesting feature of the analysis is that magnitude codes that are catastrophic may perform better than those that are noncatastrophic.

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*BINARY CONVOLUTIONAL CODES WITH APPLICATION TO MAGNETIC RECORDING.*Dec. 1986, p. 42.