# BINARY CONVOLUTIONAL CODES WITH APPLICATION TO MAGNETIC RECORDING.

Journal Article

Motivated by an idealized model of the magnetic recording channel, codes were designed for a partial response channel with transfer function (1-D**N)/2 where the channel inputs are constrained to be plus or minus 1. Channel inputs are generated using a nontrivial coset of a binary convolutional code called the sign code. The probability of decoder error is determined by the minimum squared Euclidean distance between outputs corresponding to distinct inputs. This Euclidean distance is bounded below by the free distance of a second binary convolutional code called the magnitude code. The coset of the sign code is chosen to limit the zero-run length of the output of the channel and so maintain clock synchronization. The performance of rate k/k plus 1) codes on the (1-D)/2 and (1-D**2 )/2 channels was analyzed. It was found that magnitude codes that are catastrophic may perform better than those that are noncatastrophic.

### Duke Authors

### Cited Authors

- Calderbank, AR; Heegard, C; Lee, TA

### Published Date

- 1986

### Published In

- Ieee Transactions on Information Theory

### Volume / Issue

- IT-32 / 6

### Start / End Page

- 797 - 815