# COSET codes for partial response; or, codes with spectral nulls

Journal Article

Summary form only given, as follows. Known coset codes are adapted for use on partial response channels or to generate signals with spectral nulls. By use of methods of coset precoding and running digital sum feedback, any desired tradeoff can be achieved between the power and spectra of the relevant sequences, up to the optimum tradeoff possible. A fundamental theorem specifying this optimum tradeoff is given. An MLSE decoder for the original code may be used for the adapted code, and such a decoder then attains the minimum squared distance of the original code. These methods sometimes generate codes with greater minimum squared distance than that of the original code, which can be attained by augmented decoders, although such decoders inherently require long decoding delays and may be subject to quasi-catastrophic error propagation. The general conclusion is that, at least for sequences that support large number of bits per symbol, one can obtain the same kinds of performance and complexity on partial response channels, or for sequences with spectral nulls, as can be obtained with the same coset codes in the ordinary memoryless case.

### Duke Authors

### Cited Authors

- Forney, GD; Calderbank, AR

### Published Date

- December 1, 1988

### Volume / Issue

- 25 n 13 /

### Start / End Page

- 141 -

### Citation Source

- Scopus