Jr, GDF; Calderbank, AR, *Coset codes for partial response channels; or, coset codes with spectral nulls*,
IEEE Transactions on Information Theory, vol. 35 no. 5
(1989),
pp. 925-943 [doi] .
**Abstract:**

*Known coset codes are adapted for use on partial response channels or to generate signals with spectral nulls. By using 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. A maximum-likelihood-sequence-estimation (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; this distance can be attained by augmented decoders, although such decoders inherently require long decoding delays and may be subjected to quasi-catastrophic error propagation. The authors conclude that, at least for sequences supporting large numbers of bits per symbol, coset codes can be adapted to achieve effectively the same performance and complexity on partial response channels, or for sequences with spectral nulls, as they do in the ordinary memoryless case.*