Matched spectral-null codes for partial-response channels

A new family of codes is described that improve the reliability of digital communication over noisy, partial-response channels. The codes are intended for use on channels where the input alphabet size is limited. These channels arise in the context of digital data recording and certain data transmission applications. The codes-called matched-spectral-null codes -satisfy the property that the frequencies at which the code power spectral density vanishes correspond precisely to the frequencies at which the channel transfer function is zero. It is shown that matched-spectral-nul1 sequences provide a distance gain on the order of 3 dB and higher for a broad class of partial-response channels, including many of those of primary interest in practical applications. The embodiment of the matched-spectral-null coded partial-response system incorporates a sliding-block code and a Viterbi detector based upon a reduced-complexity trellis structure, both derived from canonical diagrams that characterize spectral-null sequences. The detectors are shown to achieve the same asymptotic average performance as maximum-likelihood sequence-detectors, and the sliding-block codes exclude quasicatastrophic trellis sequences in order to reduce the required path memory length and improve “worst-case” detector performance. Several examples are described in detail. Index Terms -Spectral-null codes, partial-response channels.