Matched spectral-null codes for partial-response channels

A new family of codes that improve the reliability of digital communication over noisy, partial-response channels is described. 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-null sequences provide a distance gain on the order of 3 dB and higher for a broad class of partial-response channels. The embodiment of the system incorporates a sliding-block code and a Viterbi detector based upon a reduced-complexity trellis structure. The detectors are shown to achieve the same asymptotic average performance as maximum-likelihood sequence detectors, and the sliding-block codes exclude quasi-catastrophic trellis sequences in order to reduce the required path memory length and improve worst-case detector performance. Several examples are described in detail.