Noise-Predictive Maximum-Likelihood (NPML) is a class of digital signal-processing methods suitable for magnetic data storage systems that operate at high linear recording densities. It is used for retrieval of data recorded on magnetic media.
Data are read back by the read head, producing a weak and noisy analog signal. NPML aims at minimizing the influence of noise in the detection process. Successfully applied, it allows recording data at higher areal densities. Alternatives include peak detection, partial-response maximum-likelihood (PRML), and extended partial-response maximum likelihood (EPRML) detection.
Although advances in head and media technologies historically have been the driving forces behind the increases in the areal recording density, digital signal processing and coding established themselves as cost-efficient techniques for enabling additional increases in areal density while preserving reliability. Accordingly, the deployment of sophisticated detection schemes based on the concept of noise prediction are of paramount importance in the disk drive industry.
Principles
The NPML family of sequence-estimation data detectors arise by embedding a noise prediction/whitening process into the branch metric computation of the Viterbi algorithm. The latter is a data detection technique for communication channels that exhibit intersymbol interference (ISI) with finite memory.
Reliable operation of the process is achieved by using hypothesized decisions associated with the branches of the trellis on which the Viterbi algorithm operates as well as tentative decisions corresponding to the path memory associated with each trellis state. NPML detectors can thus be viewed as reduced-state sequence-estimation detectors offering a range of implementation complexities. The complexity is governed by the number of detector states, which is equal to , , with denoting the maximum number of controlled ISI terms introduced by the combination of a partial-response shaping equalizer and the noise predictor. By judiciously choosing , practical NPML detectors can be devised that improve performance over PRML and EPRML detectors in terms of error rate and/or linear recording density.
In the absence of noise enhancement or noise correlation, the PRML sequence detector performs maximum-likelihood sequence estimation. As the operating point moves to higher linear recording densities, optimality declines with linear partial-response (PR) equalization, which enhances noise and renders it correlated. A close match between the desired target polynomial and the physical channel can minimize losses. An effective way to achieve near optimal performance independently of the operating point—in terms of linear recording density—and the noise conditions is via noise prediction. In particular, the power of a stationary noise sequence , where the operator corresponds to a delay of one bit interval, at the output of a PR equalizer can be minimized by using an infinitely long predictor. A linear predictor with coefficients ,..., operating on the noise sequence produces the estimated noise sequence . Then, the prediction-error sequence given by
is white with minimum power. The optimum predictor
...
or the optimum noise-whitening filter
,
is the one that minimizes the prediction error sequence in a mean-square sense
An infinitely long predictor filter would lead to a sequence detector structure that requires an unbounded number of states. Therefore, finite-length predictors that render the noise at the input of the sequence detector approximately white are of interest.
Generalized PR shaping polynomials of the form
,
where is a polynomial of order S and the noise-whitening filter has a finite order of , give rise to NPML systems when combined with sequence detection In this case, the effective memory of the system is limited to
,
requiring a -state NPML detector if no reduced-state detection is employed.
As an example, if
then this corresponds to the classical PR4 signal shaping. Using a whitening filter , the generalized PR target becomes
,
and the effective ISI memory of the system is limited to
symbols. In this case, the full-state NMPL detector performs maximum likelihood sequence estimation (MLSE) using the -state trellis corresponding to .
The NPML detector is efficiently implemented via the Viterbi algorithm, which recursively computes the estimated data sequence.
where denotes the binary sequence of recorded data bits and z(D) the signal sequence at the output of the noise whitening filter .