Noise-predictive maximum-likelihood detection

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.

Successfully applied, it allows recording data at higher areal densities.

[1] Although advances in head and media technologies historically have been the driving forces behind the increases in the areal recording density,[citation needed] digital signal processing and coding established themselves as cost-efficient techniques for enabling additional increases in areal density while preserving reliability.

[1] Accordingly, the deployment of sophisticated detection schemes based on the concept of noise prediction are of paramount importance in the disk drive industry.

The NPML family of sequence-estimation data detectors arise by embedding a noise prediction/whitening process[2][3][4] 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.

⁠ denoting the maximum number of controlled ISI terms introduced by the combination of a partial-response shaping equalizer and the noise predictor.

A close match between the desired target polynomial and the physical channel can minimize losses.

⁠ 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.

⁠ in a mean-square sense[2][3][4][5][6] 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.

In this case, the full-state NMPL detector performs maximum likelihood sequence estimation (MLSE) using the

The NPML detector is efficiently implemented via the Viterbi algorithm, which recursively computes the estimated data sequence.

Reduced-state sequence-detection schemes[7][8][9] have been studied for application in the magnetic-recording channel[2][4] and the references therein.

Depending on the surface roughness and particle size, particulate media might exhibit nonstationary data-dependent transition or medium noise rather than colored stationary medium noise.

[1][10][11][12] By modeling the data-dependent noise as a finite-order Markov process, the optimum MLSE for channels with ISI has been derived.

In other words, the optimum MLSE can be implemented efficiently by using the Viterbi algorithm, in which the branch-metric computation involves data-dependent noise prediction.

[11] Because the predictor coefficients and prediction error both depend on the local data pattern, the resulting structure has been called a data-dependent NPML detector.

[1][12][10] Reduced-state sequence detection schemes can be applied to data-dependent NPML, reducing implementation complexity.

NPML and its various forms represent the core read-channel and detection technology used in recording systems employing advanced error-correcting codes that lend themselves to soft decoding, such as low-density parity check (LDPC) codes.

In this way it is possible to iteratively improve the error-rate performance at the decoder output in successive soft detection/decoding rounds.

Beginning in the 1980s several digital signal-processing and coding techniques were introduced into disk drives to improve the drive error-rate performance for operation at higher areal densities and for reducing manufacturing and servicing costs.

In the early 1990s, partial-response class-4[14][15][16] (PR4) signal shaping in conjunction with maximum-likelihood sequence detection, eventually known as PRML technique[14][15][16] replaced the peak detection systems that used run-length-limited (RLL) (d,k)-constrained coding.

This development paved the way for future applications of advanced coding and signal-processing techniques[1] in magnetic data storage.

NPML detection was first described in 1996[4][17] and eventually found wide application in HDD read channel design.

[18][19][20] Noise prediction became an integral part of the metric computation in a wide variety of iterative detection/decoding schemes.

The pioneering research work on partial-response maximum-likelihood (PRML) and noise-predictive maximum-likelihood (NPML) detection and its impact on the industry were recognized in 2005[21] by the European Eduard Rhein Foundation Technology Award.

[22] NPML technology were first introduced into IBM's line of HDD products in the late 1990s.

[23] Eventually, noise-predictive detection became a de facto standard and in its various instantiations became the core technology of the read channel module in HDD systems.