Noise Predictive Maximum Likelihood Research Articles

Pattern-dependent noise prediction in signal-dependent noise

Maximum and near-maximum likelihood sequence detectors in signal-dependent noise are discussed. It is shown that the linear prediction viewpoint allows a very simple derivation of the branch metric expression that has previously been shown as optimum for signal-dependent Markov noise. The resulting detector architecture is viewed as a noise predictive maximum likelihood detector that operates on an expanded trellis and relies on computation of branch-specific, pattern-dependent noise predictor taps and predictor error variances. Comparison is made on the performance of various low-complexity structures using the positional-jitter/width-variation model for transition noise. It is shown that when medium noise dominates, a reasonably low complexity detector that incorporates pattern-dependent noise prediction achieves a significant signal-to-noise ratio gain relative to the extended class 4 partial response maximum likelihood detector. Soft-output detectors as well as the use of soft decision feedback are discussed in the context of signal-dependent noise.

Noise predictive maximum likelihood detection combined with parity-based post-processing

The performance of magnetic recording systems that include conventional modulation codes combined with multiple parity bits is studied. Various performance measures, including bit error rate at the output of time inverse precoder, byte error probability at the input of the Reed-Solomon (RS) decoder and sector error rate, are used to evaluate the performance of various coding/detection schemes. Suboptimum detection/decoding schemes consisting of a 16-state noise-predictive maximum-likelihood (NPML) detector followed by parity-based noise-predictive post-processing, and maximum-likelihood sequence detection/decoding on the combined channel/parity trellis are considered. For conventional modulation codes, it is shown that although the dual-parity post-processor gains 0.5 dB over the single-parity post-processor in terms of bit- and byte-error-rate performance, the sector-error-rate performance of both schemes is almost the same. Furthermore, the sector-error-rate performance of optimum 64-state combined channel/parity detection for the dual-parity code is shown to be approximately 0.1 dB better than that of optimum 32-state combined channel/parity detection for the single-parity code. These performance gains can be even more substantial if appropriate coding techniques that eliminate certain error events and minimize error burst length or multiparity codes in conjunction with combined parity/channel detection are used.

Noise-predictive maximum-likelihood method combined with infinite impulse response equalization

An infinite impulse response (IIR) can closely approximate the high density magnetic recording channel response with only a single pole and a small number of zeros. As a consequence, a near-optimal performance can be achieved with the Viterbi algorithm (VA) incorporating a single-tap noise predictor. The number of states in the VA trellis is determined by the number of zeros used in the IIR modeling of the channel response. The single noise-predictor tap corresponds to the single pole in the IIR model. The overall complexity for a given level of performance is smaller with this approach than with the noise-predictive maximum-likelihood (NPML) method based on conventional partial response equalization.

Noise-predictive maximum likelihood (NPML) detection

Sequence detectors for the digital magnetic recording channel that are based on noise-predictive partial-response equalization are described. Called Noise-Predictive Maximum Likelihood (NPML) detectors, they arise by imbedding a noise prediction/whitening process into the branch metric computation of a Viterbi detector. NPML detectors can be realized in a form that allows RAM table look-up implementation of the imbedded feedback. Alternatively, the noise prediction/whitening mechanism can be implemented as an infinite impulse response (IIR) filter. For a Lorentzian channel with operating points in the range 0.5<PW50/T<3.5, IIR predictors with at most two zeros and two poles offer the best possible performance. Simulation results obtained for Lorentzian channels show that a judicious tradeoff between performance and state complexity leads to practical schemes offering substantial performance gains over both PRML and extended PRML detectors. An important practical advantage of the family of NPML detectors is that they can be conveniently integrated into existing PRML architectures.

Improving performance of PRML/EPRML through noise prediction

Sequence estimation detectors for the digital magnetic recording channel based on noise-predictive partial-response equalization are described. Called noise-predictive maximum-likelihood (NPML) detectors, they imbed a noise prediction/whitening process into the branch metric computation of a Viterbi detector. Simulation results show that a judicious tradeoff between system parameters leads to substantial performance gains over both PRML and EPRML systems. A programmable 8-state NPML detector without decision feedback is presented.