Multidimensional signal processing and detection for storage systems with data-dependent transition noise

Abstract

In the last decade, significant research on detection algorithms capable of mitigating the effects of colored Gaussian thermal noise and transition noise in storage systems, has been performed. In this paper, we present a new detection scheme based on a multidimensional detector front end and multidimensional linear prediction, applied to maximum a posteriori probability (MAP) sequence detection. This method improves the bit-error-rate (BER) performance with respect to previous approaches and makes the detector quite insensitive to transition noise. We show that the gain in terms of BER versus signal-to-noise ratio with our detector increases with the user density. The results obtained for a magnetic storage channel are extendable to optical storage systems as well.Index Terms-Longitudinal and perpendicular recording, magnetic storage systems, multidimensional linear prediction, multidimensional signal processing, optical storage systems, transition noise.

Oversampled Detector for Transition-Noise-Limited Digital Storage Systems

“…In [5], [6] it was shown that, in the presence of transition noise, the need for statistical sufficiency yield a detector front-end with a number of filters proportional to the modeling order of the transition noise: this approach, together with multidimensional linear prediction, was applied to MAP sequence detection and the improvement in terms of Signal-to-Noise Ratio (SNR) with respect to a conventional detector, shown in Fig. 2, was demonstrated by bit error rate simulations.…”

“…We now derive a new set of sufficient statistics, different from those proposed in [5], [6], and suggest a decoding algorithm based on this new quantities. First, it is possible to observe that the noiseless signal…”

“…Note that, for a given value of ν, the number of prediction coefficients changes with respect to the number of past samples, indexed by , defined in the conditioning event and that the prediction coefficients are data-dependent [5], [6]. The solution of the Wiener-Hopf matrix equation for linear prediction based on an oversampled observable will be presented in Section V.…”

“…Note finally that a similar approach was used in [5], [6], where a different set of sufficient statistics yields a detector with a multidimensional front-end and the detection strategy yields a formulation of a multidimensional linear estimate: the approach in this article can be viewed as multidimensional linear prediction applied not in space as in [5], [6] but in time.…”

“…In this paper the position jitter and width variation model [3], [4] is used. Based on this channel model, a multidimensional detection front-end based on a number of filters proportional to the modeling order of the transition noise was presented in [5], [6]. Extending previous work on optimal prefiltering [7], we now propose a new set of sufficient statistics which can be extracted from the continuous read back waveform at the output of the channel by means of oversampling.…”