Graph-Based Channel Detection for Multitrack Recording Channels

Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2008, Article ID 738281, 9 pages doi:10.1155/2008/738281 Research Article Graph-Based Channel Detection for Multitrack Recording Channels Jun Hu,1 Tolga M. Duman,2 and M. Fatih Erden3 1 Qualcomm Inc., San Diego, CA 92121, USA 2 Electrical Engineering Department, Ira A. Fulton School of Engineering, Arizona State University, Tempe, AZ 85287-5706, USA 3 Seagate Technology, Pittsburgh, PA 15222-4215, USA Correspondence should be addressed to Tolga M. Duman, Received 26 March 2008; Accepted 28 November 2008 Recommended by Geert Leus We propose a low complexity detection technique for multihead multitrack recording systems. By exploiting sparseness of twodimensional partial response (PR) channels, we develop an algorithm which performs belief propagation (BP) over corresponding factor graphs. We consider the BP-based detector not only for partial response channels but also for more practical conventional media and bit-patterned media storage systems, with and without media noise. Compared to the maximum likelihood detector which has a prohibitively high complexity that is exponential with both the number of tracks and the number of intersymbol interference (ISI) taps, the proposed detector has a much lower complexity and a fast parallel structure. For the multitrack recording systems with PR equalization, the price is a small performance penalty (less than one dB if the intertrack interference (ITI) is not too high). Furthermore, since the algorithm is soft-input soft-output in nature, turbo equalization can be employed if there is an outer code. We show that a few turbo equalization iterations can provide significant performance improvement even when the ITI level is high. Copyright © 2008 Jun Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. INTRODUCTION In the past few years, magnetic recording systems have seen great breakthroughs both in fabrication techniques and in the development of signal processing algorithms. As recording densities increase, data recovery processes become more complicated. Due to the reduction of island separations in both along-track and cross-track directions, the amount of intersymbol interference (ISI) and intertrack interference (ITI) increases rapidly which potentially results in significant degradations in the performance of traditional systems. In addition, the implementation of timing and gain control becomes more difficult. Multihead multitrack recording represents a promising direction to improve detection capabilities with increased recording densities. Such methods not only offer a better performance by suppressing the ITI and ISI efficiently but also increase efficiency in control information overhead. So far, multihead multitrack recording has been proposed in the context of conventional media recording systems, and several studies have been reported [1–11]. Due to the “superparamagnetic effect,” conventional media storage systems have approached their maximum achievable recording densities. To further extend this storage density limit, several new technologies have been proposed recently, among which patterned media recording [12–19] has attracted a significant interest due to its potential to achieve ultrahigh recording densities. In this paper, we deal with general multihead multitrack recording systems, however, we also pay special attention to their use for patterned media recording systems. A major concern on multihead multitrack recording is the exploitation of its benefits while maintaining a reasonable computational complexity. It is well known that the optimal maximum likelihood (ML) detector [1, 2] for this system has a complexity exponential with both the number of tracks and the number of ISI taps. Even with a modest number of tracks, the resulting computational complexity of a multidimensional Viterbi algorithm becomes prohibitively high. Therefore, the development of low complexity alternatives is necessary. In the literature, there are several approaches to 2 EURASIP Journal on Advances in Signal Processing solve this problem. For example, detection can be performed iteratively on rows and columns of the 2D ISI channel [20], or as an alternative, one can consider a simplified trellis, either by reducing the number of states [8], or by reducing the number of branches per state [10, 11]. In this paper, instead of using a multidimensional Viterbi algorithm, we consider the detection problem from a different perspective and develop an efficient algorithm for multitrack systems with an acceptable computational complexity. To this end, we propose to use belief propagation (BP) [21, 22] to perform inference on factor graphs of multihead multitrack recording channels. This idea has been recently applied to generalized 2D ISI channels and it is shown that the detection performance is poor for very loopy channel conditions [23]. Meanwhile, an enhanced BP detector is proposed to achieve near optimal performance with some complexity increase. Here, we note that although the proposed detector is not optimal in general, it suffers from only a small performance penalty at low to medium ITI levels for multitrack recording with PR equalization. At the same time, due to the inherent sparseness of the channel, the detector maintains a low complexity and a fast parallel structure. It is applicable to both conventional and bit-patterned media storage systems. In our development, instead of working on 2D multitrack recording channels directly, we consider channel detection over an equivalent 1D channel. Furthermore, since the detector is soft-input soft-output in nature, we also consider turbo equalization to further improve the data recovery performance, which has also been considered in [24, 25] for 2D ISI channels with different detection algorithms. The rest of the paper is organized as follows. In Section 2, we introduce the system model. In Section 3, we discuss the equivalent 1D channel model and develop the BP-based detection algorithm. Performance evaluations for different channels are illustrated and discussed in Section 4. Finally, some remarks are presented in Section 5 to conclude the paper. 2. SYSTEM MODEL We consider a multihead multitrack recording system with an array of NR heads flying over NT adjacent tracks. For each group of NT tracks, there are two guard bands (no information written) on each side. The signal read by the rth head is given by yr (t) = NT  +∞  s=1 i=−∞ xsi gr,s (t − iT) + nr (t), 1 ≤ r ≤ NR , (1) where xsi is the ith bit stored on the sth track with the value {+1/ − 1}, gr,s (t) is the channel response incorporating both ISI and ITI (from the sth track to the rth head), and the noise nr (t) is assumed to be additive white Gaussian wi (...truncated)