Graph-Based Channel Detection for Multitrack Recording Channels

Abstract

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.

Investigation of Graph-Based Detection in Iterative Decoding for Bit-Patterned Media Recording

“…The GB detector was proposed in [6] for multi-track recording channels (e.g., BPMR), which exploits the knowledge of the bits from the adjacent tracks in detection process. To do so, the three readback sequences [r k,l-1 , r k,l , r k,l+1 ] are reshaped into a 1D data array with a sequential order before feeding to the GB detector, which employs a message passing algorithm (MPA) [7] over the factor graph designed based on the channel constraint in Eq.…”

“…Let A i denote all the bit nodes connected to the i th factor node, and ĩ j A is equal to A i excluding the j th bit node. To reduce the complexity, the max-log approximation is utilized to compute the LLR for the i th factor node sent to the j th bit node at the n th iteration according to [6] ( ) ( ) ( )…”

“…It should be noted that the complexity of the GB detector is mainly determined by that of the factor node, which is linear with N GB and is exponential with the number of nonzero channel coefficients [6].…”

“…Several works have recently been proposed to overcome the 2D interference in BPMR [1][2][3][4][5][6]. For a single-head BPMR system, Nabavi et al [1] proposed a modified Viterbi detector, whose trellis has three parallel branches between any two connected states, to mitigate the ITI.…”

“…To tackle the ITI problem, Myint et al proposed a partial ITI mitigation (PIMM) method [5] for multi-track processing in iterative detection, which utilizes the estimates of the data on the sidetracks to improve the detection on the center track. Also, Hu et al [6] introduced a graph-based (GB) detector for multi-track processing, which has a much lower complexity and a fast parallel structure if compared to the 2D Viterbi detector [2]. However, this paper proposes to employ the GB detector in iterative decoding for a multi-head multi-track BPMR system.…”