Author name / Procedia Engineering 00 (2011) 000–0001
A Novel Iterative Detection Method for Four-Grain Based Two-Dimensional Magnetic Recording
T. Losuwana,e1, C. Warisarna,e2, S. Koonkarnkhaib,e3, P. Kovintavewatb,e4
aCollege of Data Storage Innovation, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand
bData Storage Technology Research Center, Nakhon Pathom Rajabhat University, Nakhon Pathom, Thailand
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Abstract
Two-dimensional magnetic recording (TDMR) is one of a novel magnetic recording technology that has been proposed to increase a storage densitybeyond 10 Tb/in2[1]. However, at high areal densities, the readback signal is extremely corrupted from both the inter-symbolinterference (ISI) and the inter-track interference (ITI). This problemcan be alleviated by utilizing anadvanced iterative decodingtechnique to decode data. This paper proposes a novel iterative decoding technique that cooperates between theiterative detectorsand the iterative decoder to combat the severeISI/ITI. Simulation results show that the proposed technique can reduce the ISI/ITI effect and provides a significant performance improvement in terms of bit-error rate if compared to the conventional receiver, which employs a non-iterative detector.
Keywoads: Areal density, Iterative detector, Multi-track 2D-SOVA, Two-dimensional magnetic recording (TDMR)
1. Introduction
Currently, hard disk drives (HDDs) use a perpendicular magnetic recording (PMR) technology to store data bits. However, the storage capacity based on this PMR technology will shortly reach its limit at about 1 Tb/in2,known as a super-paramagnetic limit. Several new technologies have been proposed to increase a storage capacity of HDDs. Among these technologies, two-dimensional magnetic recording (TDMR) is an attractive choice because it can achieve the storage capacityup to 10 Tb/in2 by storing one data bit using few grains in a magnetic medium, which an ultimate goal of storing one data bit per one grain. However, at this high areal density,the TDMR system cannot circumvent the severe intersymbol interference (ISI) and intertrack interference (ITI). Therefore, we purpose a novel iterative decoding technique that utilizes theiterative detectors and the iterative decoder to combat this sever ISI/ITI.
2. Channel Model
Figure 1 illustrates theTDMR systembased ona four-grain channel model. A message input sequence of a main track is encoded by a low-density parity-check (LDPC) code, while the closet two adjacent tracks (i.e., and ) do not need to be encoded (because we are interested in decoding data in the main track). The readback signal v(x,y) can be then expressed as
Fig.1.A TDMR channel model.
/ (1)wherex is an along-track direction, y is an cross-track direction,m(x, y) {1} is medium magnetization, h(x,y) the reader sensitivity function [2], is additive white Gaussian noise (AWGN).
The readback signalis filtered by a seventh-order Butterworth low-pass filter (LPF) and is sampled at time t = kT, assuming perfect synchronization. The readout data sequence is assumed to be recoveredsimultaneously from the readback signals of the three tracksvl(x,y), where l is the lth-track. The read out data sequence, is equalized by a 2D equalizer. Finally, the sequence is fed to a turbo equalizer, which iteratively exchanges soft information between the iterative 2D-SOVA detectors and the LDPC decoder.
3. Proposed Method
Practically, a conventional 2D-SOVAdetector [3]does not directly exchanges soft information with adjacent 2D-SOVA detectors. Here, we propose the iterative 2D-SOVA detectors, which consist of three 2D-SOVA detectors, one for each track. Then, these three 2D-SOVA detectors will exchange soft information among them for a pre-determined round before sending soft information to the LDPC decoder. The detail on how the proposed iterative decoding scheme works is given below.
Turbo loop (N=3)
SOVA loop(NSOVA = 3)
1st iteration: All SOVA’s receive thesequences for all tracks and then perform thefirst log-likelihood ratio (LLR) estimatewithout using a prioriprobability (assumed to be zero).
2nd iteration: SOVA I and SOVA III perform the second LLR estimate with assistance from a priori probability
obtained from SOVA II (during the first iteration)and themselves.
3rd iteration: SOVA II performsthe third estimateusing a prioriprobability obtainedfrom SOVA I, SOVA III, and itself.
End
LDPC loop (Nin=3)
LDPC decoder performsthe sum of product algorithmusing only soft information obtained from SOVA II.
End
End
4. Numerical Result
We consider a rate of 0.89 coded systems in which a block of 3638 message bits is encoded by an LDPC encoder, resulting in a coded block length of 4066 bits. The signal-to-noise ratio (SNR) is defined as , where A is a saturation level of an isolated pulse [2], and is standard deviation of AWGN. Each BER point is computed using as many 4066-bit data sectors as needed to collect 500 error bits, whereas the equalizer taps is designed using only one data sector. Figure 2 compares the BER performance of different detection as a function of SNRs, where “Conv-Iteration” and “Prop-Iteration” denote the conventional and the proposed iteration schemes, respectively. Note that the number inside the parenthesis in Fig. 2represents the total number of turbo iterations required to generate each curve. It is apparent that the proposedscheme provides better performance than the conventional scheme.
Fig. 2 BER performance of different schemes at 2.37 Tb/in2
5. Reference
[1]Wood R., Williams M., Kavcic A., and Miles J., “The feasibility of magnetic recording at 10 terabits per square inch on conventional media,” IEEE Trans. Magn., vol. 45, no. 2, pp. 917–923, Feb. 2009.
[2]Yamashita M., Osawa H., Okamoto Y., Nakamura Y., Suzuki Y., Miura K., and Muraoka H., “Read/Write Channel Modeling and Two-Dimensional Neural Network Equalization for Two-Dimensional Magnetic Recording,” IEEE Trans. Magn., vol. 47, no. 10, pp. 3558–3561, Oct. 2011
[3]Koonkarnkhai S., Keeratiwintakorn P., Chirdchoo N., and Kovintavewat P., “Two-Dimensional Cross-Track Asymmetric Target Design for High-Density Bit-Patterned Media Recording,” in Proc. of ISPACS 2011, Chiang Mai, Thailand, December 7 – 9, 2011.