Double-layer magnetic recording with multilayer perceptron decoder for single-reader/two-track reading in BPMR systems

Several magnetic recording technologies have been proposed to transcend the superparamagnetic limit in a current perpendicular magnetic recording (PMR)^1,2 technology. Bit-patterned magnetic recording (BPMR) is one of the promising technologies for the next-generation magnetic recording system, because it can increase an areal density (AD) up to 4.0 tera-bit per square inch (Tb/in.²)¹ by using a patterned medium instead of a granular medium as employed in a conventional PMR technology.

To reach higher ADs, the distance between the bit islands must be moved closer to one another, leading to the two-dimensional (2-D) interference consisting of inter-symbol interference (ISI) and inter-track interference (ITI), which can degrade¹ the overall system performance. Practically, the modulation code³ and a multilayer perceptron (MLP) decoder can be used in a BPMR system^4–6 to cope with the 2-D interference and help improve the performance of the conventional Viterbi-based decoder, respectively. Specifically, the modulation code can prevent the fatal data patterns to be recorded onto a recording medium, thus alleviating the effect of ISI and ITI.

Additionally, to further enhance the storage capacity of a magnetic recording system, three-dimensional (3-D) magnetic recording with double recording layers is attracting much attention as the next-generation reading method.^7–12 For example, Nakamura et al.^11,12 evaluated the 2-D partial-response maximum-likelihood channel and developed the 3-D equalization using a 2-D finite impulse response filter for the 3-D magnetic recording system with a double-layer magnetic recording medium, which can provide a good bit-error rate (BER) performance. Aboutaleb et al.¹³ introduced the use of convolutional neural networks for equalization and detection in a double-layer magnetic recording system, which can help improve the performance of the conventional linear equalizer and the trellis-based detector in the presence of pattern-dependent media noise and jitter noise.

Nonetheless, this paper focuses on the double-layer magnetic recording under a single-reader/two-track reading (SRTR) staggered-array BPMR system, which is performed together with the rate-3/5 modulation code.³ Then, we propose to utilize the MLP to decode and estimate the log-likelihood ratio (LLR) values of the estimated recorded bit sequence that is obtained from an one-dimensional (1-D) modified soft-output Viterbi algorithm (m-SOVA).¹⁴ As shown in simulation result, the proposed system is superior to other systems, even though it has to encounter the position fluctuation effect.

The remainder of this work is structured as follows. Section II briefly describes our proposed BPMR channel model. The proposed double-layer magnetic recording system is explained in Sec. III, and Sec. IV presents the simulation results. Finally, Sec. V concludes this paper.

Fig. 1 displays the proposed channel model, where a user bit u_k ∈ {±1} with bit period T_x is encoded by a low-density parity-check (LDPC) encoder¹⁵ followed by a rate-3/5 modulation encoder,^3,14 which produces two recorded bit sequences {x_k,l, x_k,l+1}. Then, these two recorded sequences will be stored onto the double-layer recording medium, whose structure is illustrated in Fig. 2. Specifically, the bit islands are arranged as a staggered-array placement, where an odd data sequence {x_k,0} and an even data sequence {x_k,1} are recorded onto the upper and lower layers, respectively.

In addition, we also employ the SRTR technique in a reading process, where one reader is used to read two data tracks (one for each recording layer) simultaneously. A single reader is adopted and always positioned above the double-layer recording medium to retrieve one readback signal, r(t), which contains the data from the two recording layers as depicted in Fig. 2. Next, this readback signal is oversampled at time t = kT_x/2 to obtain a data sequence {r_k}. The 1-D equalizer¹⁶ and the 1-D m-SOVA¹⁴ detector are used to equalize and determine the LLR of the recorded bits, λ_k, respectively. Hence, these LLRs are further decoded by an MLP decoder to obtain the LLR of the coded bits, λ′_k. To further enhance the equality of these LLRs, we also utilize the MLP-based LLR estimator³ to reproduce the improved version of LLRs, λ″_k, which will be sent to the LDPC decoder to produce the estimated user bit, $ûk$⁠, for the 1st global iteration (N_G = 1). Note that the LDPC decoder is implemented based on the message passing algorithm¹⁵ with N_LDPC internal iterations. For the next global iteration, the LLR sequence {λ″_k} is feedback to the rate-3/5 soft encoder^3,14 to produce the soft information for the 1-D m-SOVA¹⁴ detector. For simplicity, this paper considers the case where N_LDPC = N_G = 3 iterations.

As depicted in Fig. 2, this paper assumes that each layer provides AD = 2.5 Tb/in.² with a regular array arrangement as shown in Fig. 3(a), thus resulting in the total AD of 5.0 Tb/in² for the proposed system. For each layer, the bit period (T_x) and track pitch (T_z) are set to be 16 nm, and the bit-island diameter (L_x) is set to be 10 nm. Moreover, both layers were arranged in a staggered manner as illustrated in Fig. 3(b).

Clearly, our BPMR channel is not only disturbed by ISI and ITI on its own layer but also deteriorated from inter-layer interference (ILI) between layers. In addition, we investigate the effect of media noise determined by position fluctuation. We also assume that the isolation layer is non-magnetic material so that each stray field does not influence another recording layer.^11,12 We define the magnetic spacing between the bottom of the reader and the top of each recording layer as ∆₁ and ∆₂, which are fixed to be 2 nm and 5 nm, respectively. In the reading process, the reader is assumed to position between the upper data track of the 1st layer and the lower data track of the 2nd layer as shown in Fig. 3(b).

In practice, the readback waveform of each layer can be obtained by convolving the magnetization pattern of each layer and the reader sensitivity function as presented by Nakamura.¹² In this work, the single reader simultaneously reads a leaking stray magnetic field from both upper and lower layers. Thus, the readback signal obtained from the reader, r(t), is a linear combination of the readback waveforms from the upper and lower recording layers. Furthermore, an additive white Gaussian noise (AWGN) is also added to the readback signal as an electronics noise. We define a signal-to-noise ratio (SNR) at the reading point as SNR = 10log₁₀(1/σ²) in decibel (dB), where σ² is AWGN power. Finally, the readback signal is sent to the receiver to retrieve the estimated user data bits.

This paper evaluates the BER performance of four recording systems, where all systems employ the LDPC encoder, the 1-D equalizer, and the iterative decoding as shown in Fig. 1. To make a fair comparison, all systems operate at the same user density (UD) of 3.0 Tb/in.², where the UD is defined at the output of the LDPC encoder according to UD = AD × R, where R is a code rate of the modulation code. This means that the system with a modulation code (referred to as a coded system) must operate at a higher AD than the one without a modulation code (referred to as an uncoded system). Specifically, the four considered systems are

• “Conv-Uncoded” is the conventional system without the modulation code and the MLP decoder, which operates at AD = UD = 3.0 Tb/in.².

• “Conv-Coded” is the conventional system with the rate-3/5 modulation code^3,14 and without the MLP decoder, which operates at AD = UD/R = 5.0 Tb/in.² and R = 3/5.

• “MLP-Coded” is the proposed system³ but using a one-layer recording medium (the same medium as employed in the conventional system), which operates at AD = UD/R = 5.0 Tb/in.² and R = 3/5.

• “Proposed” is the proposed system using a double-layer recording medium, which operates at AD = 5.0 Tb/in.² where each layer has AD = 2.5 Tb/in.².

We first investigate the BER performance of different systems without the effect of position fluctuation as shown in Fig. 4(a). It is apparent that “Proposed” is superior to other systems. Specifically, to achieve a BER of 10⁻⁴, “Proposed” needs to operate at the SNR of about 11.8 dB, which is lower than “Conv-Uncoded,” “Conv-Coded,” and “MLP-Coded” by 4.4, 3.2, and 1.2 dBs, respectively. Moreover, we also compare the performance of several systems in the presence of position fluctuation at 5% as depicted in Fig. 4(b). Again, “Proposed” still provides the best BER performance if compared with other systems. Specifically, at BER = 10⁻⁴, “Proposed” provides an improvement gain of about 5.2, 3.7, and 1.2 dBs over “Conv-Uncoded,” “Conv-Coded,” and “MLP-Coded,” respectively. In addition, the result implies that the proposed system is more robust to the position fluctuation than other systems.

In this work, we propose to use a double-layer recording medium and a multilayer perceptron decoder for bit-patterned magnetic recording (BPMR) to increase storage capacity and improve a bit-error rate (BER) performance. The upper and lower recording layers are placed on top of each other in a staggered pattern, while the bit islands of each layer are arranged as a regular pattern. The single reader/two-track reading (SRTR) technique, where a single reader reads two desired data tracks simultaneously, is employed in a reading process. Then, the retrieved readback signal obtained from the single reader is processed by a 1-D equalizer followed by a 1-D modified soft-output Viterbi algorithm detector and a multilayer perceptron decoder. At the same user recording density, we found that the proposed system can provide the best BER performance if compared with other systems, even in the presence of position fluctuation.

This paper was supported by King Mongkut’s Institute of Technology Ladkrabang Doctoral Scholarships (KDS), King Mongkut’s Institute of Technology Ladkrabang (KMITL), Thailand.

The authors have no conflicts to disclose.

N. Rueangnetr: Investigation (supporting); Methodology (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). S. Koonkarnkhai: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). P. Kovintavewat: Funding acquisition (equal); Investigation (supporting); Methodology (supporting); Writing – original draft (supporting); Writing – review & editing (equal). C. Warisarn: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.