非二进制原型LDPC码解决2-D-ISI磁记录通道

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"基于非二进制基于原型的LDPC码在2-D-ISI磁记录通道中的应用" 在信息存储技术领域，二维符号间干扰（2-D-ISI）是一个关键问题，它由下轨方向的ISI（符号间干扰）和横向轨道方向的轨间干扰共同构成，对超高密度电磁性能产生严重影响。为了克服这一挑战，低密度奇偶校验（LDPC）码因其优异的纠错性能而受到广泛关注。特别是基于原型的LDPC码，由于其高效的编码和解码结构，被认为是处理2-D-ISI的有效手段。然而，尽管原型码有其优势，但目前尚未有关于为2-D-ISI通道设计非二进制基于原型的LDPC（NP-LDPC）码的深入研究。在该研究论文中，作者们首次提出了一种改进的原型外在信息传递分析方法，这是一种理论工具，用于评估和设计适用于2-D-ISI通道的NP-LDPC码。通过结合渐近集合权重分布分析，这种方法能够更准确地预测和分析NP-LDPC码在实际通道环境下的性能。进一步，研究者应用了一种快速搜索策略，构建了两种类型的NP-LDPC码，这些码被专门设计以适应2-D-ISI信道的特性。实证分析和仿真结果显示，无论是低信噪比（SNR）还是高SNR条件下，提出的NP-LDPC码相比现有的针对2-D-ISI优化的二进制LDPC码和非二进制准循环LDPC码，都表现出更优的性能。这篇发表在IEEETRANSACTIONSONMAGNETICS上的研究论文，由陈平平、蔡奎、孔令军、陈再春和张木共同完成，他们在福州大学、新加坡科技与设计大学和南京邮电大学的相关学院任职。他们的工作不仅填补了非二进制基于原型的LDPC码在2-D-ISI通道设计领域的空白，也为未来超高密度磁记录系统的性能提升提供了新的理论基础和实用方案。

IEEE TRANSACTIONS ON MAGNETICS, VOL. 53, NO. 11, NOVEMBER 2017 8108905

Non-Binary Protograph-Based LDPC Codes for 2-D-ISI

Magnetic Recording Channels

Pingping Chen

1,2

,KuiCai

, Lingjun Kong

, Zaichun Chen

,andMuZhang

Fuzhou University, Fujian 350106, China

Singapore University of Technology and Design, Singapore 487372

College of Telecommunication and Information Engineering, Nanjing University of Posts and Telecommunications,

Nanjing 210023, China

2-D inter-symbol-interference (2-D-ISI), consisting of ISI in the down track direction and inter-track interference along the cross-

track direction, is a major factor that severely degrades the performance of ultra-high density magnetic recording systems. Due to its

superior performance and the protograph structure which facilitates high-speed encoding and decoding, the protograph codes have

shown a high potential to tackle 2-D-ISI. However, so far, no work has been reported on the design of non-binary protograph-based

low-density parity-check (NP-LDPC) codes for 2-D-ISI channels. In this paper, we ﬁrst propose a modiﬁed protograph extrinsic

information transfer analysis. In conjunction with the asymptotic ensemble weight distribution analysis, they both serve as theoretical

tools to analyze the performance of NP-LDPC codes designed for the 2-D-ISI channels. By further applying a fast search approach, we

construct two types of NP-LDPC codes for 2-D-ISI channels. Both theoretical analyses and simulated results show that the proposed

codes outperform the existing binary LDPC codes that optimized for 2-D-ISI channels as well as the non-binary quasi-cyclic LDPC

code, at both low and high SNR regions.

Index Terms— 2-D inter-symbol-interference (2-D-ISI), extrinsic information transfer (EXIT) analysis, magnetic recording channels,

protograph low-density parity-check (LDPC) codes.

I. INTRODUCTION

HE conventional perpendicular magnetic recording sys-

tem is approaching its area density (AD) limit [1], the bit-

patterned magnetic recording (BPMR), heat (or microwave)

assisted magnetic recording, and shingled writing/2-D mag-

netic recording, which have been proposed in recent years

to extend the storage density beyond 1 Tb/in

[2]–[4].

Correspondingly, both the bit length and track pitch of the

magnetic storage media are reduced signiﬁcantly, leading

to severe inter-symbol-interference (ISI) in the down track

direction, and inter-track interference (ITI) along the cross-

track direction. ISI and ITI together give rise to a 2-D-ISI

for ultra-high density magnetic recording systems. Advanced

channel coding and signal processing techniques play a critical

role to effectively mitigate the 2-D-ISI and enable a higher AD

for the magnetic recording systems [5]–[9].

Due to their superior capacity-approaching performance,

the low-density parity-check (LDPC) codes have been widely

applied in the read channel of magnetic recording systems.

Many works have been done to investigate the binary LDPC

codes and their error ﬂoor performance in the 1-D-ISI mag-

netic recording channels, which are also modeled as the par-

tial response (PR) channels [10]–[12]. For ultra-high density

magnetic recording systems with 2-D-ISI, the binary irregular

LDPC codes have been optimized by using extrinsic informa-

tion transfer (EXIT) curve ﬁtting [13]. Since non-binary LDPC

(NB-LDPC) codes are found to outperform their binary coun-

terparts for additive white Gaussian noise (AWGN) channels,

Jeon and Kumar [14] investigated the performance of non-

Manuscript received March 6, 2017; accepted April 19, 2017. Date of

publication April 24, 2017; date of current version October 24, 2017.

Corresponding author: C. Kui (e-mail: cai_kui@sutd.edu.sg).

Digital Object Identiﬁer 10.1109/TMAG.2017.2697075

binary quasi-cyclic (NQC) LDPC codes based on progressive-

edge-growth algorithm for the PR channels. On the other

hand, the protograph-based LDPC codes, constructed from

the small base matrices or protographs, have shown excellent

performance with simple hardware implementation for AWGN

channels and PR channels [10], [15]. Recently, several types

of binary protograph-based LDPC codes have been designed

for 2-D-ISI channels [16]–[18]. However, so far, no work has

been reported on the design of non-binary protograph-based

LDPC (NP-LDPC) codes for 2-D-ISI channels.

In this paper, we present novel NP-LDPC codes designed for

2-D-ISI magnetic recording channels, based on a modiﬁed pro-

tograph EXIT analysis, together with the asymptotic ensemble

weight distribution (AWE) analysis. By further applying a fast

search approach, we construct two types of NP-LDPC codes.

The EXIT-chart analysis, the AWE analysis, and the error rate

simulations have demonstrated the superior performance of the

proposed codes over the existing binary LDPC codes and the

NQC LDPC code for 2-D-ISI channels.

This paper is organized as follows. In Section II, we intro-

duce the system model of a non-binary LDPC coded system

with 2-D-ISI. In Section III, we propose a modiﬁed protograph

EXIT analysis, together with the AWE analysis, for analyzing

the codes’ performance for 2-D-ISI channels. Two types of

NP-LDPC codes are constructed for 2-D-ISI magnetic record-

ing channels in Section IV, and their performances are evalu-

ated in Section V. Finally, Section VI concludes this paper.

II. S

YSTEM MODEL

In a magnetic recording channel with 2-D-ISI [5], each bit

suffers interferences from both the down-track and cross-track

directions. The channel response before equalization can be

represented by an L

× L

matrix H, with L

and L

See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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