Non-Binary Protograph-Based LDPC Codes for 2-D-ISI Magnetic Recording Channels

Chen, Pingping; Cai, Kui; Kong, Lingjun; Chen, Zaichun; Zhang, Mu

doi:10.1109/tmag.2017.2697075

Cited by 13 publications

(14 citation statements)

References 19 publications

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“…Proof: In Case 2.1, the number of instances is the number of ways to choose 3 overlaps out of t {i1,i2} overlaps (the pattern has three c 1 − c 2 overlaps), which is given by (10). In Case 2.2, the number of instances is the number of ways to choose 2 overlap out of t {i1,i2} and 1 overlap out of t {i1+(r−e)γ,i2+(r−e)γ} , which is given by (11).…”

Section: A Proof Of Lemmamentioning

confidence: 99%

A Channel-Aware Combinatorial Approach to Design High Performance Spatially-Coupled Codes

Hareedy

Dolecek

2020

IEEE Trans. Inform. Theory

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Because of their capacity-approaching performance and their complexity/latency advantages, spatially-coupled (SC) codes are among the most attractive error-correcting codes for use in modern dense data storage systems. SC codes are constructed by partitioning an underlying block code and coupling the partitioned components. Here, we focus on circulant-based SC codes. Recently, the optimal overlap (OO), circulant power optimizer (CPO) approach was introduced to construct high performance SC codes for additive white Gaussian noise (AWGN) and Flash channels. The OO stage operates on the protograph of the SC code to derive the optimal partitioning that minimizes the number of graphical objects that undermine the performance of SC codes under iterative decoding. Then, the CPO optimizes the circulant powers to further reduce this number. Since the nature of detrimental objects in the graph of a code critically depends on the characteristics of the channel of interest, extending the OO-CPO approach to construct SC codes for channels with intrinsic memory is not a straightforward task. In this paper, we tackle one relevant extension; we construct high performance SC codes for practical 1-D magnetic recording channels, i.e., partial-response (PR) channels. Via combinatorial techniques, we carefully build and solve the optimization problem of the OO partitioning, focusing on the objects of interest in the case of PR channels. Then, we customize the CPO to further reduce the number of these objects in the graph of the code. SC codes designed using the proposed OO-CPO approach for PR channels outperform prior state-of-the-art SC codes by up to around 3 orders of magnitude in frame error rate (FER) and 1.1 dB in signal-to-noise ratio (SNR). More intriguingly, our SC codes outperform structured block codes of the same length and rate by up to around 1.8 orders of magnitude in FER and 0.4 dB in SNR. The performance advantage of SC codes designed using the devised OO-CPO approach over block codes of the same parameters is not only pronounced in the error floor region, but also in the waterfall region. I. INTRODUCTIONAs other data storage systems, magnetic recording (MR) systems operate at very low frame error rate (FER) levels [2]-[5]. Consequently, to ensure high error correction capability in such systems, binary [3], [4], [6] and non-binary (NB) [5], [7]-[10]graph-based codes are used. Under iterative decoding, the objects that dominate the error floor region of low-density paritycheck (LDPC) codes simulated in partial-response (PR) and additive white Gaussian noise (AWGN) systems are different in their combinatorial nature because of the detector-decoder looping and the intrinsic memory in PR systems [5]. In particular, the authors in [5] introduced balanced absorbing sets (BASs) to characterize the detrimental objects in the case of PR (1-D MR) channels. Moreover, the weight consistency matrix (WCM) framework was introduced to systematically remove any type of absorbing sets (ASs) from the graph of an NB-LDPC code [11], [12...

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Section: A Proof Of Lemmamentioning

confidence: 99%

A Channel-Aware Combinatorial Approach to Design High Performance Spatially-Coupled Codes

Hareedy

Dolecek

2020

IEEE Trans. Inform. Theory

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“…We refer an S × T adjacency matrix B B corresponding to a protograph as the base matrix, with b st being the (s, t)th entry of B B. For example, the base matrix of the AR4JA protograph code which shows superior performance over the AWGN channel [10] is given by…”

Section: Analysis Of Protograph Codes For the Awsαsn Channelmentioning

confidence: 99%

“…Through a sequence of 'copy-and-permute' operations on B B, the Tanner graph of an LDPC code with any desired block length can be derived [9]. During the design of protograph LDPC codes, the P-EXIT analysis [9,11], together with the AWD analysis [10], are effective theoretical methods to evaluate the decoding performance of the designed protograph code at the waterfall region and error floor region, respectively.…”

Section: Analysis Of Protograph Codes For the Awsαsn Channelmentioning

confidence: 99%

“…In the recent few years, the protograph LDPC codes have been found to achieve superior error performance over the additive white Gaussian noise (AWGN) channel, the partial response channels and the high-density magnetic recording channels [9][10][11]. Furthermore, their protograph structure facilitates low-complexity encoding with readily parallelisable decoder implementations [12].…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, their protograph structure facilitates low-complexity encoding with readily parallelisable decoder implementations [12]. For example, the AR4JA codes are well-known capacityapproaching protograph codes optimised for the AWGN channels [10]. However, up till now, no work has been carried out for designing protograph LDPC codes for the AWSαSN channel.…”

Section: Introductionmentioning

confidence: 99%

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Design of protograph codes for additive white symmetric alpha‐stable noise channels

et al. 2020

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The protograph low-density parity-check (LDPC) codes possess many attractive properties, such as the low encoding/decoding complexity and better error floor performance, and hence have been successfully applied to different types of communication and data storage channels. In this paper, we design protograph LDPC codes for communication systems corrupted by the impulsive noise, which are modeled as additive white symmetric alpha-stable noise (AWSαSN) channels. We start by presenting a novel simulation-based protograph extrinsic information transfer (P-EXIT) analysis to derive the iterative decoding threshold of the protograph codes. By further applying the asymptotic weight distribution (AWD) analysis, we design new protograph codes for the AWSαSN channel. Both theoretical analysis and simulation results demonstrate that the proposed protograph codes can provide better error rate performance than the prior art AR4JA code, the irregular codes optimized for the AWGN channel, as well as the irregular codes optimized for the AWSαSN channel.

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Design and Analysis of Spatially Coupled Protograph LDPC Codes for Two-Dimensional Magnetic Recording Systems

Yang

Fang

Han

et al. 2018

2018 Asia-Pacific Magnetic Recording Conference (APMRC)

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Non-Binary Protograph-Based LDPC Codes for 2-D-ISI Magnetic Recording Channels

Cited by 13 publications

References 19 publications

A Channel-Aware Combinatorial Approach to Design High Performance Spatially-Coupled Codes

A Channel-Aware Combinatorial Approach to Design High Performance Spatially-Coupled Codes

Design of protograph codes for additive white symmetric alpha‐stable noise channels

Design and Analysis of Spatially Coupled Protograph LDPC Codes for Two-Dimensional Magnetic Recording Systems

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