Spatially Coupled Codes Optimized for Magnetic Recording Applications

Esfahanizadeh, Homa; Hareedy, Ahmed; Dolecek, Lara

doi:10.1109/tmag.2016.2609937

Cited by 21 publications

(40 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The performance of Code 3 is better than the performance of Code 5 not only in the error floor region, but also in the waterfall region. An interesting observation is that, in the error profile of Code 3, we found no codewords of weights ∈ {6, 8} (which are (6, 0, 0, 9, 0) and (8, 0, 0, 12, 0) BASTs) despite the dominant presence of such low weight codewords in the error profiles of Codes 1, 2, and 5 (see also [5], [12], and [16]). From Fig.…”

Section: Resultsmentioning

confidence: 81%

“…THE COMMON SUBSTRUCTURE AND ITS PATTERNS The idea of focusing on a common substructure in the design of the unlabeled graph of an SC code simplifies the optimization procedure. Additionally, minimizing the number of instances of the common substructure significantly reduces the multiplicity of several different types of detrimental objects simultaneously [16], [23], which is a lot more feasible compared with operating on all these detrimental objects separately (especially for partitioning). It was shown in [16] that the (4, 4(γ − 2)) UAS/UTS, γ ≥ 3, is the common substructure of interest for PR channels (unlike the case for AWGN [22], [23] and Flash channels [24], where the substructure of interest is the (3, 3(γ − 2))).…”

Section: Preliminariesmentioning

confidence: 99%

“…Spatially-coupled (SC) codes [13]-[15] are graph-based codes constructed by partitioning an underlying block code into components of the same size, then rewiring these components multiple times [16]. Literature works studying the asymptotic performance of SC codes include [15], [17], [18].…”

Section: Introductionmentioning

confidence: 99%

“…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].Spatially-coupled (SC) codes [13]-[15] are graph-based codes constructed by partitioning an underlying block code into components of the same size, then rewiring these components multiple times [16]. Literature works studying the asymptotic performance of SC codes include [15], [17], [18].…”

mentioning

confidence: 99%

See 3 more Smart Citations

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

Hareedy

Dolecek

2020

IEEE Trans. Inform. Theory

Self Cite

View full text Add to dashboard Cite

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...

show abstract

Section: Resultsmentioning

confidence: 81%

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

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

Hareedy

Dolecek

2020

IEEE Trans. Inform. Theory

Self Cite

View full text Add to dashboard Cite

show abstract

“…Recent results on SC codes include asymptotic analysis, e.g., [7], and finite length designs, e.g., [8]- [10]. Non-binary SC (NB-SC) codes designed using cutting vector (CV) partitioning and optimized for 1-D magnetic recording applications were introduced in [11]. The idea of partitioning the underlying block code by minimizing the overlap of its rows of circulants (so called minimum overlap (MO)) was recently introduced and applied to AWGN channels in [12].…”

Section: Introductionmentioning

confidence: 99%

High performance non-binary spatially-coupled codes for flash memories

Hareedy

Esfahanizadeh

Dolecek

2017

2017 IEEE Information Theory Workshop (ITW)

Self Cite

View full text Add to dashboard Cite

Modern dense Flash memory devices operate at very low error rates, which require powerful error correcting coding (ECC) techniques. An emerging class of graph-based ECC techniques that has broad applications is the class of spatiallycoupled (SC) codes, where a block code is partitioned into components that are then rewired multiple times to construct an SC code. Here, our focus is on SC codes with the underlying circulant-based structure. In this paper, we present a three-stage approach for the design of high performance non-binary SC (NB-SC) codes optimized for practical Flash channels; we aim at minimizing the number of detrimental general absorbing sets of type two (GASTs) in the graph of the designed NB-SC code. In the first stage, we deploy a novel partitioning mechanism, called the optimal overlap partitioning, which acts on the protograph of the SC code to produce optimal partitioning corresponding to the smallest number of detrimental objects. In the second stage, we apply a new circulant power optimizer to further reduce the number of detrimental GASTs. In the third stage, we use the weight consistency matrix framework to manipulate edge weights to eliminate as many as possible of the GASTs that remain in the NB-SC code after the first two stages (that operate on the unlabeled graph of the code). Simulation results reveal that NB-SC codes designed using our approach outperform state-of-theart NB-SC codes when used over Flash channels.

show abstract

Integer programming‐based non‐uniform window decoding schedules for spatially coupled low‐density parity‐check codes

2022

View full text Add to dashboard Cite

Spatially coupled low‐density parity‐check (SC‐LDPC) codes generally use a window decoding scheme, which is known to yield a near‐optimal decoding, compared to full block decoding. Recently, a non‐uniform schedule has been proposed to eliminate unnecessary updates of variable nodes within a window: this schedule is generated based on the behaviour of variable node updates analysed by density evolution. Here, the authors present a new non‐uniform schedule based on integer programming, whereby the objective functions and constraints are derived from a protograph‐based extrinsic information transfer chart. Our design is more flexible than the previous design, because the integer programming‐based design allows reduction of update numbers and performance losses through the constraints function, whereas the previous design requires observation of variable node update behaviour. The authors report the performance of their designs of non‐uniform schedules in additive white Gaussian noise (AWGN) and inter‐symbol interference (ISI) channels. Particularly, in the ISI channel, the authors’ non‐uniform schedules are designed with cooperative decoding between a Bahl‐Cocke‐Jelinek‐Raviv (BCJR) detector and an SC‐LDPC decoder.

show abstract

Spatially Coupled Codes Optimized for Magnetic Recording Applications

Cited by 21 publications

References 34 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

High performance non-binary spatially-coupled codes for flash memories

Integer programming‐based non‐uniform window decoding schedules for spatially coupled low‐density parity‐check codes

Contact Info

Product

Resources

About