Construction of Time Invariant Spatially Coupled LDPC Codes Free of Small Trapping Sets

Naseri, Sima; Banihashemi, Amir H.

doi:10.1109/tcomm.2021.3060797

Cited by 13 publications

(21 citation statements)

References 49 publications

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“…In addition, the effect of the coupling width w on scaling parameters and resulting finite-length performances is still an open problem. It has been pointed out that the coupling width w is related to the girth property [17], [18], trapping sets [21], and convergence speed [22]. They share an intuitive conclusion that large w has a positive impact on the finitelength performance.…”

Section: Introductionmentioning

confidence: 92%

“…In this paper, we consider (l, r, w, L, M ) finite-length SC-LDPC codes, where w is the coupling width that determines the number of consecutive positions to be coupled and M is the number of variable nodes at each position [4]. Based on comprehensive asymptotic analysis, researches on the code design of (l, r, w, L, M ) SC-LDPC codes having superior finite-length performance have been followed [13]- [21]. It is desirable to construct practically good codes showing superior finite-length performances for a given code rate and code length.…”

Section: Introductionmentioning

confidence: 99%

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Optimizing Code Parameters of Finite-Length SC-LDPC Codes Using the Scaling Law

Kwak

Kim

2021

IEEE Access

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In this paper, we optimize code parameters of finite-length spatially coupled low-density parity-check (SC-LDPC) codes, represented by a set of code parameters (l, r, w, L, M ). Although the finitelength scaling behavior of SC-LDPC codes was studied in the existing literature, the previous works impose a constraint such that the coupling width w is equal to the variable node degree l and they do not focus on optimizing the code parameters for given code and decoder specifications such as the code rate, frame size, and decoding complexity. In order to optimize the code parameters with the target specifications, we first extend the scaling law of SC-LDPC codes without the constraint w = l. Using the scaling law formulated with a new variable w, we show that the coupling width w directly affects the slope of the performance curve and performance comparisons are given to investigate trade-offs inherent in the code parameters. It is shown that there are trade-offs for the code parameters in the perspective of the asymptotic performance limit, code rate, and scaling behaviors. In addition, the scaling law allows us to find the optimal code parameter set showing the best finite-length performance. Interestingly, the optimal code parameter set (l, r, w) varies depending on the coupling length L and uncoupled code length M that determine the code and decoder specifications, which means there is no specific code parameter set prevailing over different kinds of applications. Finally, we illustrate this result using the investigated trade-offs on the code parameters, which gives us useful insight on how to choose the code parameters. INDEX TERMSCoupling width, finite-length performance, low-density parity-check (LDPC) code, scaling law, spatially coupled LDPC (SC-LDPC) code VOLUME x, 20xx

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Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Optimizing Code Parameters of Finite-Length SC-LDPC Codes Using the Scaling Law

Kwak

Kim

2021

IEEE Access

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“…The error floor is attributed to certain harmful graphical structures within the code's Tanner graph, referred to as trapping sets (TSs). The error floor of LDPC codes has been widely studied from different perspectives including code constructions with low error floor [1]- [15], decoder design for improved error floor performance [16]- [24], enumeration of TS structures [25]- [30], and error floor estimation [31]- [45]. July 27, 2021 DRAFT arXiv:2107.11479v1 [cs.IT] 23 Jul 2021…”

Section: Introductionmentioning

confidence: 99%

Error Floor Analysis of LDPC Column Layered Decoders

Farsiabi

Banihashemi

2022

IEEE Commun. Lett.

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In this paper, we analyze the error floor of column layered decoders, also known as shuffled decoders, for low-density parity-check (LDPC) codes under saturating sum-product algorithm (SPA).To estimate the error floor, we evaluate the failure rate of different trapping sets (TSs) that contribute to the frame error rate in the error floor region. For each such TS, we model the dynamics of SPA in the vicinity of the TS by a linear state-space model that incorporates the information of the layered message-passing schedule. Consequently, the model parameters and the failure rate of the TS change as a result of the change in the order by which the messages of different layers are updated. This, in turn, causes the error floor of the code to change as a function of scheduling. Based on the proposed analysis, we then devise an efficient search algorithm to find a schedule that minimizes the error floor.Simulation results are presented to verify the accuracy of the proposed error floor estimation technique.

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“…It is known that the performance of an SC code improves as its memory increases. This is a byproduct of improved node expansion and additional degrees of freedom that can be utilized to decrease the number of short cycles and detrimental objects [9], [10], [12]- [14]. A plethora of existing works [9], [10], [15], [16] focus on minimizing the number of short cycles in the graph of the SC code.…”

Section: Introductionmentioning

confidence: 99%

“…However, this method is hard to execute in practice for high-memory codes due to the increasing computational complexity. Heuristic methods that search for good SC codes with high memories are derived in [14]- [17]. However, high-memory codes designed by purely heuristic methods are unable to reach the potential performance gain that can be achieved through high memories due to lack of theoretical properties; several of these codes can even be beat by optimally designed QC-SC codes with lower memories under the same constraint length [16].…”

Section: Introductionmentioning

confidence: 99%

Breaking the Computational Bottleneck: Design of Near-Optimal High-Memory Spatially-Coupled Codes

Yang,

Hareedy,

Calderbank

et al. 2021

Preprint

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Spatially-coupled (SC) codes, known for their threshold saturation phenomenon and low-latency windowed decoding algorithms, are ideal for streaming applications and data storage systems. SC codes are constructed by partitioning an underlying block code, followed by rearranging and concatenating the partitioned components in a convolutional manner. The number of partitioned components determines the memory of SC codes. In this paper, we investigate the relation between the performance of SC codes and the density distribution of partitioning matrices. While adopting higher memories results in improved SC code performance, obtaining finite-length, high-performance SC codes with high memory is known to be computationally challenging. We break this computational bottleneck by developing a novel probabilistic framework that obtains (locally) optimal density distributions via gradient descent. Starting from random partitioning matrices abiding by the obtained distribution, we perform low-complexity optimization algorithms that minimize the number of detrimental objects to construct high-memory, high-performance quasicyclic SC codes. We apply our framework to various objects of interests, from the simplest short cycles, to more sophisticated objects such as concatenated cycles aiming at finer-grained optimization. Simulation results show that codes obtained through our proposed method notably outperform state-of-the-art SC codes with the same constraint length and optimized SC codes with uniform partitioning. The performance gain is shown to be universal over a variety of channels, from canonical channels such as additive white Gaussian noise and binary symmetric channels, to practical channels underlying flash memory and magnetic recording systems.

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Construction of Time Invariant Spatially Coupled LDPC Codes Free of Small Trapping Sets

Cited by 13 publications

References 49 publications

Optimizing Code Parameters of Finite-Length SC-LDPC Codes Using the Scaling Law

Optimizing Code Parameters of Finite-Length SC-LDPC Codes Using the Scaling Law

Error Floor Analysis of LDPC Column Layered Decoders

Breaking the Computational Bottleneck: Design of Near-Optimal High-Memory Spatially-Coupled Codes

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