Finite-Length Construction of High Performance Spatially-Coupled Codes via Optimized Partitioning and Lifting

Esfahanizadeh, Homa; Hareedy, Ahmed; Dolecek, Lara

doi:10.1109/tcomm.2018.2867493

Cited by 43 publications

(114 citation statements)

References 26 publications

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“…For example for γ = 3, N ndi = 19. Building upon the results of [6], we show that the number of cycles-6 in the protograph of an irregular SC code can be expressed as a function of parameters in O ndi . Theorem 1.…”

Section: Proofmentioning

confidence: 75%

“…Similar to the case of regular SC codes [6], for an irregular SC code with maximum VN degree γ, the maximum degree for an overlap parameter with non-zero value is γ. Additionally, if there is at least one pair of distinct row indices (i u , i v ) such that i u , i v ∈ {i 1 , · · · , i d } and i u = i v (mod γ), then, t {i1,··· ,i d } = 0. Lemma 2.…”

Section: Optimal Partitioning For Irregular Sc Codesmentioning

confidence: 98%

“…In the finite-length regime, SC codes also offer excellent performance and are endowed with low-latency windowed decoding algorithms [5]. As a result, they have recently emerged as an excellent choice for error correction in modern data storage and communication systems that require high levels of reliability [6], [7]. SC codes are constructed by coupling together disjoint (and identical) block codes into one long chain [1] as follows: the parity-check matrix H of a block code is partitioned into component matrices H k , where k ∈ {0, 1, · · · , m} and m is the memory.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Finite-Length Construction of Irregular Spatially-Coupled Codes

Esfahanizadeh

Dolecek

2019

2019 IEEE Information Theory Workshop (ITW)

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Spatially-coupled (SC) LDPC codes have recently emerged as an excellent choice for error correction in modern data storage and communication systems due to their outstanding performance. It has long been known that irregular graph codes offer performance advantage over their regular counterparts. In this paper, we present a novel combinatorial framework for designing finite-length irregular SC LDPC codes. Our irregular SC codes have the desirable properties of regular SC codes thanks to their structure while offering significant performance benefits that come with the node degree irregularity. Coding constructions proposed in this work contribute to the existing portfolio of finitelength graph code designs.

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Section: Proofmentioning

confidence: 75%

Section: Optimal Partitioning For Irregular Sc Codesmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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A Finite-Length Construction of Irregular Spatially-Coupled Codes

Esfahanizadeh

Dolecek

2019

2019 IEEE Information Theory Workshop (ITW)

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“…Clearly, the harmful objects of the SC-LDPCCs arise from related objects in the underlying LDPC block codes, and their multiplicity depends on the adopted edge spreading method. Some efforts have been devoted to the graph optimization from an absorbing set standpoint of array-based SC-LDPCCs [12]- [18]. These approaches have been restricted to certain code structures and harmful objects to enable a feasible search.…”

Section: Introductionmentioning

confidence: 99%

Efficient Search and Elimination of Harmful Objects for the Optimization of QC-SC-LDPC Codes

Battaglioni

Chiaraluce

Baldi

et al. 2019

2019 IEEE Global Communications Conference (GLOBECOM)

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The error correction performance of low-density parity-check (LDPC) codes under iterative message-passing decoding is degraded by the presence of certain harmful objects existing in their Tanner graph representation. Depending on the context, such harmful objects are known as stopping sets, trapping sets, absorbing sets, or pseudocodewords. In this paper, we propose a general procedure based on edge spreading that enables the design of quasi-cyclic (QC) spatially coupled lowdensity parity-check codes (SC-LDPCCs) that are derived from QC-LDPC block codes and possess a significantly reduced multiplicity of harmful objects with respect to the original QC-LDPC block code. This procedure relies on a novel algorithm that greedily spans the search space of potential candidates to reduce the multiplicity of the target harmful object(s) in the Tanner graph.The effectiveness of the method we propose is validated via examples and numerical computer simulations.

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“…If the SC code is non-binary, the WCM framework [11], [12] is used to optimize the edge weights after applying the OO-CPO approach.In this paper, we propose an approach based on tools from combinatorics, optimization, and graph theory, to construct high performance time-invariant SC codes for PR channels. Unlike the case of AWGN and Flash channels (see [23] and [24]), the common substructure, whose number of instances we seek to minimize, in the case of PR channels can appear in different ways in the protograph of the SC code, making the optimization problem considerably more challenging. For that reason, we introduce the concept of the pattern, which is a configuration in the protograph that can result in instances of the common A. Hareedy, R. Wu, and L. Dolecek are with the [12].…”

mentioning

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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Finite-Length Construction of High Performance Spatially-Coupled Codes via Optimized Partitioning and Lifting

Cited by 43 publications

References 26 publications

A Finite-Length Construction of Irregular Spatially-Coupled Codes

A Finite-Length Construction of Irregular Spatially-Coupled Codes

Efficient Search and Elimination of Harmful Objects for the Optimization of QC-SC-LDPC Codes

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

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