A General Non-Binary LDPC Code Optimization Framework Suitable for Dense Flash Memory and Magnetic Storage

Hareedy, Ahmed; Lanka, Chinmayi; Dolecek, Lara

doi:10.1109/jsac.2016.2603719

Cited by 28 publications

(85 citation statements)

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“…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].…”

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confidence: 99%

“…EASs have the property that all satisfied CNs are of degree 2, and all unsatisfied CNs are of degree 1 [11], [27]. Unique characteristics of storage channels (compared with the AWGN channel) result in changing the combinatorial properties of detrimental objects in graph-based codes simulated over such channels [11].The intrinsic memory in PR channels [2], [5] can result in VN errors having high magnitudes, which is typically not the case for canonical channels. These VN errors with high magnitudes make it very difficult for unsatisfied CNs with degree > 1 to participate in correcting an AS error.…”

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confidence: 99%

“…Our extensive simulations confirm these combinatorial properties of the detrimental objects in the case of PR channels. BASs and BASs of type two (BASTs) were introduced in [5] and [11] to capture such detrimental objects.We now present the definitions of different objects of interest. Examples of these objects of interest are in Fig.…”

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confidence: 99%

“…Set all the VNs in V to values ∈ GF(q)\{0} and set all other VNs to 0. The set V is said to be an (a, b, d 1 , d 2 , d 3 ) balanced absorbing set of type two (BAST) over GF(q) if the size of V is a, the number of unsatisfied CNs connected to V is b, 0 ≤ b ≤ ag 2 , the number of degree-1 (resp., 2 and > 2) CNs connected to V is d 1 (resp., d 2 and d 3 ), d 2 > d 3 , all the unsatisfied CNs connected to V (if any) have either degree 1 or degree 2, and each VN in V is connected to strictly more satisfied than unsatisfied neighboring CNs, for some set of VN values.While the above definition was introduced in the context of non-binary codes [5], [11], it is valid in the binary case as well (set q = 2, and b becomes the number of odd-degree CNs). An (a, d 1 , d 2 , d 3 ) unlabeled BAST (UBS) is a BAST with the weights of all edges of its graph replaced by 1's.…”

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confidence: 99%

“…A UTS is an unlabeled elementary absorbing set (UAS) if each VN in V is connected to strictly more neighbors in T than in O.A binary protograph configuration is also defined by (a, d 1 ) for simplicity. The WCM framework removes a BAST from the graph of an NB code by careful processing of its edge weights (see [5], [11], and [12] for details).…”

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confidence: 99%

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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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