Non-Binary Constrained Codes for Two-Dimensional Magnetic Recording

Dabak, Beyza; Hareedy, Ahmed; Calderbank, Robert

doi:10.1109/tmag.2020.3017511

Cited by 10 publications

(22 citation statements)

References 25 publications

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“…Substituting (15) in g(c) = m−1 i=0 g i (c i ) gives (10). For brevity, we skip the sixth step, which is to assemble the encoding and decoding algorithms.…”

Section: Rr-loco Coding Over Gf(2)mentioning

confidence: 99%

“…For brevity, we skip the sixth step, which is to assemble the encoding and decoding algorithms. These algorithms are a direct consequence of the rule in (10), and we refer the reader to [2], [18], [21], and [24] for details. Note that we sometimes refer to RC m as a 1D RR-LOCO code.…”

Section: Rr-loco Coding Over Gf(2)mentioning

confidence: 99%

“…They can also be combined with robust signal detection using machine learning [9]. They find application in the emerging two-dimensional (2D) magnetic recording devices as well [10], [11]. Moreover, constrained codes are used to achieve DC balance and self-calibration in optical recording devices [12] in addition to many computer standards for data transmission [13].…”

Section: Introductionmentioning

confidence: 99%

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Read-and-Run Constrained Coding for Modern Flash Devices

Hareedy,

Zheng,

Siegel

et al. 2021

Preprint

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The pivotal storage density win achieved by solidstate devices over magnetic devices in 2015 is a result of multiple innovations in physics, architecture, and signal processing. One of the most important innovations in that regard is enabling the storage of more than one bit per cell in the Flash device, i.e., having more than two charge levels per cell. Constrained coding is used in Flash devices to increase reliability via mitigating intercell interference that stems from charge propagation among cells. Recently, capacity-achieving constrained codes were introduced to serve that purpose in modern Flash devices, which have more than two levels per cell. While these codes result in minimal redundancy via exploiting the underlying physics, they result in non-negligible complexity increase and access speed limitation since pages cannot be read separately. In this paper, we suggest new constrained coding schemes that have low-complexity and preserve the desirable high access speed in modern Flash devices. The idea is to eliminate error-prone patterns by coding data only on the left-most page while leaving data on all the remaining pages uncoded. Our coding schemes work for any number of levels per cell, offer systematic encoding and decoding, and are capacity-approaching. Since the proposed schemes enable the separation of pages, we refer to them as read-and-run (RR) constrained coding schemes as opposed to schemes adopting readand-wait for other pages. We analyze the new RR coding schemes and discuss their impact on the probability of occurrence of different charge levels. We also demonstrate the performance improvement achieved via RR coding on a practical triple-level cell Flash device.

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“…Substituting (15) in g(c) = m−1 i=0 g i (c i ) gives (10). For brevity, we skip the sixth step, which is to assemble the encoding and decoding algorithms.…”

Section: Rr-loco Coding Over Gf(2)mentioning

confidence: 99%

Section: Rr-loco Coding Over Gf(2)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Read-and-Run Constrained Coding for Modern Flash Devices

Hareedy,

Zheng,

Siegel

et al. 2021

Preprint

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“…DRAFT Constrained codes preventing certain, error-prone TD patterns increase the reliability of TDMR devices [17]. Constrained codes find application in optical recording devices [18].…”

Section: Introductionmentioning

confidence: 99%

“…We also developed constrained codes for Flash devices with more than 2 levels per cell [14] and for TDMR devices [17]. All our codes are capacity-achieving, offer simple encoding-decoding, and reconfiguring them is as simple as reprogramming an adder.…”

Section: Introductionmentioning

confidence: 99%

Power Spectra of Constrained Codes with Level-Based Signaling: Overcoming Finite-Length Challenges

Centers¹,

Tan²,

Hareedy³

et al. 2020

Preprint

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In various practical systems, certain data patterns are prone to errors if written or transmitted.In magnetic recording and communication over transmission lines, data patterns causing consecutive transitions that are not sufficiently separated are prone to errors. In Flash memory with two levels per cell, data patterns causing high-low-high charge levels on adjacent cells are prone to errors.Constrained codes are used to eliminate error-prone patterns, and they can also achieve other goals.Recently, we introduced efficient binary symmetric lexicographically-ordered constrained (LOCO) codes and asymmetric LOCO (A-LOCO) codes to increase density in magnetic recording systems and lifetime in Flash systems by eliminating the relevant detrimental patterns. Due to their application, LOCO and A-LOCO codes are associated with level-based signaling. Studying the power spectrum of a random signal with certain properties is principal for any storage or transmission system. It reveals important properties such as the average signal power at DC, the bandwidth of the signal, and whether there are discrete power components at certain frequencies. In this paper, we first modify a framework from the literature in order to introduce a method to derive the power spectrum of a sequence of constrained data associated with level-based signaling. We apply our method to infinitely long sequences satisfying symmetric and asymmetric constraints. Next, we show how to generalize the method such that it works for a stream of finite-length codewords as well, thus demonstrating how to overcome the associated finite-length challenges. We use the generalized method to devise closed forms for the spectra of finitelength LOCO and A-LOCO codes from their transition diagrams. Our LOCO and A-LOCO spectral derivations can be performed for any code length and can be extended to other constrained codes. We

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