The Secret Arithmetic of Patterns: A General Method for Designing Constrained Codes Based on Lexicographic Indexing

Hareedy, Ahmed; Dabak, Beyza; Calderbank, Robert

doi:10.1109/tit.2022.3170692

Cited by 8 publications

(14 citation statements)

References 47 publications

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“…This scheme is the binary RR-LOCO coding scheme. The constrained code we apply is a binary LOCO code devised according to the general method in [22]. We start by defining the proposed LOCO code.…”

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

confidence: 99%

“…These algorithms are a direct consequence of the rule in (10), and we refer the reader to [3], [19], [22], and [26] for details. Note that we sometimes refer to RC 2 m as a 1D binary RR-LOCO code.…”

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

confidence: 99%

“…Note that we sometimes refer to RC 2 m as a 1D binary RR-LOCO code. The encoding-decoding rule of a LOCO code is the reason behind its low complexity algorithms, where reconfiguration becomes as easy as reprogramming an adder [8], [22].…”

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

confidence: 99%

“…We extended our result to single-level cell (SLC) Flash memories (q = 2) [21] then to Flash memories with any number q of levels per cell [19]. Moreover, we devised a general method to design LOCO codes for any finite set of patterns to forbid [22], which will be useful in this paper. We studied the power spectra of binary LOCO codes in [23].…”

Section: Introductionmentioning

confidence: 97%

“…We studied the power spectra of binary LOCO codes in [23]. LOCO codes are capacity-achieving, simple, and easily reconfigurable [19], [22].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Efficient Constrained Codes That Enable Page Separation in Modern Flash Memories

Hareedy¹,

Zheng²,

Siegel³

et al. 2023

Preprint

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The pivotal storage density win achieved by solid-state 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 inter-cell 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 either only on the left-most page (binary coding) or only on the two left-most pages (4-ary coding) while leaving data on all the remaining pages uncoded. Our coding schemes work for any number of levels q ≥ 4 per cell, offer systematic encoding and decoding, and are capacity-approaching. Since the proposed schemes enable the separation of pages, except the two left-most pages in the case of 4-ary coding, we refer to them as read-and-run (RR) constrained coding schemes as opposed to schemes adopting read-and-wait for other pages. The 4-ary RR coding scheme is introduced in order to limit the rate loss incurred by the binary RR coding schemes, and we show that our 4-ary RR coding scheme is also competitive when it comes to complexity and error propagation. We analyze the new RR coding schemes and discuss their impact on the probability of

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

confidence: 99%

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

confidence: 99%

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

confidence: 99%

Section: Introductionmentioning

confidence: 97%

“…We studied the power spectra of binary LOCO codes in [23]. LOCO codes are capacity-achieving, simple, and easily reconfigurable [19], [22].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Efficient Constrained Codes That Enable Page Separation in Modern Flash Memories

Hareedy¹,

Zheng²,

Siegel³

et al. 2023

Preprint

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Quasi-Enumerative Coding of Balanced Run-Length Limited Codes

Palunčić,

Maharaj

2024

IEEE Access

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Various methods have been proposed for the construction of balanced run-length limited codes. Amongst these methods is the enumerative coding approach by Kurmaev. The advantage of this approach is that the code has maximum cardinality and thus approaches capacity with increasing codeword length. However, enumerative coding has the disadvantage of becoming prohibitively complex for large codeword lengths. We propose an alternative enumerative coding method that reduces the encoding and decoding complexity. We call it quasi-enumerative coding as it does not follow a strict lexicographic order, but retains a one-to-one mapping between rank and the corresponding balanced run-length limited codeword.INDEX TERMS Enumerative coding, balanced codes, run-length limited codes.

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LDPC Decoders Prefer More Reliable Parity Bits: Unequal Data Protection Over BSC

Dabak,

Tiryaki,

Calderbank

et al. 2023

2023 12th International Symposium on Topics in Coding (ISTC)

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The Secret Arithmetic of Patterns: A General Method for Designing Constrained Codes Based on Lexicographic Indexing

Cited by 8 publications

References 47 publications

Efficient Constrained Codes That Enable Page Separation in Modern Flash Memories

Efficient Constrained Codes That Enable Page Separation in Modern Flash Memories

Quasi-Enumerative Coding of Balanced Run-Length Limited Codes

LDPC Decoders Prefer More Reliable Parity Bits: Unequal Data Protection Over BSC

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