Constructions for constant-weight ICI-free codes

Kayser, Scott; Siegel, Paul H.

doi:10.1109/isit.2014.6875069

Cited by 20 publications

(15 citation statements)

References 8 publications

(8 reference statements)

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“…See [16] for a study of balanced constrained codes that alleviate ICI in Flash systems by eliminating the pattern (q − 1)0(q − 1), where q is the number of levels in the cell and also the Galois field (GF) order 1 . Another related work is [17]. Furthermore, line codes find application in computer standards for data transmission, such as universal serial bus (USB) and peripheral component interconnect express (PCIe).…”

Section: Introductionmentioning

confidence: 99%

LOCO Codes: Lexicographically-Ordered Constrained Codes

Hareedy

Calderbank

2020

IEEE Trans. Inform. Theory

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Line codes make it possible to mitigate interference, to prevent short pulses, and to generate streams of bipolar signals with no direct-current (DC) power content through balancing. They find application in magnetic recording (MR) devices, in Flash devices, in optical recording devices, and in some computer standards. This paper introduces a new family of fixed-length, binary constrained codes, named lexicographically-ordered constrained codes (LOCO codes), for bipolar non-return-to-zero signaling. LOCO codes are capacity-achieving, the lexicographic indexing enables simple, practical encoding and decoding, and this simplicity is demonstrated through analysis of circuit complexity. LOCO codes are easy to balance, and their inherent symmetry minimizes the rate loss with respect to unbalanced codes having the same constraints. Furthermore, LOCO codes that forbid certain patterns can be used to alleviate inter-symbol interference in MR systems and inter-cell interference in Flash systems. Numerical results demonstrate a gain of up to 10% in rate achieved by LOCO codes with respect to other practical constrained codes, including run-length-limited codes, designed for the same purpose. Simulation results suggest that it is possible to achieve a channel density gain of about 20% in MR systems by using a LOCO code to encode only the parity bits, limiting the rate loss, of a low-density parity-check code before writing.

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Section: Introductionmentioning

confidence: 99%

LOCO Codes: Lexicographically-Ordered Constrained Codes

Hareedy

Calderbank

2020

IEEE Trans. Inform. Theory

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“…We are interested in both the optimal asymptotic rates and efficient encoding/decoding algorithms for the codes that are capacity-achieving. Our results answer some open questions in [42,59].…”

Section: Coding For Multilevel Cell Flash Memories One Dimensional Cosupporting

confidence: 65%

“…Recently, dynamic thresholds and constrained coding have been combined to mitigate both ICI and charge leakage in flash memories [42,59]. In [59], Qin et al…”

Section: Coding For Multilevel Cell Flash Memories One Dimensional Comentioning

confidence: 99%

“…While the asymptotic rates of q-ary balanced I(0, q − 1)-avoiding codes were not explicitly determined for q > 3, the asymptotic rate of binary balanced I(0, 1)-avoiding codes was shown to be 2% less than the capacity of the I(0, 1)-avoiding constraint channel. In [42], Kayser and Siegel gave a construction for binary constant weight I(0, 1)-avoiding codes. In the same paper, they also showed that the supremum of the rates of binary constant weight I(0, 1)-avoiding codes equals the capacity of the I(0, 1)-avoiding constraint.…”

Section: Coding For Multilevel Cell Flash Memories One Dimensional Comentioning

confidence: 99%

“…Other techniques, such as enumerative coding, have been developed for constrained codes avoiding some patterns with weight constraints [6,37,47,57]. Recently, applications in flash memories have attracted more research on balanced constrained codes and constrained codes with constant weight [42,59]. Many interesting questions in…”

Section: Chapter 1 Introduction 11 Constrained Codesmentioning

confidence: 99%

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Constrained codes for intercell interference mitigation and dynamic thresholding in flash memories

Vu¹

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for the great advice and guidance through my time in NTU. They helped me a lot to open my view, to explore and pursue interesting research problems, to find out the best of myself. I also very much appreciate their patience and belief in me. It is my great honour and best luck to work with them. I am very fortunate to have chances to work with many great researchers in Singapore and around the world during my PhD programme, which makes my research fruitful. I am indebted to all my co-authors for works in flash memories and permutation channel:

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Asymmetric LOCO Codes: Constrained Codes for Flash Memories

Hareedy

Calderbank

2019

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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In data storage and data transmission, certain patterns are more likely to be subject to error when written (transmitted) onto the media. In magnetic recording systems with binary data and bipolar non-return-to-zero signaling, patterns that have insufficient separation between consecutive transitions exacerbate inter-symbol interference. Constrained codes are used to eliminate such error-prone patterns. A recent example is a new family of capacity-achieving constrained codes, named lexicographically-ordered constrained codes (LOCO codes). LOCO codes are symmetric, that is, the set of forbidden patterns is closed under taking pattern complements. LOCO codes are suboptimal in terms of rate when used in Flash devices where block erasure is employed since the complement of an error-prone pattern is not detrimental in these devices. This paper introduces asymmetric LOCO codes (A-LOCO codes), which are lexicographically-ordered constrained codes that forbid only those patterns that are detrimental for Flash performance. A-LOCO codes are also capacity-achieving, and at finite-lengths, they offer higher rates than the available stateof-the-art constrained codes designed for the same goal. The mapping-demapping between the index and the codeword in A-LOCO codes allows low-complexity encoding and decoding algorithms that are simpler than their LOCO counterparts. 1 We directly map the GF elements to consecutive integers representing threshold voltage levels in order to follow the references.

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Constructions for constant-weight ICI-free codes

Cited by 20 publications

References 8 publications

LOCO Codes: Lexicographically-Ordered Constrained Codes

LOCO Codes: Lexicographically-Ordered Constrained Codes

Constrained codes for intercell interference mitigation and dynamic thresholding in flash memories

Asymmetric LOCO Codes: Constrained Codes for Flash Memories

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