The Capacity of Count-Constrained ICI-Free Systems

Kashyap, Navin; Roth, Ron M.; Siegel, Paul H.

doi:10.1109/isit.2019.8849473

Cited by 4 publications

(3 citation statements)

References 6 publications

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“…Moreover, the dominant eigenvalue of B G×G (y) is the same as that of T G×G (y). Then, by strong duality, computing (2) is equivalent to solving the following dual problem [18,19] (see also, [20]):…”

Section: Review Of Gilbert-varshamov Boundmentioning

confidence: 99%

Evaluating the Gilbert–Varshamov Bound for Constrained Systems

Goyal,

Kiah

2024

Entropy

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We revisit the well-known Gilbert–Varshamov (GV) bound for constrained systems. In 1991, Kolesnik and Krachkovsky showed that the GV bound can be determined via the solution of an optimization problem. Later, in 1992, Marcus and Roth modified the optimization problem and improved the GV bound in many instances. In this work, we provide explicit numerical procedures to solve these two optimization problems and, hence, compute the bounds. We then show that the procedures can be further simplified when we plot the respective curves. In the case where the graph presentation comprises a single state, we provide explicit formulas for both bounds.

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Section: Review Of Gilbert-varshamov Boundmentioning

confidence: 99%

Evaluating the Gilbert–Varshamov Bound for Constrained Systems

Goyal,

Kiah

2024

Entropy

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show abstract

“…Moreover, the dominant eigenvalue of B G×G (y) is the same as that of T G×G (y). Then by strong duality, computing (2) is equivalent to solving the following dual problem [20], [21] (see also, [22]).…”

mentioning

confidence: 99%

Evaluating the Gilbert-Varshamov Bound for Constrained Systems

Keshav

Kiah

2022

2022 IEEE International Symposium on Information Theory (ISIT)

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We revisit the well-known Gilbert-Varshamov (GV) bound for constrained systems. In 1991, Kolesnik and Krachkovsky showed that GV bound can be determined via the solution of some optimization problem. Later, Marcus and Roth (1992) modified the optimization problem and improved the GV bound in many instances. In this work, we provide explicit numerical procedures to solve these two optimization problems and hence, compute the bounds. We then show the procedures can be further simplified when we plot the respective curves. In the case where the graph presentation comprise a single state, we provide explicit formulas for both bounds.

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“…. , q − 1}, a formula for the (count-constrained) capacity of the constrained system forbidding patterns{β 1 β 2 β 3 | β 1 , β 3 ∈ H, β 2 ∈ L} was derived in[25].…”

mentioning

confidence: 99%

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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The Capacity of Count-Constrained ICI-Free Systems

Abstract: A Markov chain approach is applied to determine the capacity of a general class of q-ary ICI-free constrained systems that satisfy an arbitrary count constraint.

Cited by 4 publications

References 6 publications

Evaluating the Gilbert–Varshamov Bound for Constrained Systems

Evaluating the Gilbert–Varshamov Bound for Constrained Systems

Evaluating the Gilbert-Varshamov Bound for Constrained Systems

Read-and-Run Constrained Coding for Modern Flash Devices

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