A Constrained Coding Scheme for Correcting Asymmetric Magnitude-1 Errors in q-Ary Channels

Evyatar Hemo; Yuval Cassuto

doi:https://doi.org/10.1109/TIT.2017.2747558

A Constrained Coding Scheme for Correcting Asymmetric Magnitude-1 Errors in q-Ary Channels

Evyatar Hemo, Yuval Cassuto

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We present a constraint-coding scheme to correct asymmetric magnitude-1 errors in multi-level non-volatile memories. For large numbers of such errors, the scheme is shown to deliver better correction capability compared with known alternatives, while admitting low-complexity of decoding. Our results include an algebraic formulation of the constraint, necessary and sufficient conditions for correctability, a maximum-likelihood decoder running in complexity linear in the alphabet size, and upper bounds on the probability of failing to correct t errors. Besides the superior rate-correction tradeoff, another advantage of this scheme over standard error-correcting codes is the flexibility to vary the code parameters without significant modifications.

Original language	English
Article number	8023789
Pages (from-to)	918-932
Number of pages	15
Journal	IEEE Transactions on Information Theory
Volume	64
Issue number	2
DOIs	https://doi.org/10.1109/TIT.2017.2747558
State	Published - Feb 2018

Keywords

Channel coding
Flash memory
coding for memories
constraint coding
histograms

All Science Journal Classification (ASJC) codes

Information Systems
Computer Science Applications
Library and Information Sciences

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https://doi.org/10.1109/TIT.2017.2747558

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title = "A Constrained Coding Scheme for Correcting Asymmetric Magnitude-1 Errors in q-Ary Channels",

abstract = "We present a constraint-coding scheme to correct asymmetric magnitude-1 errors in multi-level non-volatile memories. For large numbers of such errors, the scheme is shown to deliver better correction capability compared with known alternatives, while admitting low-complexity of decoding. Our results include an algebraic formulation of the constraint, necessary and sufficient conditions for correctability, a maximum-likelihood decoder running in complexity linear in the alphabet size, and upper bounds on the probability of failing to correct t errors. Besides the superior rate-correction tradeoff, another advantage of this scheme over standard error-correcting codes is the flexibility to vary the code parameters without significant modifications.",

keywords = "Channel coding, Flash memory, coding for memories, constraint coding, histograms",

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N2 - We present a constraint-coding scheme to correct asymmetric magnitude-1 errors in multi-level non-volatile memories. For large numbers of such errors, the scheme is shown to deliver better correction capability compared with known alternatives, while admitting low-complexity of decoding. Our results include an algebraic formulation of the constraint, necessary and sufficient conditions for correctability, a maximum-likelihood decoder running in complexity linear in the alphabet size, and upper bounds on the probability of failing to correct t errors. Besides the superior rate-correction tradeoff, another advantage of this scheme over standard error-correcting codes is the flexibility to vary the code parameters without significant modifications.

AB - We present a constraint-coding scheme to correct asymmetric magnitude-1 errors in multi-level non-volatile memories. For large numbers of such errors, the scheme is shown to deliver better correction capability compared with known alternatives, while admitting low-complexity of decoding. Our results include an algebraic formulation of the constraint, necessary and sufficient conditions for correctability, a maximum-likelihood decoder running in complexity linear in the alphabet size, and upper bounds on the probability of failing to correct t errors. Besides the superior rate-correction tradeoff, another advantage of this scheme over standard error-correcting codes is the flexibility to vary the code parameters without significant modifications.

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KW - coding for memories

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KW - histograms

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JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

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A Constrained Coding Scheme for Correcting Asymmetric Magnitude-1 Errors in q-Ary Channels

Abstract

Keywords

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