Capacity of the (1, ∞)-RLL input-constrained erasure channel with feedback

Oron Sabag; Haim H. Permuter; Navin Kashyap

doi:10.1109/ITW.2015.7133107

Capacity of the (1, ∞)-RLL input-constrained erasure channel with feedback

Oron Sabag, Haim H. Permuter, Navin Kashyap

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

The input-constrained erasure channel with feedback is considered, where the input sequence contains no consecutive 1's, i.e. the (1, ∞)-RLL constraint. The capacity is calculated using an equivalent dynamic program, which shows that the optimal average reward is equal to the capacity. The capacity can be expressed as C_ε=max₀≤p≤1 H_b(p)/p+1/1-ε, where ε is the erasure probability and H_b(·) is the binary entropy. This capacity also serves as an upper bound on the capacity of the input-constrained erasure channel without feedback, a problem that is still open.

Original language	English
Title of host publication	2015 IEEE Information Theory Workshop, ITW 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781479955268
DOIs	https://doi.org/10.1109/ITW.2015.7133107
State	Published - 24 Jun 2015
Externally published	Yes
Event	2015 IEEE Information Theory Workshop, ITW 2015 - Jerusalem, Israel Duration: 26 Apr 2015 → 1 May 2015

Publication series

Name	2015 IEEE Information Theory Workshop, ITW 2015

Conference

Conference	2015 IEEE Information Theory Workshop, ITW 2015
Country/Territory	Israel
City	Jerusalem
Period	26/04/15 → 1/05/15

Bibliographical note

Publisher Copyright:
© 2015 IEEE.

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10.1109/ITW.2015.7133107

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title = "Capacity of the (1, ∞)-RLL input-constrained erasure channel with feedback",

abstract = "The input-constrained erasure channel with feedback is considered, where the input sequence contains no consecutive 1's, i.e. the (1, ∞)-RLL constraint. The capacity is calculated using an equivalent dynamic program, which shows that the optimal average reward is equal to the capacity. The capacity can be expressed as Cε=max0≤p≤1 Hb(p)/p+1/1-ε, where ε is the erasure probability and Hb(·) is the binary entropy. This capacity also serves as an upper bound on the capacity of the input-constrained erasure channel without feedback, a problem that is still open.",

author = "Oron Sabag and Permuter, \{Haim H.\} and Navin Kashyap",

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year = "2015",

month = jun,

day = "24",

doi = "10.1109/ITW.2015.7133107",

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publisher = "Institute of Electrical and Electronics Engineers Inc.",

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Sabag, O, Permuter, HH & Kashyap, N 2015, Capacity of the (1, ∞)-RLL input-constrained erasure channel with feedback. in 2015 IEEE Information Theory Workshop, ITW 2015., 7133107, 2015 IEEE Information Theory Workshop, ITW 2015, Institute of Electrical and Electronics Engineers Inc., 2015 IEEE Information Theory Workshop, ITW 2015, Jerusalem, Israel, 26/04/15. https://doi.org/10.1109/ITW.2015.7133107

Capacity of the (1, ∞)-RLL input-constrained erasure channel with feedback. / Sabag, Oron; Permuter, Haim H.; Kashyap, Navin.
2015 IEEE Information Theory Workshop, ITW 2015. Institute of Electrical and Electronics Engineers Inc., 2015. 7133107 (2015 IEEE Information Theory Workshop, ITW 2015).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - The input-constrained erasure channel with feedback is considered, where the input sequence contains no consecutive 1's, i.e. the (1, ∞)-RLL constraint. The capacity is calculated using an equivalent dynamic program, which shows that the optimal average reward is equal to the capacity. The capacity can be expressed as Cε=max0≤p≤1 Hb(p)/p+1/1-ε, where ε is the erasure probability and Hb(·) is the binary entropy. This capacity also serves as an upper bound on the capacity of the input-constrained erasure channel without feedback, a problem that is still open.

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Capacity of the (1, ∞)-RLL input-constrained erasure channel with feedback

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