A new bound on the capacity of the binary deletion channel with high deletion probabilities

Dalai, Marco

doi:10.1109/isit.2011.6034177

Cited by 29 publications

(41 citation statements)

References 8 publications

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“…This result is also a broad generalization of the one obtained in [9] which only holds asymptotically as d → 1. We also demonstrate that a similar improvement is possible for the case of deletion/substitution channels.…”

supporting

confidence: 75%

“…deletion channel, we prove that C 2 (d) ≤ 0.4143(1 − d) for all d ≥ 0.65. This is a stronger result than the earlier characterization in [9] which is valid only asymptotically as d → 1. Furthermore, for non-binary deletion channels, the provided upper bound results in tighter characterizations than the trivial erasure channel upper bound for the entire range of deletion probabilities.…”

Section: Discussioncontrasting

confidence: 47%

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Upper Bounds on the Capacity of Deletion Channels Using Channel Fragmentation

Rahmati

Duman

2015

IEEE Trans. Inform. Theory

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Abstract-We study memoryless channels with synchronization errors as defined by a stochastic channel matrix allowing for symbol drop-outs or symbol insertions with particular emphasis on the binary and non-binary deletion channels. We offer a different look at these channels by considering equivalent models by fragmenting the input sequence where different subsequences travel through different channels. The resulting output symbols are combined appropriately to come up with an equivalent input-output representation of the original channel which allows for derivation of new upper bounds on the channel capacity. We consider both random and deterministic types of fragmentation processes applied to binary and nonbinary deletion channels. With two specific applications of this idea, a random fragmentation applied to a binary deletion channel and a deterministic fragmentation process applied to a nonbinary deletion channel, we prove certain inequality relations among the capacities of the original channels and those of the introduced subchannels. The resulting inequalities prove useful in deriving tighter capacity upper bounds for: 1) independent identically distributed (i.i.d.) deletion channels when the deletion probability exceeds 0.65 and 2) nonbinary deletion channels. Some extensions of these results, for instance, to the case of deletion/substitution channels are also explored.

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supporting

confidence: 75%

Section: Discussioncontrasting

confidence: 47%

Upper Bounds on the Capacity of Deletion Channels Using Channel Fragmentation

Rahmati

Duman

2015

IEEE Trans. Inform. Theory

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“…We consider the expression in (2). We first note that the empty word does not contribute to the sum (2).…”

Section: B Proof Of Theorem 3: D →mentioning

confidence: 99%

“…If n(1 − d) = o(1) this leads to T 2 ≤ C 1 n 2 (1 − d) 2 log n for some absolute constant C 1 > 0. Summing up and using Corollary 1, we obtain that …”

Section: B Proof Of Theorem 3: D →mentioning

confidence: 99%

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Mutual information for a deletion channel

Drmota

Szpankowski

Viswanathan

2012

2012 IEEE International Symposium on Information Theory Proceedings

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Abstract-We study the binary deletion channel where each input bit is independently deleted according to a fixed probability. We relate the conditional probability distribution of the output of the deletion channel given the input to the hidden pattern matching problem. This yields a new characterization of the mutual information between the input and output of the deletion channel. Through this characterization we are able to comment on the the deletion channel capacity, in particular for deletion probabilities approaching 0 and 1.

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An improvement of the deletion channel capacity upper bound

Rahmati

Duman

2013

2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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In this paper, we offer an alternative look at channels with deletion errors by considering equivalent models for deletion channels by 'fragmenting' the input sequence where different subsequences travel through different channels. The resulting output symbols are combined appropriately to come up with an equivalent input-output representation of the original channel which allows for derivation of new upper bounds on the channel capacity. Considering a random fragmentation processes applied to binary deletion channels, we prove an inequality relation among the capacities of the original binary deletion channel and the introduced binary deletion subchannels. This inequality enables us to provide an improved upper bound on the capacity of the i.i.d. deletion channels, i.e., C(d) ≤ 0.4143(1 - d) for d ≥ 0.65. We also consider a deterministic fragmentation process suitable for the study of non-binary deletion channels which results in improved capacity upper bounds. © 2013 IEEE

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A new bound on the capacity of the binary deletion channel with high deletion probabilities

Abstract: Abstract-Let C(d) be the capacity of the binary deletion channel with deletion probability d.

Cited by 29 publications

References 8 publications

Upper Bounds on the Capacity of Deletion Channels Using Channel Fragmentation

Upper Bounds on the Capacity of Deletion Channels Using Channel Fragmentation

Mutual information for a deletion channel

An improvement of the deletion channel capacity upper bound

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