Novel Bounds on the Capacity of the Binary Deletion Channel

Fertonani, D.; Duman, Tolga M.

doi:10.1109/tit.2010.2046210

Cited by 52 publications

(119 citation statements)

References 11 publications

(57 reference statements)

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“…The procedure is similar to [3]. Specifically, we obtain upper bounds by giving some kind of side-information to the encoder and decoder, and calculating or upper bounding the capacity of this genie-aided channel.…”

Section: B Upper Bounds On the Capacitymentioning

confidence: 99%

“…After introducing a useful function g(k, n) through uniform insertion model in Section II, we obtain upper bounds on the capacity of the intermittent communication with i.i.d. insertions in Section III by giving some kind of side-information to the encoder and decoder, and calculating or upper bounding the capacity of this genie-aided channel, which is similar to the method used in [3] and [4]. Also, by obtaining an upper bound for the function g(k, n), we are able to tighten the upper bounds for the i.i.d.…”

Section: Introductionmentioning

confidence: 99%

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Upper bounds on the capacity of binary intermittent communication

Khoshnevisan

Laneman

2013

2013 Information Theory and Applications Workshop (ITA)

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Abstract-This paper focuses on obtaining upper bounds on the capacity of a special case of intermittent communication, introduced in [1], in which the channel is binary-input binaryoutput noiseless with i.i.d. number of zeros inserted in between the binary codeword symbols. Upper bounds are obtained by providing the encoder and the decoder with various amounts of side-information, and calculating or upper bounding the capacity of this genie-aided system. The results suggest that the linear scaling of the receive window with respect to the codeword length considered in the system model is relevant since the upper bounds imply a tradeoff between the capacity of the channel and the intermittency rate.

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Section: B Upper Bounds On the Capacitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Upper bounds on the capacity of binary intermittent communication

Khoshnevisan

Laneman

2013

2013 Information Theory and Applications Workshop (ITA)

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“…For example, the recent paper [7] provides an approximation of the capacity of the binary deletion channel to within a factor 9 in general. Tighter bounds have been obtained for some specific regimes of the deletion probability: For instance, in [12] [13], upper and lower bounds are provided and vanishing gap is shown in the asymptotically small deletion-probability regime; while improved upper bounds based on a numerical approach are obtained in [11]. The main difficulty in analyzing these channels arises from to the channel memory introduced by the duplications and deletions, which prevents a direct application of the standard information-theoretic tools.…”

Section: A Related Workmentioning

confidence: 99%

Energy-efficient communication in the presence of synchronization errors

Huang

Niesen²,

Gupta³

2013

2013 IEEE International Symposium on Information Theory

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Communication systems are traditionally designed to have tight transmitter-receiver synchronization. This requirement has negligible overhead in the high-SNR regime. However, in many applications, such as wireless sensor networks, communication needs to happen primarily in the energy-efficient regime of low SNR, where requiring tight synchronization can be highly suboptimal.In this paper, we model the noisy channel with synchronization errors as a duplication/deletion/substitution channel. For this channel, we propose a new communication scheme that requires only loose transmitter-receiver synchronization. We show that the proposed scheme is asymptotically optimal for the Gaussian channel with synchronization errors in terms of energy efficiency as measured by the rate per unit energy. In the process, we also establish that the lack of synchronization causes negligible loss in energy efficiency. We further show that, for a general discrete memoryless channel with synchronization errors and a general input cost function admitting a zero-cost symbol, the rate per unit cost achieved by the proposed scheme is within a factor two of the informationtheoretic optimum.I. INTRODUCTION Traditionally, data transmission in a communication system is based on tight synchronization between the transmitter and the receiver. This tight synchronization is usually achieved through either of two strategies. In the first strategy, synchronization is achieved through periodic transmission of pilot signals, followed by transmission of information over the synchronized channel (see, e.g., [1, Chapter 6.3]). In the second strategy, data bits are differentially encoded and then modulated (e.g., differential pulse-positionmodulation) [1, Chapter 4.3.2], which implicitly achieves tight synchronization.The above strategies work well at high signal-to-noise ratios (SNRs) as the energy overhead of achieving tight synchronization is negligible compared to that of data transmission. However, in many applications, such as wireless sensor networks, space communication, or in general any communication system requiring high energy efficiency, communication by necessity has to primarily take place in the low-SNR regime (due to the concavity of the power-rate function). In such scenarios, the energy overhead to achieve tight synchronization becomes significant and can render the aforementioned strategies highly suboptimal in terms of energy efficiency. In fact, requiring tight transmitter-receiver synchronization can have arbitrarily large loss in performance in terms of energy efficiency (see Example 3 in Section III).To mitigate this, in this paper, we develop and analyze a framework to perform data transmission while only requiring loose synchronization between the transmitter and the receiver. To focus on the energyefficiency aspect, we choose the rate per unit cost (with energy being a prime example of the cost) as our performance metric. We model synchronization errors through channel duplications/deletions-an approach introduced in [2]...

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“…In the regime of large blocks and small synchronization errors we have: 4 4 We say that f (ℓ) = O(g(ℓ)) if there exists a positive real number k such that…”

Section: Asymptoticsmentioning

confidence: 99%

“…where E i = −1 if the i-th block experienced a deletion, E i = 1 if the i-th block experienced a duplication, and E i = 0 otherwise [4], [14]. When this side information is provided to the receiver, each block can be considered in complete isolation and we obtain the so-called "one-bit" deletion and duplication channel.…”

Section: Introductionmentioning

confidence: 99%

On the capacity of the one-bit deletion and duplication channel

Mirghasemi

Tchamkerten

2012

2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Abstract-The one-bit deletion and duplication channel is investigated. An input to this channel consists of a block of ℓ ≥ 1 bits which experiences a deletion with probability p, a duplication with probability q, and remains unchanged with probability 1 − p − q. For this channel a capacity expression is obtained in the asymptotic regime where p + q = o(1/ log ℓ). As a corollary, we obtain an asymptotic expression for the capacity of the so called "segmented" deletion and duplication channel where the input now consists of several blocks and each block independently experiences either a deletion, or a duplication, or remains unchanged.

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Novel Bounds on the Capacity of the Binary Deletion Channel

Cited by 52 publications

References 11 publications

Upper bounds on the capacity of binary intermittent communication

Upper bounds on the capacity of binary intermittent communication

Energy-efficient communication in the presence of synchronization errors

On the capacity of the one-bit deletion and duplication channel

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