Mutual information for a deletion channel

Drmota, Michael; Szpankowski, Wojciech; Viswanathan, K.

doi:10.1109/isit.2012.6283980

Cited by 11 publications

(11 citation statements)

References 14 publications

(29 reference statements)

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“…Below we define a function computing the number of possible ways that a fixed length-n sequence is deleted to form a fixed shorter length-m sequence. Previous studies have been focusing on similar quantities, Drmota et al defined a similar quantity as the number of occurrences of a shorter sequence in a longer sequence, Liron and langberg characterized the number of subsequences obtained from a fixed length-n sequence via deletions [27,29], to name just a few. Over the years it has been repeatedly noted that the number of deletion patterns plays an important role in finding the capacity C(d ).…”

Section: Definition 7 (Deletion Pattern)mentioning

confidence: 99%

Maximum Likelihood Upper Bounds on the Capacities of Discrete Information Stable Channels

2018

2018 IEEE Information Theory Workshop (ITW)

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Motivated by a greedy approach for generating information stable processes, we prove a universal maximum likelihood (ML) upper bound on the capacities of discrete information stable channels, including the binary erasure channel (BEC), the binary symmetric channel (BSC) and the binary deletion channel (BDC). The bound is derived leveraging a system of equations obtained via the Karush-Kuhn-Tucker conditions. Intriguingly, for some memoryless channels, e.g., the BEC and BSC, the resulting upper bounds are tight and equal to their capacities. For the BDC, the universal upper bound is related to a function counting the number of possible ways that a length-m binary subsequence can be obtained by deleting n − m bits (with n − m close to nd and d denotes the deletion probability) of a length-n binary sequence. To get explicit upper bounds from the universal upper bound, it requires to compute a maximization of the matching functions over a Hamming cube containing all length-n binary sequences. Calculating the maximization exactly is hard. Instead, we provide a combinatorial formula approximating it. Under certain assumptions, several approximations and an explicit upper bound for deletion probability d ≥ 1/2 are derived.

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Section: Definition 7 (Deletion Pattern)mentioning

confidence: 99%

Maximum Likelihood Upper Bounds on the Capacities of Discrete Information Stable Channels

2018

2018 IEEE Information Theory Workshop (ITW)

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“…We refer the reader to [3] and references therein for a survey on this topic up to 2009. Some of the work that has appeared since 2009 is [4], [5], [6], [7], [8].…”

Section: Related Workmentioning

confidence: 99%

“…Substituting (11) and (25) into (8) shows that the overall probability of error is at most P (E) < ε for N large enough. Since the total energy used during transmission is no more than NP 1 + KNP 2 by (5) and (7), the achieved bits per unit energy is…”

Section: Rate Per Unit Energymentioning

confidence: 99%

Energy-Efficient Communication Over the Unsynchronized Gaussian Diamond Network

Kolte

Niesen

Gupta

2014

IEEE Trans. Inform. Theory

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Communication networks are often designed and analyzed assuming tight synchronization among nodes. However, in applications that require communication in the energy-efficient regime of low signal-to-noise ratios, establishing tight synchronization among nodes in the network can result in a significant energy overhead. Motivated by a recent result showing that near-optimal energy efficiency can be achieved over the AWGN channel without requiring tight synchronization, we consider the question of whether the potential gains of cooperative communication can be achieved in the absence of synchronization. We focus on the symmetric Gaussian diamond network and establish that cooperative-communication gains are indeed feasible even with unsynchronized nodes. More precisely, we show that the capacity per unit energy of the unsynchronized symmetric Gaussian diamond network is within a constant factor of the capacity per unit energy of the corresponding synchronized network. To this end, we propose a distributed relaying scheme that does not require tight synchronization but nevertheless achieves most of the energy gains of coherent combining.R. Kolte is with the Department of Electrical Engineering at Stanford University. U. Niesen and P. Gupta are with Bell Labs, Alcatel-Lucent.

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“…The hidden pattern matching problem, especially for large patterns, finds many ap-plications from intrusion detection, to trace reconstruction, to deletion channel, to DNAbased storage systems [1,4,5,6,12,17]. Here we discuss below in some detail two of them, namely the deletion channel and the trace reconstruction problem.…”

Section: Introductionmentioning

confidence: 99%

“…Here we discuss below in some detail two of them, namely the deletion channel and the trace reconstruction problem. A deletion channel [5,6,7,14,17,20] with parameter d takes a binary sequence Ξ n = ξ 1 • • • ξ n where ξ i ∈ A as input and deletes each symbol in the sequence independently with probability d. The output of such a channel is then a subsequence ζ = ζ(x) = ξ i 1 . .…”

Section: Introductionmentioning

confidence: 99%

Hidden Words Statistics for Large Patterns

Janson¹,

Szpankowski²

2021

Electron. J. Combin.

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We study here the so called subsequence pattern matching also known as hidden pattern matching in which one searches for a given pattern $w$ of length $m$ as a subsequence in a random text of length $n$. The quantity of interest is the number of occurrences of $w$ as a subsequence (i.e., occurring in not necessarily consecutive text locations). This problem finds many applications from intrusion detection, to trace reconstruction, to deletion channel, and to DNA-based storage systems. In all of these applications, the pattern $w$ is of variable length. To the best of our knowledge this problem was only tackled for a fixed length $m=O(1)$. In our main result we prove that for $m=o(n^{1/3})$ the number of subsequence occurrences is normally distributed. In addition, we show that under some constraints on the structure of $w$ the asymptotic normality can be extended to $m=o(\sqrt{n})$. For a special pattern $w$ consisting of the same symbol, we indicate that for $m=o(n)$ the distribution of number of subsequences is either asymptotically normal or asymptotically log normal. After studying some special patterns (e.g., alternating) we conjecture that this dichotomy is true for all patterns. We use Hoeffding's projection method for $U$-statistics to prove our findings.

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Mutual information for a deletion channel

Cited by 11 publications

References 14 publications

Maximum Likelihood Upper Bounds on the Capacities of Discrete Information Stable Channels

Maximum Likelihood Upper Bounds on the Capacities of Discrete Information Stable Channels

Energy-Efficient Communication Over the Unsynchronized Gaussian Diamond Network

Hidden Words Statistics for Large Patterns

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