The problem of channel coding with the erasure option is revisited for discrete memoryless channels. The interplay between the code rate, the undetected and total error probabilities is characterized. Using the inform...
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The problem of channel coding with the erasure option is revisited for discrete memoryless channels. The interplay between the code rate, the undetected and total error probabilities is characterized. Using the information spectrum method, a sequence of codes of increasing blocklengths n is designed to illustrate this tradeoff. Furthermore, for additive discrete memoryless channels with uniform input distribution, we establish that our analysis is tight with respect to the ensemble average. This is done by analyzing the ensemble performance in terms of a tradeoff between the code rate, the undetected and total errors. This tradeoff is parameterized by the threshold in a generalized likelihood ratio test. Two asymptotic regimes are studied. First, the code rate tends to the capacity of the channel at a rate slower than n(-1/2) corresponding to the moderate deviations regime. In this case, both error probabilities decay subexponentially and asymmetrically. The precise decay rates are characterized. second, the code rate tends to capacity at a rate of n(-1/2). In this case, the total error probability is asymptotically a positive constant, while the undetected error probability decays as exp(-bn(1/2)) for some b > 0. The proof techniques involve the applications of a modified (or shifted) version of the Gartner-Ellis theorem and the type class enumerator method to characterize the asymptotic behavior of a sequence of cumulant generating functions.
We present a novel nonasymptotic or finite blocklength achievability bounds for three side-information problems in network information theory. These include: 1) the Wyner-Ahlswede-Korner (WAK) problem of almost-lossle...
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We present a novel nonasymptotic or finite blocklength achievability bounds for three side-information problems in network information theory. These include: 1) the Wyner-Ahlswede-Korner (WAK) problem of almost-lossless source coding with rate-limited side-information;2) the Wyner-Ziv (WZ) problem of lossy source coding with side-information at the decoder;and 3) the Gel'fand-Pinsker (GP) problem of channel coding with noncausal state information available at the encoder. The bounds are proved using ideas from channel simulation and channel resolvability. Our bounds for all three problems improve on all previous nonasymptotic bounds on the error probability of the WAK, WZ, and GP problems-in particular those derived by Verdu. Using our novel nonasymptotic bounds, we recover the general formulas for the optimal rates of these side-information problems. Finally, we also present achievable second-order coding rates by applying the multidimensional Berry-Esseen theorem to our new nonasymptotic bounds. Numerical results show that the second-order coding rates obtained using our nonasymptotic achievability bounds are superior to those obtained using existing finite blocklength bounds.
In 1975, Carleial presented a special case of an interference channel, called the very strong interference regime, in which the interference does not reduce the capacity of the constituent point-to-point Gaussian chan...
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In 1975, Carleial presented a special case of an interference channel, called the very strong interference regime, in which the interference does not reduce the capacity of the constituent point-to-point Gaussian channels. In this paper, we show that in the strictly very strong interference regime, the dispersions are similarly unaffected. More precisely, in this paper, we characterize the second-order coding rates of the Gaussian interference channel in the strictly very strong interference regime. In other words, we characterize the speed of convergence of rates of optimal block codes toward a boundary point of the (rectangular) capacity region. These second-order coding rates are expressed in terms of the average probability of error and variances of appropriately defined information densities which coincide with the dispersion of the (single-user) Gaussian channel. This allows us to conclude that the dispersions are unaffected by interference in this channel model.
We analyze the dispersions of distributed lossless source coding (the Slepian-Wolf problem), the multiple-access channel, and the asymmetric broadcast channel. For the two-encoder Slepian-Wolf problem, we introduce a ...
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We analyze the dispersions of distributed lossless source coding (the Slepian-Wolf problem), the multiple-access channel, and the asymmetric broadcast channel. For the two-encoder Slepian-Wolf problem, we introduce a quantity known as the entropy dispersion matrix, which is analogous to the scalar dispersions that have gained interest recently. We prove a global dispersion result that can be expressed in terms of this entropy dispersion matrix and provides intuition on the approximate rate losses at a given blocklength and error probability. To gain better intuition about the rate at which the nonasymptotic rate region converges to the Slepian-Wolf boundary, we define and characterize two operational dispersions: 1) the local dispersion and 2) the weighted sum-rate dispersion. The former represents the rate of convergence to a point on the Slepian-Wolf boundary, whereas the latter represents the fastest rate for which a weighted sum of the two rates converges to its asymptotic fundamental limit. Interestingly, when we approach either of the two corner points, the local dispersion is characterized not by a univariate Gaussian, but a bivariate one as well as a subset of off-diagonal elements of the aforementioned entropy dispersion matrix. Finally, we demonstrate the versatility of our achievability proof technique by providing inner bounds for the multiple-access channel and the asymmetric broadcast channel in terms of dispersion matrices. All our proofs are unified by a so-called vector rate redundancy theorem, which is proved using the multidimensional Berry-Esseen theorem.
This paper shows that the logarithm of the epsilon-error capacity (average error probability) for n uses of a discrete memoryless channel (DMC) is upper bounded by the normal approximation plus a third-order term that...
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This paper shows that the logarithm of the epsilon-error capacity (average error probability) for n uses of a discrete memoryless channel (DMC) is upper bounded by the normal approximation plus a third-order term that does not exceed 1/2 log n + O(1) if the epsilon-dispersion of the channel is positive. This matches a lower bound by Y. Polyanskiy (2010) for DMCs with positive reverse dispersion. If the epsilon-dispersion vanishes, the logarithm of the epsilon-error capacity is upper bounded by n times the capacity plus a constant term except for a small class of DMCs and epsilon >= 1/2.
The problem of separately encoding and subsequently transmitting correlated sources over a discrete memoryless multiple-access channel is revisited. In particular, we examine the sufficient conditions on the source an...
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ISBN:
(纸本)9781467345392;9781467345378
The problem of separately encoding and subsequently transmitting correlated sources over a discrete memoryless multiple-access channel is revisited. In particular, we examine the sufficient conditions on the source and the channel under which there exists a n-length block code satisfying the condition that the error probability of reconstructing the discrete memoryless multiple source is no larger than some fixed constant epsilon > 0, or in short, epsilon-lossless transmission. We modify the decoding rule of Cover-El Gamal-Salehi and analyze the error probability using Gaussian approximations to derive a second-order generalization their sufficient condition for the epsilon-lossless transmission of the correlated sources.
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