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This paper investigates the achievable rates of an additive white Gaussian noise (AWGN) energy-harvesting (EH) channel with an infinite battery under the assumption that the error probabilities do not vanish as the blocklength increases. The EH process is characterized by a sequence of blocks of harvested energy. The harvested energy remains constant within a block while the harvested energy across...
We derive upper and lower bounds on the reliability function for the discrete memoryless broadcast channel with common message and variable-length feedback. We show that the bounds are tight when the broadcast channel is stochastically degraded. We adapt and supplement new ideas to Yamamoto and Itoh's two-phase coding scheme for the direct part and Burnashev's proof technique for the converse part.
This paper is motivated by the error-control problem in communication channels in which the transmitted sequences are subjected to random permutations, in addition to being impaired with insertions, deletions, substitutions, and erasures of symbols. Bounds on the size of optimal codes in this setting are derived, and their asymptotic behavior examined in the fixed-minimum-distance regime. A family...
Given a sufficient statistic for a parametric family of distributions, one can estimate the parameter without access to the data itself. However, the memory or code size for storing the sufficient statistic may nonetheless still be prohibitive. Indeed, for n independent data samples drawn from a k-nomial distribution with d = k − 1 degrees of freedom, the length of the code scales as d log n + O(1)...
This work investigates the limits of communication over a noisy channel that wears out, in the sense of signal-dependent catastrophic failure. In particular, we consider a channel that starts as a memoryless binary-input channel and when the number of transmitted ones causes a sufficient amount of damage, the channel ceases to convey signals. We restrict attention to constant composition codes. Since...
We analyse families of codes for classical data transmission over quantum channels that have both a vanishing probability of error and a code rate approaching capacity as the code length increases. To characterise the fundamental tradeoff between decoding error, code rate and code length for such codes we introduce a quantum generalisation of the moderate deviation analysis proposed by Altŭg and Wagner...
In this paper, a streaming transmission setup is considered where an encoder observes a new message in the beginning of each block and a decoder sequentially decodes each message after a delay of T blocks. In this streaming setup, the fundamental interplay between the coding rate, the error probability, and the blocklength in the moderate deviations regime is studied. For output symmetric channels,...
The problem of publishing privacy-guaranteed data for hypothesis testing is studied using the maximal leakage (ML) as a metric for privacy and the type-II error exponent as the utility metric. The optimal mechanism (random mapping) that maximizes utility for a bounded leakage guarantee is determined for the entire leakage range for binary datasets. For non-binary datasets, approximations in the high...
We characterize the information-theoretic limits of the Gaussian multiple access channel (MAC) when variable-length stop-feedback is available at the encoder and a non-vanishing error probability is permitted. Due to the continuous nature of the channel and the presence of expected power constraints, we need to develop new achievability and converse techniques. Due to the multi-terminal nature of...
This paper considers a multimessage network where each node may send a message to any other node in the network. Under the discrete memoryless model, we prove the strong converse theorem for any network with tight cut-set bound, i.e., whose cut-set bound is achievable. Our result implies that for any network with tight cut-set bound and any fixed rate vector that resides outside the capacity region,...
In this paper, we revisit the content identification problem with lossy recovery (Tuncel and Gündüz, 2014) and establish the exponential strong converse theorem for the problem. Further, we derive an upper bound on the joint excess-distortion and error exponent for the problem.
Motivated by streaming multi-view video coding, we consider the problem of blockwise streaming compression of a pair of correlated sources, which we term streaming Slepian-Wolf coding. We study the moderate deviations regime in which the rate pairs of a sequence of codes converges, along a straight line, to various points on the boundary of the Slepian-Wolf region at a speed slower than the inverse...
The multiplicative update (MU) algorithm has been used extensively to estimate the basis and coefficient matrices in nonnegative matrix factorization (NMF) problems under a wide range of divergences and regularizations. However, theoretical convergence guarantees have only been derived for a few special divergences. In this work, we provide a conceptually simple, self-contained, and unified proof...
We propose a geometric assumption on nonnegative data matrices such that under this assumption, we are able to provide upper bounds (both deterministic and probabilistic) on the relative error of nonnegative matrix factorization (NMF). The algorithm we propose first uses the geometric assumption to obtain an exact clustering of the columns of the data matrix; subsequently, it employs several rank-one...
Binary hypothesis testing under the Neyman-Pearson formalism is a statistical inference framework for distinguishing data generated by two different source distributions. Privacy restrictions may require the curator of the data or the data respondents themselves to share data with the test only after applying a randomizing privacy mechanism. Using mutual information as the privacy metric and the relative...
In this paper, we analyze the asymptotic expansion for additive white Gaussian noise (AWGN) channels with feedback under an expected power constraint and the average error probability formalism. We show that the ε-capacity depends on ε in general and so the strong converse fails to hold. Furthermore, we provide bounds on the second-order term in the asymptotic expansion. We show that the second-order...
We study the asymptotics of the remaining uncertainty of a source when a compressed version of it and correlated side-information is observed. Instead of measuring the remaining uncertainty using Shannon measures, we do so using two forms of the conditional Rényi entropy. We show that these asymptotic results are generalizations of the strong converse exponent and the error exponent of Slepian-Wolf...
This paper investigates the information-theoretic limits of the additive white Gaussian noise (AWGN) energy-harvesting (EH) channel in the finite blocklength regime. The EH process is characterized by a sequence of i.i.d. random variables with finite variances. We use the save-and-transmit strategy proposed by Ozel and Ulukus (2012) together with Shannon's non-asymptotic achievability bound to obtain...
We study the second-order asymptotics of information transmission using random Gaussian codebooks and nearest neighbor (NN) decoding over a power-limited additive stationary memoryless non-Gaussian channel. We show that the dispersion term depends on the non-Gaussian noise only through its second and fourth moments. We also characterize the second-order performance of point-to-point codes over Gaussian...
We prove that 2-user Gaussian broadcast channels admit the strong converse. This implies that for every sequence of block codes with an asymptotic maximal error probability smaller than one, the limit points of the corresponding sequence of rate pairs must lie within the capacity region derived by Cover and Bergmans. The main mathematical tool required for our analysis is a logarithmic Sobolev inequality...
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