Related papers: An Extended Fano's Inequality for the Finite Block…
Quantum Fano inequality (QFI) in quantum information theory provides an upper bound to the entropy exchange by a function of the entanglement fidelity. We give various Fano-like upper bounds to the entropy exchange and QFI is a special case…
In this technical note, we give two extensions of the classical Fano inequality in information theory. The first extends Fano's inequality to the setting of estimation, providing lower bounds on the probability that an estimator of a…
In statistical inference problems, we wish to obtain lower bounds on the minimax risk, that is to bound the performance of any possible estimator. A standard technique to obtain risk lower bounds involves the use of Fano's inequality. In an…
Fano's inequality is one of the most elementary, ubiquitous, and important tools in information theory. Using majorization theory, Fano's inequality is generalized to a broad class of information measures, which contains those of Shannon…
We consider upper bounds on the error probability in channel coding. We derive an improved maximum-likelihood union bound, which takes into account events where the likelihood of the correct codeword is tied with that of some competitors.…
This paper introduces equal-image-size source partitioning, a new tool for analyzing channel and joint source-channel coding in a multi-terminal discrete memoryless channel environment. Equal-image-size source partitioning divides the…
Information theory provides tools to predict the performance of a learning algorithm on a given dataset. For instance, the accuracy of learning an unknown parameter can be upper bounded by reducing the learning task to hypothesis testing…
The discrimination between non-orthogonal quantum states plays a pivotal role in quantum information processing and quantum technology. Strategies that minimize the error probability are of particular importance, but they are only known for…
We extend Fano's inequality, which controls the average probability of events in terms of the average of some $f$--divergences, to work with arbitrary events (not necessarily forming a partition) and even with arbitrary $[0,1]$--valued…
Information theory plays an indispensable role in the development of algorithm-independent impossibility results, both for communication problems and for seemingly distinct areas such as statistics and machine learning. While numerous…
This paper gives upper and lower bounds on the minimum error probability of Bayesian $M$-ary hypothesis testing in terms of the Arimoto-R\'enyi conditional entropy of an arbitrary order $\alpha$. The improved tightness of these bounds over…
"Bounds on information combining" are entropic inequalities that determine how the information (entropy) of a set of random variables can change when these are combined in certain prescribed ways. Such bounds play an important role in…
The existing upper and lower bounds between entropy and error probability are mostly derived from the inequality of the entropy relations, which could introduce approximations into the analysis. We derive analytical bounds based on the…
Consider communication over the binary erasure channel BEC using random low-density parity-check codes with finite-blocklength n from `standard' ensembles. We show that large error events is conveniently described within a scaling theory,…
The decoding error probability of codes is studied as a function of their block length. It is shown that the existence of codes with a polynomially small decoding error probability implies the existence of codes with an exponentially small…
We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme…
Generalizations of the quantum Fano inequality are considered. The notion of $q$-entropy exchange is introduced. This quantity is concave in each of its two arguments. For $q\geq0$, the inequality of Fano type with $q$-entropic functionals…
In the study of the capacity problem for multiple access channels (MACs), a lower bound on the error probability obtained by Han plays a crucial role in the converse parts of several kinds of channel coding theorems in the…
Fano effect arising from interference between two dissipation channels to the radiation continuum enables to tune the photon statistics. Understanding the role of Fano effect and exploiting to achieve strong photon correlations are of both…
We derive novel upper and lower finite-length bounds of the error probability in joint source-channel coding when the source obeys an ergodic Markov process and the channel is a Markovian additive channel or a Markovian conditional additive…