Publication

To code or not to code

Résumé

It is well known and surprising that the uncoded transmission of an independent and identically distributed Gaussian source across an additive white Gaussian noise channel is optimal: No amount of sophistication in the coding strategy can ever perform better. What makes uncoded transmission optimal? In this thesis, it is shown that the optimality of uncoded transmission can be understood as the perfect match of four involved measures: the probability distribution of the source, its distortion measure, the conditional probability distribution of the channel, and its input cost function. More generally, what makes a source-channel communication system optimal? Inspired by, and in extension of, the results about uncoded transmission, this can again be understood as the perfect match, now of six quantities: the above, plus the encoding and the decoding functions. The matching condition derived in this thesis is explicit and closed-form. This fact is exploited in various ways, for example to analyze the optimality of source-channel coding systems of finite block length, and involving feedback. In the shape of an intermezzo, the potential impact of our findings on the understanding of biological communication is outlined: owing to its simplicity, uncoded transmission must be an interesting strategy, e.g., for neural communication. The matching condition of this thesis shows that, apart from being simple, uncoded transmission may also be information-theoretically optimal. Uncoded transmission is also a useful point of view in network information theory. In this thesis, it is used to determine network source-channel communication results, including a single-source broadcast scenario, to establish capacity results for Gaussian relay networks, and to give a new example of the fact that separate source and channel coding does not lead to optimal performance in general networks.

À propos de ce résultat
Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.
Concepts associés (33)
Error correction code
In computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The central idea is that the sender encodes the message in a redundant way, most often by using an error correction code or error correcting code (ECC). The redundancy allows the receiver not only to detect errors that may occur anywhere in the message, but often to correct a limited number of errors.
Théorème du codage de canal
En théorie de l'information, le théorème du codage de canal aussi appelé deuxième théorème de Shannon montre qu'il est possible de transmettre des données numériques sur un canal bruité avec un taux d'erreur arbitrairement faible si le débit est inférieur à une certaine limite propre au canal. Ce résultat publié par Claude Shannon en 1948 est fondé sur des travaux antérieurs de Harry Nyquist et Ralph Hartley. La première preuve rigoureuse fut établie par Amiel Feinstein en 1954.
Linear network coding
In computer networking, linear network coding is a program in which intermediate nodes transmit data from source nodes to sink nodes by means of linear combinations. Linear network coding may be used to improve a network's throughput, efficiency, and scalability, as well as reducing attacks and eavesdropping. The nodes of a network take several packets and combine for transmission. This process may be used to attain the maximum possible information flow in a network.
Afficher plus
Publications associées (138)

On Speed and Advantage : Results in Information Velocity and Monitoring Problems

Reka Inovan

Information theory has allowed us to determine the fundamental limit of various communication and algorithmic problems, e.g., the channel coding problem, the compression problem, and the hypothesis testing problem. In this work, we revisit the assumptions ...
EPFL2024

Quantifying uncertain system outputs via the multi-level Monte Carlo method --- distribution and robustness measures

Fabio Nobile, Sebastian Krumscheid, Sundar Subramaniam Ganesh

In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk, of output quantities of complex random differential models by the MLM ...
2022

A Unified Discretization Approach to Compute–Forward: From Discrete to Continuous Inputs

Michael Christoph Gastpar, Sung Hoon Lim, Adriano Pastore, Chen Feng

Compute–forward is a coding technique that enables receiver(s) in a network to directly decode one or more linear combinations of the transmitted codewords. Initial efforts focused on Gaussian channels and derived achievable rate regions via nested lattice ...
2022
Afficher plus
MOOCs associés (14)
Information, Calcul, Communication: Introduction à la pensée informatique
Dans une première partie, nous étudierons d’abord comment résoudre de manière très concrète un problème au moyen d’un algorithme, ce qui nous amènera dans un second temps à une des grandes questions d
Information, Calcul, Communication: Introduction à la pensée informatique
Dans une première partie, nous étudierons d’abord comment résoudre de manière très concrète un problème au moyen d’un algorithme, ce qui nous amènera dans un second temps à une des grandes questions d
Neuronal Dynamics - Computational Neuroscience of Single Neurons
The activity of neurons in the brain and the code used by these neurons is described by mathematical neuron models at different levels of detail.
Afficher plus

Graph Chatbot

Chattez avec Graph Search

Posez n’importe quelle question sur les cours, conférences, exercices, recherches, actualités, etc. de l’EPFL ou essayez les exemples de questions ci-dessous.

AVERTISSEMENT : Le chatbot Graph n'est pas programmé pour fournir des réponses explicites ou catégoriques à vos questions. Il transforme plutôt vos questions en demandes API qui sont distribuées aux différents services informatiques officiellement administrés par l'EPFL. Son but est uniquement de collecter et de recommander des références pertinentes à des contenus que vous pouvez explorer pour vous aider à répondre à vos questions.