Publication

On the use of training sequences for channel estimation

Résumé

Suppose Q is a family of discrete memoryless channels. An unknown member of Q will be available, with perfect, causal output feedback for communication. We study a scenario where communication is carried by first testing the channel by means of a training sequence, then coding according to the channel estimate. We provide an upper bound on the maximum achievable error exponent of any such coding scheme. If we consider the Binary Symmetric and the Z families of channels this bound is much lower than Burnashev's exponent. For example, in the case of Binary Symmetric Channels this bound has a slope that vanishes at capacity. This is to be compared with our previous result that demonstrates the existence of coding schemes that achieve Burnashev's exponent (that has a nonzero slope at capacity) even though the channel is revealed neither to the transmitter nor to the receiver. Hence, the present result suggests that, in terms of error exponent, a good universal feedback scheme entangles channel estimation with information delivery, rather than separating them.

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Concepts associés (35)
Théorie des codes
En théorie de l'information, la théorie des codes traite des codes et de leurs propriétés et de leurs aptitudes à servir sur différents canaux de communication. On distingue deux modèles de communication : avec et sans bruit. Sans bruit, le codage de source suffit à la communication. Avec bruit, la communication est possible avec les codes correcteurs. En définissant l'information de façon mathématique, l'étape fondatrice de la théorie des codes a été franchie par Claude Shannon.
Capacité d'un canal
La capacité d'un canal, en génie électrique, en informatique et en théorie de l'information, est la limite supérieure étroite du débit auquel l'information peut être transmise de manière fiable sur un canal de communication. Suivant les termes du théorème de codage du canal bruyant, la capacité d'un canal donné est le débit d'information le plus élevé (en unités d'information par unité de temps) qui peut être atteint avec une probabilité d'erreur arbitrairement faible. La théorie de l'information, développée par Claude E.
Error exponent
In information theory, the error exponent of a channel code or source code over the block length of the code is the rate at which the error probability decays exponentially with the block length of the code. Formally, it is defined as the limiting ratio of the negative logarithm of the error probability to the block length of the code for large block lengths. For example, if the probability of error of a decoder drops as , where is the block length, the error exponent is . In this example, approaches for large .
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