Elements of information theory
Elements of information theory
Information theory and statistics: a tutorial
Communications and Information Theory
The error exponent of variable-length codes over Markov channels with feedback
IEEE Transactions on Information Theory
On the universality of Burnashev's error exponent
IEEE Transactions on Information Theory
Unequal error protection: an information-theoretic perspective
IEEE Transactions on Information Theory
Variations on a theme by Schalkwijk and Kailath
IEEE Transactions on Information Theory
| Hi-index | 754.96 |
In a remarkable paper published in 1976, Burnashev determined the reliability function of variable-length block codes over discrete memoryless channels (DMCs) with feedback. Subsequently, an alternative achievability proof was obtained by Yamamoto and Itoh via a particularly simple and instructive scheme. Their idea is to alternate between a communication and a confirmation phase until the receiver detects the codeword used by the sender to acknowledge that the message is correct. We provide a converse that parallels the Yamamoto-Itoh achievability construction. Besides being simpler than the original, the proposed converse suggests that a communication and a confirmation phase are implicit in any scheme for which the probability of error decreases with the largest possible exponent. The proposed converse also makes it intuitively clear why the terms that appear in Burnashev's exponent are necessary.