The Single-Serving Channel Capacity

@article{Renner2006TheSC,
  title={The Single-Serving Channel Capacity},
  author={Renato Renner and Stefan Wolf and J{\"u}rg Wullschleger},
  journal={2006 IEEE International Symposium on Information Theory},
  year={2006},
  pages={1424-1427}
}
In this paper we provide the answer to the following question: given a noisy channel PY|X and epsi > 0, how many bits can be transmitted with an error of at most epsi by a single use of the channel 
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References

SHOWING 1-10 OF 27 REFERENCES
Privacy Amplification by Public Discussion
In this paper, we investigate how the use of a channel with perfect authenticity but no privacy can be used to repair the defects of a channel with imperfect privacy but no authenticity. More preci...
The wire-tap channel
  • A. Wyner
  • Computer Science
    The Bell System Technical Journal
  • 1975
TLDR
This paper finds the trade-off curve between R and d, assuming essentially perfect (“error-free”) transmission, and implies that there exists a Cs > 0, such that reliable transmission at rates up to Cs is possible in approximately perfect secrecy.
A Mathematical Theory of Communication
This paper opened the new area the information theory. Before this paper, most people believed that the only way to make the error probability of transmission as small as desired is to reduce the
Broadcast channels with confidential messages
TLDR
Given two discrete memoryless channels (DMC's) with a common input, a single-letter characterization is given of the achievable triples where R_{e} is the equivocation rate and the related source-channel matching problem is settled.
Approximation theory of output statistics
TLDR
The notion of resolvability of a channel is introduced, defined as the number of random bits required per channel use in order to generate an input that achieves arbitrarily accurate approximation of the output statistics for any given input process, and a general formula is obtained which holds regardless of the channel memory structure.
Common randomness in information theory and cryptography - I: Secret sharing
As the first part of a study of problems involving common randomness at distance locations, information-theoretic models of secret sharing (generating a common random key at two terminals, without
Zero-error information and applications in cryptography
TLDR
It is shown that the new notion, together with two operators introduced in the same context, namely the common random variable of two random variables and the dependent part of a random variable with respect to another, is useful for giving characterizations of the possibility of realizing cryptographic tasks from correlated pieces of information.
Pseudo-signatures, Broadcast, and Multi-party Computation from Correlated Randomness
TLDR
This paper considers the scenario where three players have access to random variables X, Y, and Z, respectively, and gives the exact condition on the joint distribution P XYZ under which unconditional broadcast is possible and shows that this condition characterizes the possibility of realizing so-called pseudo-signatures between the players.
Simple and Tight Bounds for Information Reconciliation and Privacy Amplification
TLDR
It is shown that the two new quantities, and related notions, do not only extend Shannon entropy in the described contexts, but they also share central properties of the latter such as the chain rule as well as sub-additivity and monotonicity.
Secret key agreement by public discussion from common information
  • U. Maurer
  • Mathematics, Computer Science
    IEEE Trans. Inf. Theory
  • 1993
TLDR
It is shown that such a secret key agreement is possible for a scenario in which all three parties receive the output of a binary symmetric source over independent binary asymmetric channels, even when the enemy's channel is superior to the other two channels.
...
1
2
3
...