Zero-Rate Feedback Can Achieve the Empirical Capacity

@article{Eswaran2010ZeroRateFC,
  title={Zero-Rate Feedback Can Achieve the Empirical Capacity},
  author={Krishnan Eswaran and Anand D. Sarwate and Anant Sahai and Michael Gastpar},
  journal={IEEE Transactions on Information Theory},
  year={2010},
  volume={56},
  pages={25-39}
}
The utility of limited feedback for coding over an individual sequence of discrete memoryless channels is investigated. This study complements recent results showing how limited or noisy feedback can boost the reliability of communication. A strategy with fixed input distribution P is given that asymptotically achieves rates arbitrarily close to the mutual information induced by P and the state-averaged channel. When the capacity-achieving input distribution is the same over all channel states… 

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References

SHOWING 1-10 OF 84 REFERENCES
Variable-length channel coding with noisy feedback
TLDR
It is demonstrated that as the desired rate of communication approaches the capacity of the forward channel, the Burnashev upper bound on the reliability function is achievable given any positive-capacity noisy feedback channel and implies that in a shared medium, to maximize the reliabilityfunction some degrees of freedom should be allocated to feedback.
On the Reliability of Gaussian Channels with Noisy Feedback
We derive bounds on the reliability of the additive white Gaussian noise channel Y = X +Z with output fed back to the transmitter over independent additive white Gaussian noise channel Ỹ = Y + Z̃ .
Fast Iterative Coding Techniques for Feedback Channels
A class of capacity-achieving, low-complexity, high-reliability, variable-rate coding schemes is developed for communication over discrete memoryless channels with noiseless feedback. Algorithms for
On the Gaussian MAC with Imperfect Feedback
  • A. Lapidoth, M. Wigger
  • Mathematics, Computer Science
    2006 IEEE 24th Convention of Electrical & Electronics Engineers in Israel
  • 2006
TLDR
It is shown that the Cover-Leung region (which was originally proposed for perfect-feedback channels but which was later shown to be achievable also with partial feedback) is not tight, and proposes a coding scheme for the case where the receiver is cognizant of the realization of the noise on the feedback-link.
Gaussian feedback capacity
TLDR
An asymptotic equipartition theorem for nonstationary Gaussian processes is proved and it is proved that the feedback capacity C/sub FB/ in bits per transmission and the nonfeedback capacity C satisfy C > C >.
Binary additive channels with individual noise sequences and limited active feedback
TLDR
This work shows how to eliminate the need for full-rate passive channel output feedback by using common randomness and limited active feedback in the style of Hybrid ARQ while still asymptotically achieving the empirical capacity.
Rateless Coding for Non-Ergodic Channels with Decoder Channel State Information
Rateless coding has recently been the focus of much practical as well as theoretical research. In this paper we argue that rateless codes find a natural application in non-ergodic channels where the
Outage minimization with limited feedback for the fading relay channel
TLDR
This work suggests that there is minimal power savings from using spatial power allocation at the transmitters, and finds practical methods to approach the theoretical performance limits through the use of power control with finite rate feedback.
Rateless Coding for Arbitrary Channel Mixtures With Decoder Channel State Information
TLDR
In this paper, rateless codes are shown to find a natural application in channels where the channel law varies unpredictably, and can be usefully understood as an incremental form of erasure decoding.
Feedback communication over individual channels
  • Y. Lomnitz, M. Feder
  • Computer Science, Mathematics
    2009 IEEE International Symposium on Information Theory
  • 2009
TLDR
This work presents achievable rates as a function of the channel input and output sequences known a-posteriori for discrete and continuous channels and presents a rate-adaptive scheme employing feedback which achieves these rates asymptotically without prior knowledge of theChannel behavior.
...
1
2
3
4
5
...