# 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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## 34 Citations

Communication Over Individual Channels

- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 2011

A rate-adaptive scheme employing feedback which achieves these rates asymptotically with a guaranteed reliability, without prior knowledge of the channel behavior, is presented.

Some observations on limited feedback for multiaccess channels

- Computer Science2009 IEEE International Symposium on Information Theory
- 2009

It is of interest to look at systems where the feedback is rate-limited, particularly for multiaccess channels where the rate required by the feedback link may exceed the capacity gains in the forward link.

Communication over the Gaussian channel with rate-limited feedback

- Computer Science, Mathematics2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
- 2010

This work considers communication over an AWGN discrete time memoryless channel with noiseless delay-less rate-limited feedback with an upper bound for the error exponent and proposes an iterative scheme that achieves an error probability decaying L-fold exponentially.

Universal Prior Prediction for Communication

- Mathematics, Computer ScienceArXiv
- 2011

This paper focuses on the problem of determining the input behavior, or more specifically, a prior which is used to randomly generate a codebook, and shows it is possible to asymptotically approach the best rate that can be attained by any system using a fixed prior.

Universal Communication Over Arbitrarily Varying Channels

- Computer Science, MathematicsIEEE Transactions on Information Theory
- 2013

It is shown that there is a communication system using feedback and common randomness that asymptotically attains, with high probability, the capacity of the time-averaged channel, universally for every sequence of channels.

Universal Communication Over Arbitrarily Varying Channels

- Mathematics, Computer ScienceIEEE Trans. Inf. Theory
- 2013

It is shown that there is a communication system using feedback and common randomness that asymptotically attains, with high probability, the capacity of the time-averaged channel, universally for every sequence of channels.

Communication over Individual Channels -- a general framework

- Computer Science, MathematicsArXiv
- 2012

A unifying framework which includes the two previous results as particular cases is presented, and it is shown that asymptotically the rate function is equivalent to a conditional distribution of the channel input given the output.

Power adaptive feedback communication over an additive individual noise sequence channel

- Computer Science, Mathematics2009 IEEE International Symposium on Information Theory
- 2009

A simple sequential communication scheme based on the celebrated Schalkwijk-Kailath scheme is presented, which varies the transmit power according to the power of the sequence, so that asymptotically the relation between the SNR and the rate matches the Gaussian channel capacity R ≈ 1/2 log(1 + SNR) for almost every noise sequence.

Achievable Error Exponents in the Gaussian Channel With Rate-Limited Feedback

- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 2013

The results show that the error exponent as a function of RFB has a strong discontinuity at R, where it jumps from a finite value to infinity.

Prediction of priors for communication over arbitrarily varying channels

- Mathematics, Computer Science2011 IEEE International Symposium on Information Theory Proceedings
- 2011

This paper focuses on the problem of determining the input behavior, or more specifically, a prior which is used to randomly generate a codebook, and shows it is possible to asymptotically approach the best rate that can be attained by any system using a fixed prior.

## References

SHOWING 1-10 OF 84 REFERENCES

Variable-length channel coding with noisy feedback

- Engineering, Computer ScienceEur. Trans. Telecommun.
- 2008

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

- 2007

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

- Mathematics, Computer ScienceIEEE Trans. Inf. Theory
- 1998

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

- Mathematics, Computer Science2006 IEEE 24th Convention of Electrical & Electronics Engineers in Israel
- 2006

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

- Mathematics, Computer ScienceIEEE Trans. Inf. Theory
- 1989

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

- Computer Science
- 2007

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

- 2006

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

- Engineering, Computer ScienceIEEE Transactions on Communications
- 2006

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

- Computer ScienceIEEE Transactions on Information Theory
- 2009

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

- Computer Science, Mathematics2009 IEEE International Symposium on Information Theory
- 2009

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.