Why block length and delay behave differently if feedback is present
<|reference_start|>Why block length and delay behave differently if feedback is present: For output-symmetric DMCs at even moderately high rates, fixed-block-length communication systems show no improvements in their error exponents with feedback. In this paper, we study systems with fixed end-to-end delay and show that feedback generally provides dramatic gains in the error exponents.   A new upper bound (the uncertainty-focusing bound) is given on the probability of symbol error in a fixed-delay communication system with feedback. This bound turns out to have a similar form to Viterbi's bound used for the block error probability of convolutional codes as a function of the fixed constraint length. The uncertainty-focusing bound is shown to be asymptotically achievable with noiseless feedback for erasure channels as well as any output-symmetric DMC that has strictly positive zero-error capacity. Furthermore, it can be achieved in a delay-universal (anytime) fashion even if the feedback itself is delayed by a small amount. Finally, it is shown that for end-to-end delay, it is generally possible at high rates to beat the sphere-packing bound for general DMCs -- thereby providing a counterexample to a conjecture of Pinsker.<|reference_end|>
@article{sahai2006why,
    title={Why block length and delay behave differently if feedback is present},
    author={Anant Sahai},
    journal={arXiv preprint arXiv:cs/0610138},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0610138},
    primaryClass={cs.IT math.IT}
}