Error Exponents for Variable-length Block Codes with Feedback and Cost Constraints
<|reference_start|>Error Exponents for Variable-length Block Codes with Feedback and Cost Constraints: Variable-length block-coding schemes are investigated for discrete memoryless channels with ideal feedback under cost constraints. Upper and lower bounds are found for the minimum achievable probability of decoding error $P_{e,\min}$ as a function of constraints $R, \AV$, and $\bar \tau$ on the transmission rate, average cost, and average block length respectively. For given $R$ and $\AV$, the lower and upper bounds to the exponent $-(\ln P_{e,\min})/\bar \tau$ are asymptotically equal as $\bar \tau \to \infty$. The resulting reliability function, $\lim_{\bar \tau\to \infty} (-\ln P_{e,\min})/\bar \tau$, as a function of $R$ and $\AV$, is concave in the pair $(R, \AV)$ and generalizes the linear reliability function of Burnashev to include cost constraints. The results are generalized to a class of discrete-time memoryless channels with arbitrary alphabets, including additive Gaussian noise channels with amplitude and power constraints.<|reference_end|>
@article{nakiboglu2006error,
    title={Error Exponents for Variable-length Block Codes with Feedback and Cost
  Constraints},
    author={B. Nakiboglu, R. G. Gallager},
    journal={IEEE Transactions on Information Theory, 54(3):945-963, March 2008},
    year={2006},
    doi={10.1109/TIT.2007.915913 10.1109/ISIT.2006.261677},
    archivePrefix={arXiv},
    eprint={cs/0612097},
    primaryClass={cs.IT math.IT}
}