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On AWGN Channels and Gaussian MACs with Variable-Length Feedback

Lan V. Truong,V. Tan

Published 2016 in arXiv.org

ABSTRACT

We characterize the information-theoretic limits of the additive white Gaussian noise (AWGN) channel and the Gaussian multiple access channel (MAC) when variable-length feedback is available at the encoder and a non-vanishing error probability is permitted. For the AWGN channel, we establish the $\varepsilon$-capacity (for $0<\varepsilon<1$) and show that it is larger than the corresponding $\varepsilon$-capacity when fixed-length feedback is available. Due to the continuous nature of the channel and the presence of expected power constraints, we need to develop new achievability and converse techniques. In addition, we show that a variable-length feedback with termination (VLFT) code outperforms a stop-feedback code in terms of the second-order asymptotic behavior. Finally, we extend out analyses to the Gaussian MAC with the two types of variable-length feedback where we establish the $\varepsilon$-capacity region. Due to the multi-terminal nature of the channel model, we are faced with the need to bound the asymptotic behavior of the expected value of the maximum of several stopping times. We do so by leveraging tools from renewal theory developed by Lai and Siegmund.

PUBLICATION RECORD

  • Publication year

    2016

  • Venue

    arXiv.org

  • Publication date

    2016-09-02

  • Fields of study

    Mathematics, Computer Science

  • Identifiers
    arXiv 1609.00594
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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