On the reliability function for a noisy feedback Gaussian channel: Zero rate

Authors:
M. V. Burnashev;H. Yamamoto
Affiliations:
Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia;School of Frontier Sciences, The University of Tokyo, Tokyo, Japan
Venue:
Problems of Information Transmission
Year:
2012

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Abstract

A discrete-time channel with independent additive Gaussian noise is used for information transmission. There is also a feedback channel with independent additive Gaussian noise, and the transmitter observes all outputs of the forward channel without delay via this feedback channel. Transmission of a nonexponential number of messages is considered (i.e., the transmission rate is zero), and the achievable decoding error exponent for such a combination of channels is investigated. It is shown that for any finite noise in the feedback channel the achievable error exponent is better than the similar error exponent for a no-feedback channel. The transmission/decoding method developed in the paper strengthens the method earlier used by the authors for a BSC. In particular, for small feedback noise, it provides a gain of 23.6% (instead of 14.3% obtained earlier for a BSC).