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The authors investigate the achievable error probability in communication over an AWGN discrete time memoryless channel with noiseless delay-less rate-limited feedback. For the case where the feedback rate RFB is lower than the data rate R transmitted over the forward channel, they show that the decay of the probability of error is at most exponential in block-length, and obtain an upper bound for increase in the error exponent due to feedback. Furthermore, they show that the use of feedback in this case results in an error exponent that is at least RFB higher than the error exponent in the absence of feedback.
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