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Moderate Deviation Asymptotics for Variable-Length Codes with Feedback
We consider data transmission across discrete memoryless channels (DMCs)
using variable-length codes with feedback. We consider the family of such codes
whose rates are below the channel capacity , where is a
positive sequence that tends to zero slower than the reciprocal of the square
root of the expectation of the (random) blocklength . This is known as the
moderate deviations regime and we establish the optimal moderate deviations
constant. We show that in this scenario, the error probability decays
sub-exponentially with speed , where is the maximum
relative entropy between output distributions of the DMC.Comment: 30 pages; No figures. Revision submitted to the IEEE Transactions on
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