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One-Shot Capacity of Discrete Channels

Costa, R.C. ; Langberg, M.L. ; Barros, J.

One-Shot Capacity of Discrete Channels, Proc IEEE International Symp. on Information Theory - ISIT, Austin, United States, Vol. 1, pp. 1 - 5, June, 2010.

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Abstract
Shannon defined channel capacity as the highest
rate at which there exists a sequence of codes of block length
n such that the error probability goes to zero as n goes to
infinity. In this definition, it is implicit that the block length,
which can be viewed as the number of available channel uses, is
unlimited. This is not the case when the transmission power must
be concentrated on a single transmission, most notably in military
scenarios with adversarial conditions or delay-tolerant networks
with random short encounters. A natural question arises: how
much information can we transmit in a single use of the channel?
We give a precise characterization of the one-shot capacity of
discrete channels, defined as the maximum number of bits that
can be transmitted in a single use of a channel with an error
probability that does not exceed a prescribed value. This capacity
definition is shown to be useful and significantly different from
the zero-error problem statement.