  The rising interest in applications requiring the transmission of small
amounts of data has recently lead to the development of accurate performance
bounds and of powerful channel codes for the transmission of short-data packets
over the AWGN channel. Much less is known about the interaction between error
control coding and channel estimation at short blocks when transmitting over
channels with states (e.g., fading channels, phase-noise channels, etc...) for
the setup where no a priori channel state information (CSI) is available at the
transmitter and the receiver. In this paper, we use the mismatched-decoding
framework to characterize the fundamental tradeoff occurring in the
transmission of short data packet over an AWGN channel with unknown gain that
stays constant over the packet. Our analysis for this simplified setup aims at
showing the potential of mismatched decoding as a tool to design and analyze
transmission strategies for short blocks. We focus on a pragmatic approach
where the transmission frame contains a codeword as well as a preamble that is
used to estimate the channel (the codeword symbols are not used for channel
estimation). Achievability and converse bounds on the block error probability
achievable by this approach are provided and compared with simulation results
for schemes employing short low-density parity-check codes. Our bounds turn out
to predict accurately the optimal trade-off between the preamble length and the
redundancy introduced by the channel code.
