  We consider a communication problem in which the receiver must first detect
the presence of an information packet and, if detected, decode the message
carried within it. We present general nonasymptotic upper and lower bounds on
the maximum coding rate that depend on the blocklength, the probability of
false alarm, the probability of misdetection, and the packet error probability.
The bounds, which are expressed in terms of binary-hypothesis-testing
performance metrics, generalize finite-blocklength bounds derived previously
for the scenario when a genie informs the receiver whether a packet is present.
The bounds apply to detection performed either jointly with decoding on the
entire data packet, or separately on a dedicated preamble. The results
presented in this paper can be used to determine the blocklength values at
which the performance of a communication system is limited by its ability to
perform packet detection satisfactorily, and to assess the difference in
performance between preamble-based detection, and joint detection and decoding.
Numerical results pertaining to the binary-input AWGN channel are provided.
