On Joint Detection and Decoding in Short-Packet Communications

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 er-ror 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 block-length values at which the performance of a communication system is limited by its ability to perform packet detection satisfacto-rily, and to assess the difference in performance between preamble-based detection, and joint detection and decoding. Numerical re-sults pertaining to the binary-input AWGN channel are provided.