We present nonasymptotic upper and lower bounds on the maximum coding rate
achievable when transmitting short packets over a Rician memoryless
block-fading channel for a given requirement on the packet error probability.
We focus on the practically relevant scenario in which there is no \emph{a
priori} channel state information available at the transmitter and at the
receiver. An upper bound built upon the min-max converse is compared to two
lower bounds: the first one relies on a noncoherent transmission strategy in
which the fading channel is not estimated explicitly at the receiver; the
second one employs pilot-assisted transmission (PAT) followed by
maximum-likelihood channel estimation and scaled mismatched nearest-neighbor
decoding at the receiver. Our bounds are tight enough to unveil the optimum
number of diversity branches that a packet should span so that the energy per
bit required to achieve a target packet error probability is minimized, for a
given constraint on the code rate and the packet size. Furthermore, the bounds
reveal that noncoherent transmission is more energy efficient than PAT, even
when the number of pilot symbols and their power is optimized. For example, for
the case when a coded packet of 168 symbols is transmitted using a channel
code of rate 0.48 bits/channel use, over a block-fading channel with block
size equal to 8 symbols, PAT requires an additional 1.2 dB of energy per
information bit to achieve a packet error probability of 10−3 compared to
a suitably designed noncoherent transmission scheme. Finally, we devise a PAT
scheme based on punctured tail-biting quasi-cyclic codes and ordered statistics
decoding, whose performance are close (1 dB gap at 10−3 packet error
probability) to the ones predicted by our PAT lower bound. This shows that the
PAT lower bound provides useful guidelines on the design of actual PAT schemes.Comment: 30 pages, 5 figures, journa
