  Broadcast/multicast communication systems are typically designed to optimize
the outage rate criterion, which neglects the performance of the fraction of
clients with the worst channel conditions. Targeting ultra-reliable
communication scenarios, this paper takes a complementary approach by
introducing the conditional value-at-risk (CVaR) rate as the expected rate of a
worst-case fraction of clients. To support differential quality-of-service
(QoS) levels in this class of clients, layered division multiplexing (LDM) is
applied, which enables decoding at different rates. Focusing on a practical
scenario in which the transmitter does not know the fading distribution, layer
allocation is optimized based on a dataset sampled during deployment. The
optimality gap caused by the availability of limited data is bounded via a
generalization analysis, and the sample complexity is shown to increase as the
designated fraction of worst-case clients decreases. Considering this
theoretical result, meta-learning is introduced as a means to reduce sample
complexity by leveraging data from previous deployments. Numerical experiments
demonstrate that LDM improves spectral efficiency even for small datasets;
that, for sufficiently large datasets, the proposed mirror-descent-based layer
optimization scheme achieves a CVaR rate close to that achieved when the
transmitter knows the fading distribution; and that meta-learning can
significantly reduce data requirements.
