Capacity Results for Non-Ergodic Multi-Modal Broadcast Channels with Controllable Statistics
CoRR(2024)
Abstract
Movable antennas and reconfigurable intelligent surfaces enable a new
paradigm in which channel statistics can be controlled and altered. Further,
the known trajectory and operation protocol of communication satellites results
in networks with predictable statistics. The predictability of future changes
results in a non-ergodic model for which the fundamentals are largely unknown.
We consider the canonical two-user broadcast erasure channel in which channel
statistics vary at a priori known points. We consider a multi-modal setting
with two non-transient modes (whose lengths scale linearly with the
blocklength) and an arbitrary number of transient modes. We provide a new set
of outer-bounds on the capacity region of this problem when the encoder has
access to causal ACK/NACK feedback. The outer-bounds reveal the significant
role of the non-transient mode with higher erasure probability both on the
outer and the inner bounds. We show the outer-bounds are achievable in
non-trivial regimes, characterizing the capacity region for a wide range of
parameters. We also discuss the regimes where the inner and outer bounds
diverge and analyze the gap between the two. A key finding of this work is the
significant gain of inter-modal coding over the separate treating of individual
modes.
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