We consider the optimal design of sequential transmission over broadcast
channel with nested feedback. Nested feedback means that the channel output of
the outer channel is also available at the decoder of the inner channel. We
model the communication system as a decentralized team with three decision
makers---the encoder and the two decoders. Structure of encoding and decoding
strategies that minimize a total distortion measure over a finite horizon are
determined. The results are applicable for real-time communication as well as
for the information theoretic setup.
The $n$-step delayed sharing information structure is investigated. This
information structure comprises of $K$ controllers that share their information
with a delay of $n$ time steps. This information structure is a link between
the classical information structure, where information is shared perfectly
between the controllers, and a non-classical information structure, where there
is no "lateral" sharing of information among the controllers. Structural
results for optimal control strategies for systems with such information
structures are presented.
We consider communication with noiseless feedback over a channel that is
either BSC(p) or BSC(1-p); neither the transmitter nor the receiver know which
one. The parameter $p \in [0, 1/2]$ is known to both. We propose a variable
length training-based scheme for this channel. The error exponent of this
scheme is within a constant fraction of the best possible error exponent. Thus,
contrary to popular belief, variable length training-based schemes need not
have poor error exponents.