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Causal Asymmetric State Communication Over the Degraded Broadcast Channel

The Rate-and-Asymmetric-State (RnAS) capacity region of a state-dependent two-user discrete memoryless degraded broadcast channel with a state-cognizant encoder is the set of rate-pairs at which data can be transmitted over the channel when the “higher quality” user-in addition to reliably decoding its message-must also reconstruct the state sequence with some defined fidelity. We show that feedback from the channel output to the encoder can increase this capacity region even for degraded broadcast channels that are memoryless with memoryless states. This capacity region is calculated here for such channels in the absence as well as in the presence of feedback when the state reconstruction fidelity is measured using a single-letter distortion function and the state sequence is revealed to the encoder in one of two different ways: strictly-causally or causally.