Feedback and Partial Message Side-Information on the Semideterministic Broadcast Channel

TL;DR

This paper characterizes the capacity of the semideterministic broadcast channel with partial message side-information at receivers, revealing how feedback and side-information interplay to enhance communication rates.

Contribution

It provides the first capacity results for SD-BC with P-MSI, clarifies conditions under which P-MSI and feedback increase capacity, and links feedback to P-MSI as a mitigation strategy.

Findings

P-MSI to the stochastic receiver increases capacity.

P-MSI to the deterministic receiver increases capacity only with a common message.

Feedback can increase capacity or sum-rate capacity when P-MSI is absent or partial.

Abstract

The capacity of the semideterministic discrete memoryless broadcast channel (SD-BC) with partial message side-information (P-MSI) at the receivers is established. In the setting without a common message, it is shown that P-MSI to the stochastic receiver alone can increase capacity, whereas P-MSI to the deterministic receiver can only increase capacity if also the stochastic receiver has P-MSI. The latter holds only for the setting without a common message: if the encoder also conveys a common message, then P-MSI to the deterministic receiver alone can increase capacity. These capacity results are used to show that feedback from the stochastic receiver can increase the capacity of the SD-BC without P-MSI and the sum-rate capacity of the SD-BC with P-MSI at the deterministic receiver. The link between P-MSI and feedback is a feedback code, which---roughly speaking---turns feedback into P-MSI at the stochastic receiver and hence helps the stochastic receiver mitigate experienced interference. For the case where the stochastic receiver has full MSI (F-MSI) and can thus fully mitigate experienced interference also in the absence of feedback, it is shown that feedback cannot increase capacity.