Degraded Broadcast Diamond Channels with Non-Causal State Information at the Source

TL;DR

This paper investigates the capacity of a degraded broadcast diamond channel with non-causal state information at the source, providing capacity characterization when the destination has state info and bounds when it does not, highlighting the benefits of source-side state knowledge.

Contribution

It characterizes the capacity for a state-dependent broadcast diamond channel with non-causal source state information and derives bounds for the case without destination state information.

Findings

Joint message and state transmission via binning is optimal when destination has state info.

Lower and upper bounds on capacity are established for the general discrete memoryless model.

Numerical results show performance gains from non-causal state information at the source.

Abstract

A state-dependent degraded broadcast diamond channel is studied where the source-to-relays cut is modeled with two noiseless, finite-capacity digital links with a degraded broadcasting structure, while the relays-to-destination cut is a general multiple access channel controlled by a random state. It is assumed that the source has non-causal channel state information and the relays have no state information. Under this model, first, the capacity is characterized for the case where the destination has state information, i.e., has access to the state sequence. It is demonstrated that in this case, a joint message and state transmission scheme via binning is optimal. Next, the case where the destination does not have state information, i.e., the case with state information at the source only, is considered. For this scenario, lower and upper bounds on the capacity are derived for the general discrete memoryless model. Achievable rates are then computed for the case in which the relays-to-destination cut is affected by an additive Gaussian state. Numerical results are provided that illuminate the performance advantages that can be accrued by leveraging non-causal state information at the source.