Capacity of a Class of State-Dependent Orthogonal Relay Channels

TL;DR

This paper characterizes the capacity of a class of state-dependent orthogonal relay channels, showing that the partial decode-compress-and-forward scheme achieves capacity where other schemes are suboptimal, and compares it to the cut-set bound.

Contribution

It introduces the first relay channel model where pDCF achieves capacity, demonstrating its superiority over CF and pDF schemes in this context.

Findings

pDCF scheme achieves capacity for the considered relay channels.

CF and pDF schemes are generally suboptimal for these channels.

Capacity is often below the cut-set bound, with conditions identified for optimality.

Abstract

The class of orthogonal relay channels in which the orthogonal channels connecting the source terminal to the relay and the destination, and the relay to the destination, depend on a state sequence, is considered. It is assumed that the state sequence is fully known at the destination while it is not known at the source or the relay. The capacity of this class of relay channels is characterized, and shown to be achieved by the partial decode-compress-and-forward (pDCF) scheme. Then the capacity of certain binary and Gaussian state-dependent orthogonal relay channels are studied in detail, and it is shown that the compress-and-forward (CF) and partial-decode-and-forward (pDF) schemes are suboptimal in general. To the best of our knowledge, this is the first single relay channel model for which the capacity is achieved by pDCF, while pDF and CF schemes are both suboptimal. Furthermore, it is shown that the capacity of the considered class of state-dependent orthogonal relay channels is in general below the cut-set bound. The conditions under which pDF or CF suffices to meet the cut-set bound, and hence, achieve the capacity, are also derived.