State-Dependent Relay Channel with Private Messages with Partial Causal and Non-Causal Channel State Information

TL;DR

This paper explores a generalized state-dependent relay channel with private messages, analyzing cases with causal and non-causal channel state information, and derives achievable rate regions for both scenarios, including Gaussian models.

Contribution

It introduces a new SD-RCPM model with partial causal and non-causal CSI and derives novel achievable rate regions using Gel'fand-Pinsker and CF schemes.

Findings

Achievable rate regions are established for both causal and non-causal CSI cases.

Numerical examples compare CF and Decode-and-Forward schemes.

Gaussian SD-RCPM with perfect non-causal CSI at the source is analyzed.

Abstract

In this paper, we introduce a discrete memoryless State-Dependent Relay Channel with Private Messages (SD-RCPM) as a generalization of the state-dependent relay channel. We investigate two main cases: SD-RCPM with non-causal Channel State Information (CSI), and SD-RCPM with causal CSI. In each case, it is assumed that partial CSI is available at the source and relay. For non-causal case, we establish an achievable rate region using Gel'fand-Pinsker type coding scheme at the nodes informed of CSI, and Compress-and-Forward (CF) scheme at the relay. Using Shannon's strategy and CF scheme, an achievable rate region for causal case is obtained. As an example, the Gaussian version of SD-RCPM is considered, and an achievable rate region for Gaussian SD-RCPM with non-causal perfect CSI only at the source, is derived. Providing numerical examples, we illustrate the comparison between achievable rate regions derived using CF and Decode-and-Forward (DF) schemes.