IntroductionThe traditional relay channel was introduced by van der Meulen [1] and analyzed by Cover and El Gamal [2]. In this three-terminal model, two nodes communicate with the help of a third node. This model and its derivatives and variations have spawned a large amount of research in the past few years.
The motivation in this work is to shed light on the operational cost
of relaying in terms of loss of rate for other communications. Assume
that a node has the ability to both communicate with the nodes in its
vicinity, as well as act as a relay for them. Intuitively, the limited
channel resources will lead to a tradeoff, thus helping other nodes
will incur a cost in terms of the rate available to the node's own
communications. The goal of this work is to quantify the nature of
this cost, using a model that we denote
Relay Channel with Private Messages (RCPM).
The three nodes, indexed 1,2,3, are denoted source, relay, and destination. There are three simultaneous communications: between source and destination (assisted by the relay), as well as individual (private) communications between the source and relay, and between the relay and destination.
In this work [3] we find achievable rate regions as well as outer
bounds on the capacity region, for the discrete memoryless relay
channel with private messages. We then study the Gaussian versions of
this channel and achievable rate regions are characterized. Numerical
results are provided that give insights into the trade-offs between
private messaging and relayed messaging in this hybrid three-node
network.
Overview of Analysis
The system model for the discrete memoryless channel is depicted in
Fig. 2 below.
In our analysis we use new combinations of coding strategies inspired by the MAC channel with generalized feedback, and Marton's approach to the broadcast channel. We derive achievable rates for the discrete memoryless and Gaussian RCPM, and outer bounds for the DMC case. The discrete memoryless and Gaussian RCPM generalize their counterparts in the original relay channel and relay-broadcast channels. In this work we use regular encoding and backward decoding [4]. Backward decoding has been used previously for degraded relay channel in [5] and more recently for the general relay channel with partial decode-and-forward in [6]. As a by-product of this work, we demonstrate that backward decoding does not improve the achievable rate of a non-degraded relay channel employing compress-and-forward scheme. This work is also related to, and is in a way a generalization of, [7,8].
For the detailed equations of achievable rate regions, the interested
reader is referred to [3]. Both DMC and Gaussian cases have been
investigated.
In Figure 3 below, we show the performance of a degraded Gaussian RCPM
with 10 dB SNR at the relay input and 5 dB SNR at the destination
input. Contour plots of the achievable rate region in the R13-R23
plane are shown to demonstrate the trade-off between the relayed rate
and one of the private rates.
References:
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