Bounds on the Capacity of the Relay Channel with Noncausal State at Source

TL;DR

This paper investigates the capacity of a relay channel with non-causal state information at the source only, providing bounds and capacity characterizations for discrete and Gaussian models, relevant for cognitive radio networks.

Contribution

It introduces new coding schemes and bounds for the relay channel with asymmetric state knowledge, advancing understanding of capacity limits in state-dependent relay channels.

Findings

Established lower and upper bounds for discrete memoryless models.

Derived capacity bounds for Gaussian models under various noise conditions.

Characterized capacity in specific cases with partial source state knowledge.

Abstract

We consider a three-terminal state-dependent relay channel with the channel state available non-causally at only the source. Such a model may be of interest for node cooperation in the framework of cognition, i.e., collaborative signal transmission involving cognitive and non-cognitive radios. We study the capacity of this communication model. One principal problem is caused by the relay's not knowing the channel state. For the discrete memoryless (DM) model, we establish two lower bounds and an upper bound on channel capacity. The first lower bound is obtained by a coding scheme in which the source describes the state of the channel to the relay and destination, which then exploit the gained description for a better communication of the source's information message. The coding scheme for the second lower bound remedies the relay's not knowing the states of the channel by first computing, at the source, the appropriate input that the relay would send had the relay known the states of the channel, and then transmitting this appropriate input to the relay. The relay simply guesses the sent input and sends it in the next block. The upper bound is non trivial and it accounts for not knowing the state at the relay and destination. For the general Gaussian model, we derive lower bounds on the channel capacity by exploiting ideas in the spirit of those we use for the DM model; and we show that these bounds are optimal for small and large noise at the relay irrespective to the strength of the interference. Furthermore, we also consider a special case model in which the source input has two components one of which is independent of the state. We establish a better upper bound for both DM and Gaussian cases and we also characterize the capacity in a number of special cases.