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

机译：源为非因果状态的中继信道容量的界限

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摘要

We consider a three-terminal state-dependent relay channel with the channel state available noncausally 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 noncognitive 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 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 relay model with orthogonal channels from the source to the relay and from the source and relay to the destination in which the source input component that is heard by the relay does not depend on the channel states. We establish a better upper bound for both DM and Gaussian cases and we also characterize the capacity in a number of special cases.
机译：我们考虑一个三端状态相关的中继通道，该通道状态仅在源端无因果可用。对于认知框架中的节点合作，即涉及认知无线电和非认知无线电的协作信号传输，这种模型可能是令人感兴趣的。我们研究了这种交流模型的能力。一个主要问题是由中继器不知道信道状态引起的。对于离散无记忆（DM）模型，我们在通道容量上建立了两个下限和一个上限。第一个下限是通过一种编码方案获得的，其中源描述了到中继站和目的地的信道状态，然后，该编码方案利用获得的描述来更好地传达源的信息消息。第二个下限的编码方案通过在源端首先计算中继将发送的适当输入（如果中继知道了信道的状态）来补救中继站不知道信道状态的问题，从而中继到继电器。继电器只是猜测发送的输入，然后在下一个块中发送它。上限说明了不知道中继站和目标站的状态。对于一般的高斯模型，我们本着用于DM模型的思想，通过利用思想来推导信道容量的下界。并且我们表明，无论干扰强度如何，这些界限对于继电器上的大小噪声都是最佳的。此外，我们还考虑了一个中继模型，该模型具有从源到中继以及从源和中继到目的地的正交信道，其中中继器听到的源输入分量不依赖于信道状态。我们为DM和高斯案例建立了一个更好的上限，并且在许多特殊案例中也对容量进行了描述。

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