Universal coding theorem for relay channels

Relay channels are known as a model of multihop wireless networks which are often studied. In relay channels, the sender sends a message to the relay and the receiver, the relay encodes the channel output again and forwards it to the receiver, and the receiver decodes the message from the channel output. This paper deals with the universal coding problem for relay channels. First, we propose two new decoders based on the maximum mutual information decoder and show the existence of a universal code for relay channels by combining the proposed decoders and the coding scheme obtained by Cover and El Gamal. Second, we clarify the condition that the probability of error for each decoder decreases exponentially as the block length tends to infinity. Finally, we prove that the proposed universal code achieves the capacity of the degraded relay channel.