A simple Encoding Scheme to Achieve the Capacity of Half-Duplex Relay Channel

Abstract

In this paper, the Half-Duplex Relay Chan- nel (HDRC) is thoroughly investigated. Even though this channel model is widely studied, the capacity is not yet fully understood and particularly has not been tightly expressed. In this work, a new capacity ex- pression of the discrete memoryless HDRC is explic- itly established. In particular, a new expression of the achievable rate is derived by taking advantage of the well-known capacity results of both the degraded broad- cast channel and the multiple access channel. Specifi- cally, in order to obtain the achievable rate, the trans- mission from the source to destination is operated over two phases. In the first phase, the broadcast phase, the source broadcasts to both relay and destination. In the second phase, both source and relay transmit to des- tination to form multiple access channel. Then, we prove that the new achievable rate meets the cut-set outer bound such that the capacity of the discrete mem- oryless HDRC is attained. Next, the new derived ca- pacity result is extended to the case of additive Gaus- sian channel. Further, the attained capacity is ana- lytically and then numerically shown to encompass all well-known available findings in the literature. Addi- tional numerical examples are also shown to present the cases in which the relay is beneficial and how the achievable capacity varies with the source-relay and relay-destination channel gains