Hu Bingbing, Wang Ke, Ma Yingying, Wu Youlong
School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China.
Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China.
Entropy (Basel). 2020 Jul 17;22(7):784. doi: 10.3390/e22070784.
The four-node relay broadcast channel (RBC) is considered, in which a transmitter communicates with two receivers with the assistance of a relay node. We first investigate three types of physically degraded RBCs (PDRBCs) based on different degradation orders among the relay and the receivers' observed signals. For the discrete memoryless (DM) case, only the capacity region of the second type of PDRBC is already known, while for the Gaussian case, only the capacity region of the first type of PDRBC is already known. In this paper, we step forward and make the following progress: (1) for the first type of DM-PDRBC, a new outer bound is established, which has the same rate expression as an existing inner bound, with only a slight difference on the input distributions; (2) for the second type of Gaussian PDRBC, the capacity region is established; (3) for the third type of PDRBC, the capacity regions are established both for DM and Gaussian cases. Besides, we also consider the RBC with relay feedback where the relay node can send the feedback signal to the transmitter. A new coding scheme based on a hybrid relay strategy and a layered Marton's coding is proposed. It is shown that our scheme can strictly enlarge Behboodi and Piantanida's rate region, which is tight for the second type of DM-PDRBC. Moreover, we show that capacity regions of the second and third types of PDRBCs are exactly the same as that without feedback, which means feedback cannot enlarge capacity regions for these types of RBCs.
考虑四节点中继广播信道（RBC），其中发射机在中继节点的协助下与两个接收机进行通信。我们首先基于中继和接收机观测信号之间不同的降级顺序，研究三种类型的物理降级RBC（PDRBC）。对于离散无记忆（DM）情况，仅第二种类型的PDRBC的容量区域已知，而对于高斯情况，仅第一种类型的PDRBC的容量区域已知。在本文中，我们取得了以下进展：（1）对于第一种类型的DM - PDRBC，建立了一个新的外界，其速率表达式与现有的内界相同，仅在输入分布上有细微差异；（2）对于第二种类型的高斯PDRBC，建立了容量区域；（3）对于第三种类型的PDRBC，建立了DM和高斯情况的容量区域。此外，我们还考虑了具有中继反馈的RBC，其中中继节点可以向发射机发送反馈信号。提出了一种基于混合中继策略和分层马尔顿编码的新编码方案。结果表明，我们的方案可以严格扩大Behboodi和Piantanida的速率区域，该区域对于第二种类型的DM - PDRBC是紧的。此外，我们表明第二种和第三种类型的PDRBC的容量区域与无反馈时的容量区域完全相同，这意味着反馈不能扩大这些类型的RBC的容量区域。
